A Knowledge-Based Step Length Estimation Method Based on ... - MDPI

International Journal of

Geo-Information Article

A Knowledge-Based Step Length Estimation Method Based on Fuzzy Logic and Multi-Sensor Fusion Algorithms for a Pedestrian Dead Reckoning System Ying-Chih Lai 1, *, Chin-Chia Chang 2 , Chia-Ming Tsai 2 , Shih-Ching Huang 2 and Kai-Wei Chiang 3 1 2 3

*

Department of Aerospace and Systems Engineering, Feng Chia University, No. 100, Wenhwa Road, Seatwen District, Taichung 407, Taiwan Industrial Technology Research Institute, No. 195, Sec. 4, Chung Hsing Rd., Chutung, Hsinchu 310, Taiwan; [email protected] (C.-C.C.); [email protected] (C.-M.T.); [email protected] (S.-C.H.) Department of Geomatics Engineering, National Cheng-Kung University, No. 1, Daxue Road, East District, Tainan 701, Taiwan; [email protected] Correspondence: [email protected]; Tel.: +886-4-2451-7250 (ext. 3956); Fax: +886-4-2451-0862

Academic Editors: Georg Gartner, Haosheng Huang and Wolfgang Kainz Received: 18 December 2015; Accepted: 10 May 2016; Published: 17 May 2016

Abstract: The demand for pedestrian navigation has increased along with the rapid progress in mobile and wearable devices. This study develops an accurate and usable Step Length Estimation (SLE) method for a Pedestrian Dead Reckoning (PDR) system with features including a wide range of step lengths, a self-contained system, and real-time computing, based on the multi-sensor fusion and Fuzzy Logic (FL) algorithms. The wide-range SLE developed in this study was achieved by using a knowledge-based method to model the walking patterns of the user. The input variables of the FL are step strength and frequency, and the output is the estimated step length. Moreover, a waist-mounted sensor module has been developed using low-cost inertial sensors. Since low-cost sensors suffer from various errors, a calibration procedure has been utilized to improve accuracy. The proposed PDR scheme in this study demonstrates its ability to be implemented on waist-mounted devices in real time and is suitable for the indoor and outdoor environments considered in this study without the need for map information or any pre-installed infrastructure. The experiment results show that the maximum distance error was within 1.2% of 116.51 m in an indoor environment and was 1.78% of 385.2 m in an outdoor environment. Keywords: pedestrian dead reckoning; wearable device; multi-sensor fusion; fuzzy logic; step length estimation

1. Introduction Mobile devices, including wearable items, are increasingly popular and affordable, and are widely used in various fields and for various applications, such as sports monitoring and management, healthcare, Location-Based Services (LBS), and navigation [1,2]. The demand for LBS for pedestrians in both indoor and outdoor environments has also increased dramatically. Location and navigation technologies using the Global Navigation Satellite Systems (GNSS) are highly reliable and accurate in open, outdoor spaces. However, GNSS signals are not always available, especially in GNSS-denied environments, such as indoor environments, underground, and in urban areas. The problem of navigation in urban areas can be mitigated by integrating GNSS with the Inertial Navigation System (INS) [3,4]. Nevertheless, since GNSS signals are not available indoors, various navigation methods relying on different technologies, such as proximity, triangulation, fingerprinting, and dead reckoning, have been proposed [5]. Since the dead reckoning method requires little or no infrastructure to be ISPRS Int. J. Geo-Inf. 2016, 5, 70; doi:10.3390/ijgi5050070

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pre-installed in buildings, Pedestrian Dead Reckoning (PDR) systems have become a popular solution to indoor positioning and navigation [6,7]. Dead reckoning methods use inertial sensors, accelerometers, and gyroscopes to estimate a relative location and derive a current location by adding the estimated displacement based on data for distance and heading in relation to a previously estimated location. The moving distance and heading of the user can be acquired from an INS or Step-and-Heading System (SHS) [2]. An INS is a self-contained system [7], which means no other external signal is required, and it continuously calculates the position, orientation, and velocity of a moving object by integrating data from an accelerometer, gyroscope, and magnetometer. However, the inertial sensors have a drifting problem, in which errors accumulate over time. Moreover, most high-end inertial sensors are expensive and over-sized for most consumers. This larger size makes it more difficult to carry or wear. Meanwhile, a SHS is also a self-contained system that is used by pedestrians. It simplifies the complex computing of an INS and uses only an accelerometer and gyroscope to estimate the step count, step distance, and heading of the user. Both a gyroscope and a magnetometer can be used to derive the heading of the user, but these two sensors have drawbacks with regard to indoor positioning and navigation. A heading derived from a gyroscope suffers from the drifting problem and ends up accumulating errors over time. The drifts of a gyroscope can be reduced with the use of a rigorous calibration procedure or corrected via other methods such as fingerprinting [8] or map-matching [9–11]. A magnetometer measures the magnitudes of the Earth’s magnetic field to estimate the heading of a user, but indoors this is influenced by natural and man-made sources of magnetism. Magnetic field variations inside buildings can be found in iron, cobalt, or nickel. It could also occur from other manmade sources such as steel structures, electric power systems, and electronic appliances [12,13]. This is the main reason why magnetometers were not adopted to aid with heading estimation. However, there are some studies that have adopted magnetic fingerprints and utilized the anomalies in the magnetic field inside a building, which are assumed to be static and have sufficient local variability, to achieve global indoor self-localization [13,14]. With the rapid progress in mobile and wearable devices, inertial sensors are now commonly used in high-end devices like smartphones, which are theoretically suitable for PDR systems. The position of the inertial sensors on the body, such as a user’s hand [15], waist [16], pocket [17], and foot [18,19], has a significant influence on the accuracy, reliability, and usage of the PDRs. Moreover, due to advances in Micro Electro Mechanical Systems (MEMS) technology, wearable and miniature inertial sensors based on this have become the main sensors used for PDR. However, due to cost considerations, most consumer electronics adopt low-cost MEMS sensors, which have lower performance and generate more noise as compared to more expensive devices. Therefore, the integration and combination of different sensors and algorithms are required to enhance the accuracy and usability of PDR with low-cost sensors. Moreover, the sensor errors of low cost sensors also need to be calibrated [20,21]. Regarding the moving distance of the user, Step Length Estimation (SLE) algorithms based on accelerometers have been successfully implemented in PDR in many studies [21–23]. The SLE algorithms can be divided into model- and knowledge-based methods. The former can be categorized into two groups, one being based on biomechanical models and the other being based on empirical relationships [21]. An inverted pendulum model for the motion of the pelvis during a step was proposed by Zijlstra et al. [24,25]. However, this model requires details of leg length and is sensitive to user calibrations. To overcome these drawbacks, an approximated model which does not require leg length information was proposed by Weinberg et al. [26]. It estimates the dynamic step length from the vertical displacement of the pelvis. However, the results they reported show that step length can vary by as much as 40% between pedestrians walking at the same speed, and up to 50% across the range of walking speeds of individuals [2]. Weinberg et al. presented a strap-down waist-worn PDR system based on the model they proposed; experimental results showed that the maximum relative errors were between 4.23% to 18.44%, and the average errors were between 3% and 8% [16]. Now, with regard to the knowledge-based methods, Artificial Neural Networks (ANN) and Fuzzy Logic (FL) are the primary algorithms employed [27]. A GNSS/INS navigation system was proposed


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using a knowledge-based method to model human locomotion, and the adopted sensors of this system are continuously calibrated when GNSS signals are available [28]. There are six parameters that contain the information about a step length. They are step frequency, peak-to-peak mean acceleration, peak-to-peak variation in acceleration, terrain slope, change in barometric height during a single gait cycle, and subject’s height [28]. The results showed that the accuracy of this system is 3–5 m CEP (circular error probable) 50%. However, the study in [28] required high-performance GNSS and INS devices to calibrate its models, and the computing load of the proposed algorithms would simply not be feasible for low-cost embedded systems. The objective of this study is to develop an accurate and usable SLE method for PDR system with the features of a wide range of SLE, a self-contained system, and real-time computing. In order to achieve a self-contained capability, an inertial sensor module has been developed, and the sensor errors of this module are calibrated with a sensor calibration procedure based on the scalar calibration as well as the least squares method to improve the accuracy of the inertial sensors [29]. The applied parameters in this study are scale factors, biases, and orthogonalization angles. Other generalized calibration schemes for low-cost Inertial Measurement Unit (IMU) and smartphone sensors can be found in the studies [30,31]. With this calibrated inertial data in hand, a PDR system based on multi-sensor fusion and FL SLE algorithms has been developed. Essentially, the strengths of FL are its reduction of the depth and complexity of computations, and its improvement of accuracy and simplification of the positioning algorithm through the use of a relatively simple heuristic, which determines a combination of the most appropriate rules. Keep in mind that an advanced indoor navigation system attempting to determine the necessary information through pure number crunching, with a required high computational complexity, would likely cause a complete battery drain within a few hours, especially for portable and wearable devices. Additionally, since FL is comprised of linguistic rules, it can be easily implemented into most Micro Processing Units (MCUs) to fulfill the requirement of real-time computing. These are the reasons why FL has been chosen to be the SLE method in this study. With the advantages of FL and PDR, the method proposed herein is easy to implement on waist-mounted wearable devices in real time and is suitable for the indoor and outdoor environments considered in this study without the need for map information and any pre-installed infrastructure. 2. System Overview 2.1. Pedestrian Navigation Scheme A pedestrian PDR system was designed and implemented in this study to demonstrate the viability of the above proposed methods, with the system block diagram shown in Figure 1. In this figure, the block diagram is composed of two parts, the Sensor Calibration and Fusion Algorithm as well as the Dead Reckoning Algorithm. The data flow of the system block diagram is as follows. In the sensor calibration and fusion part, after the sensor module was set up, the inertial sensors were calibrated by using the proposed calibration procedure. Then, the obtained calibration parameters of the inertial sensors were used in the Multi-Sensor Fusion Algorithm block to calibrate the acceleration and angular rate as measured from the inertial sensors. The Multi-Sensor Fusion Algorithm block performs the sensor calibration, signal processing, and orientation estimation of the sensor module. In order to obtain more reliable moving information of a user, the acceleration data are transferred from their body frame to a local horizontal frame by using the rotation matrix with an estimated orientation. In the dead reckoning part, with the calibrated data and the estimated orientation of the sensor module, the Step Counting block provides the step count, step frequency, and step strength to the Knowledge-Based SLE block, which estimates the step length of the user using the proposed FL SLE method. The Heading Estimation block utilizes the calibrated data to calculate the walking direction of the user. With the estimated step length and heading, the Pedestrian Dead Reckoning block uses the step-and-heading-based dead reckoning algorithm to estimate a user’s location over time.

Sensor Calibration and Fusion Algorithm

Dead Reckoning Algorithm Step Counting

Accelerometer ISPRS Int.Int. J. Geo-Inf. 2016, 5,5,70 ISPRS J. Geo-Inf. 2016, 70

Gyroscope

Multi-Sensor Fusion Algorithm

Sensor Calibration and Fusion Algorithm

KnowledgeBased SLE Heading

Pedestrian Dead Reckoning

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Dead Reckoning Algorithm Estimation Step Counting

Figure 1. System block diagram of the proposed Pedestrian Dead Reckoning (PDR). Accelerometer Multi-Sensor

Fusion 2.2. System Configuration Gyroscope and Setup Algorithm

KnowledgeBased SLE

Pedestrian Dead The system configuration and setup of the proposedHeading PDR is based on a system block diagram, Reckoning as mentioned previously. With regard to the flexibility and computing power of the system, the PDR Estimation is designed to be a distributed computing scheme with two devices, including one sensor module and one monitoring device, as presented in Figure 2. The sensor module is composed of two inertial 1. System block diagram of the Pedestrian Reckoning sensors, a Figure Bluetooth module, and a MCU. Theproposed MCU used on theDead sensor module (PDR). is a 32-bit ARM Figure 1. System block diagram of the proposed Pedestrian Dead Reckoning (PDR). Cortex-M4 processor produced by STMicroelectronics. The sensor module executes the proposed system running on theSetup MCU in real time, and it is capable of transmitting the estimated step 2.2.PDR System Configuration and 2.2. System Configuration and Setup length and heading via Bluetooth to the monitor, which could be a mobile device such as a laptop, The system configuration and of proposedPDR PDR isbased basedon ona asystem system block diagram, The system configuration andsetup setup of the the proposed block diagram, smartphone, or tablet. The monitoring device displays the user is location on a preloaded map. In this as study, mentioned previously. With regard to the flexibility and computing power of the system, the PDR as mentioned previously. With regard to the flexibility computing power of the system, the PDR one Android mobile device was adopted as the monitoring device, and a self-developed is designed toto be computing scheme with two two devices, including onesensor sensor module is designed bea adistributed distributed computing scheme with devices, including one Android app was installed in said mobile device to display the user’s present location in realmodule time. and one monitoring device, as presented in Figure 2. The sensor module is composed of two inertial and one monitoring device, as presented in Figure The sensor module is composed of two inertial The used sensors in the sensor module are a low-cost MEMS accelerometer and gyroscope. These sensors, a Bluetooth module, and a MCU. The MCU used on the sensor module is a 32-bit ARM sensors, Bluetooth module, and aapplications, MCU. MCUasused on body the sensor a 32-bit ARM sensorsaare widely used in various such human motionmodule trackingisand the flight Cortex-M4 processor produced STMicroelectronics. The sensor module executes proposed Cortex-M4 produced by by STMicroelectronics. The sensor module executes thethe proposed PDR control ofprocessor consumer drones. The inertial sensors transduce inertial motion into analog or digital PDR system running on the MCU in real time, and it is capable of transmitting the estimated step system running on the MCU in real time, and it is capable of transmitting the estimated step length and signals. The advantages of MEMS sensors are their low-cost, light weight, and small size, but this also length and heading via Bluetooth to the monitor, which could be a mobile device such as a laptop, heading viathat Bluetooth to athe monitor, which could be ato mobile device such as a laptop, suggests they have lower performance compared more expensive devices. Indeed,smartphone, the major smartphone, or tablet. The monitoring displays the user on a preloaded map. Inwhy this low-cost sensors are theirdevice high measurement errors. This thethis reason or drawbacks tablet. Theofmonitoring device displays thenoise user and location onlocation a preloaded map.is In study, one study, one Android mobile device was adopted as the monitoring device, and a self-developed calibration anddevice verification of the sensor are critical to enhance its accuracy and performance Android mobile was adopted as themodule monitoring device, and a self-developed Android app was Android installed in to said mobilethe device to display user’sin present location in real time. before its use.was installed in app said mobile device display user’s present the location real time. The used sensors in the sensor module are a low-cost MEMS accelerometer and gyroscope. These sensors are widely used in various applications, such as human body motion tracking and the flight control of consumer drones. The inertial sensors transduce inertial motion into analog or digital signals. The advantages of MEMS sensors are their low-cost, light weight, and small size, but this also suggests that they have a lower performance compared to more expensive devices. Indeed, the major drawbacks of low-cost sensors are their high noise and measurement errors. This is the reason why calibration and verification of the sensor module are critical to enhance its accuracy and performance before its use.

Figure 2. 2.The moduleand andan anAndroid Androidmobile mobile device. Figure Theself-developed self-developedARM-based ARM-based sensor sensor module device.

Inused regard to thein measurements of the are inertial sensors, the accelerometer transfers the objective The sensors the sensor module a low-cost MEMS accelerometer and gyroscope. These 2 or g, the latter of which is the magnitude of the acceleration into physical values with units in m/s sensors are widely used in various applications, such as human body motion tracking and the flight Earth’s gravitational field. The gyroscope transfers the objection rotation into physical values with control of consumer drones. The inertial sensors transduce inertial motion into analog or digital the unit in deg/s. One tri-axis accelerometer and one tri-axis gyroscope are used in the developed signals. The advantages of MEMS sensors are their low-cost, light weight, and small size, but this also sensor module. In this study, the accelerometer used was a KXR94-2050 accelerometer with a fullsuggests that they have a lower performance compared to more expensive devices. Indeed, the major drawbacks of low-cost sensors are their high noise and measurement errors. This is the reason why Figure 2. The self-developed ARM-based sensor module and an Android mobile device. calibration and verification of the sensor module are critical to enhance its accuracy and performance before its use. to the measurements of the inertial sensors, the accelerometer transfers the objective In regard In regard into to the measurements of the inertial accelerometer transfers the objective acceleration physical values with units in m/s2sensors, or g, thethe latter of which is the magnitude of the acceleration into physical values with unitstransfers in m/s2 the or g, the latter of which the magnitude of the Earth’s gravitational field. The gyroscope objection rotation intoisphysical values with the unit in deg/s. One accelerometer and one tri-axis gyroscope are used in the developed Earth’s gravitational field.tri-axis The gyroscope transfers the objection rotation into physical values with the sensor module. this study, the accelerometer was a KXR94-2050 accelerometer with a fullunit in deg/s. OneIntri-axis accelerometer and one used tri-axis gyroscope are used in the developed sensor module. In this study, the accelerometer used was a KXR94-2050 accelerometer with a full-scale output

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scale output range of ±2 g (19.6 m/s2), produced by Kionix, Inc. (Ithaca, NY, USA). The gyroscope scale output range of ±2 g (19.6 m/s2), produced by Kionix, Inc. (Ithaca, NY, USA). The gyroscope used was an A3G4250D gyroscope with a full-scale output range of ±245 deg/s, produced by rangewas of ˘2ang (19.6 m/s2 ), gyroscope produced by Kionix, Inc. (Ithaca, NY,range USA).ofThe gyroscope used was by an used A3G4250D with a full-scale output ±245 deg/s, produced STMicroelectronics. The basic specifications of the two sensors used are listed directly below in Table 1. A3G4250D gyroscope with a full-scale output range of ˘245 deg/s, produced by STMicroelectronics. STMicroelectronics. The basic specifications of the two sensors used are listed directly below in Table 1. The basic specifications of the two sensors used are listed directly below in Table 1. Table 1. The basic specifications of each sensor. Table 1. The basic specifications of each sensor. Table 1. The basic specifications each sensor. A3G4250D Tri-Axis KXR94-2050of Tri-Axis

Specifications KXR94-2050 Tri-Axis Accelerometer Specifications Accelerometer KXR94-2050 Tri-Axis Measurement ±2 g Specifications Range Accelerometer Measurement Range ±2 g Sensitivity 660 mV/g Sensitivity 660 Measurement Range g mV/g Sensitivity Change over Temp 0.01˘2 (xy) 0.02 (z)%/°C Sensitivity 660 mV/g Sensitivity Change over Temp 0.01 (xy) 0.02 (z)%/°C Non-Linearity 0.1% of ˝FS Sensitivity Non-Linearity Change over Temp 0.01 (xy) 0.02 (z)%/ C 0.1% of FS Cross Axis Sensitivity 2% Non-Linearity 0.1% of FS Cross Axis Sensitivity 2% Cross Axis Sensitivity 2% Noise Density 45?μg/√𝐻𝑧 Noise Density 45 μg/√𝐻𝑧 Noise Density 45 µg/ Hz

A3G4250D Tri-Axis Gyroscope Gyroscope A3G4250D ±245 Tri-Axis deg Gyroscope ±245 deg 8.75 mdps/digit 8.75 mdps/digit ˘245 deg ±2%/°C 8.75 mdps/digit ±2%/°C 0.2% of ˝ FS ˘2%/ 0.2% ofCFS - FS 0.2% of - ? 0.03 dps/√𝐻𝑧 0.03 dps/√𝐻𝑧 0.03 dps/ Hz

The sensor module has been designed to be either waist-mounted or handheld, as shown in The sensor module has been designed to be either waist-mounted or handheld, as shown in Figures and 4 below. After the results showed that the sameas experiment The3 sensor module hassome been preliminary designed totests, be either waist-mounted or in handheld, shown in Figures 3 and 4 below. After some preliminary tests, the results showed that in the same experiment the standard of thesome estimated pitch angle degshowed measured the waist-mounted Figures 3 anddeviation 4 below. After preliminary tests,was the 1.09 results thatfrom in the same experiment the standard deviation of the estimated pitch angle was 1.09 deg measured from the waist-mounted type and 5.62 deviation deg measured the handheld type.was Therefore, the waist-mounted type was selected the standard of thefrom estimated pitch angle 1.09 deg measured from the waist-mounted type and 5.62 deg measured from the handheld type. Therefore, the waist-mounted type was selected to implement the PDR in this study its higher andthe reliability than the handheld type. type and 5.62 deg measured from thedue handheld type.accuracy Therefore, waist-mounted type was selected to implement the PDR in this study due its higher accuracy and reliability than the handheld type. The waist-mounted type has study the capability of describing andthan actions of the lower limbs to implement the PDR in this due its higher accuracythe andmotions reliability the handheld type. The The waist-mounted type has the capability of describing the motions and actions of the lower limbs more precisely. type In contrast, the handheld type is affected by how the userofholds the device and waist-mounted has the capability of describing the motions and actions the lower limbs more more precisely. In contrast, the handheld type is affected by how the user holds the device and whether user is reading a message screen. theholds following tests and precisely.the In contrast, the handheld typeon is the affected byTherefore, how the user the device andexperiments whether the whether the user is reading a message on the screen. Therefore, the following tests and experiments were on the waist-mounted type, and the sensor module was to the back of the user’s user isbased reading a message on the screen. Therefore, the following testsattached and experiments were based on were based on the waist-mounted type, and the sensor module was attached to the back of the user’s waist, as seen in Figure the waist-mounted type,3.and the sensor module was attached to the back of the user’s waist, as seen in waist, as seen in Figure 3. Figure 3.

Figure Figure 3. 3. Waist-mounted Waist-mounted type. type. Figure 3. Waist-mounted type.

Handheld type. Figure 4. Handheld Figure 4. Handheld type.


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3. Sensor Calibration and Multi-Sensor Fusion Algorithm 3.1. Sensor Error Model and Calibration Method Due to the high noise and errors of low-cost MEMS sensors, which are the result of manufacturing imperfections and other errors, a calibration procedure is required before they can be effectively and reliably used. Such errors can basically be divided into two categories: random constant and time-correlated random process errors [32]. Since the dynamic representation of random constant errors is simple, and these have a significant influence on the performance of the sensor, the selected calibration parameters for this study are the random constant errors that could result from a sensor triad of scale factors, biases, and orthogonalization angles. The sensor error model for the aforementioned specified sensor error triad is as follows [29]: Ñ

Ñ

Ñ

y “ KT u ` b

á á

(1)

Ñ

where y , u , K, T, and b denote the sensor outputs, observed physical quantity, scale factor matrix, Ñ

orthogonalization angles matrix, and bias follows [29]: » kx — K“– 0 0

vector, respectively. The details of K, T, and b are as

fi » fi 0 bx Ñ ffi — ffi 0 fl , b “ – by fl kz bz fi 1 0 0 — ffi T “ – αz 1 0 fl ´αy αx 1 0 ky 0 »

(2)

(3)

where αx , αy , and αz denote nonorthogonal angles. The sensor model was applied to two different sensor triads, which are the accelerometer triad and gyroscope triad in this study. With this study’s proposed sensor module, the calibration procedures for each sensor triad can be accomplished by rotating the sensors to various random or specified rotations. For each sensor triad, there are nine parameters to be determined: three scale factors, three biases, and three nonorthogonal angles. This means that nine or more orientations and rotations are required to determine these parameters. The calibrations for each sensor triad are accomplished by using the scalar calibration and the least squares methods [29]. 3.2. Accelerometer Calibration The calibration of the accelerometer triad can be accomplished by using the magnitude of the Earth’s gravitational field, which is constant in a specified location without the influence of other disturbances. Therefore, the reference value of the accelerometer triad is the gravitational constant represented by 1 g. It is an empirical physical constant and is independent to the orientations of the sensor module when it is static. For this reason, the precise orientations of this sensor triad are not required, but it is necessary to keep the triad static when acquiring data. The calibration of the accelerometer triad in this study was performed on a six-axis translation and rotation platform, as shown in Figure 5. By fixing the sensor triad to at least nine different orientations on the platform and applying the least squares optimization, the nine-parameter vector can be determined. The calibration results of the accelerometer triad are presented in Table 2. Figure 6 shows that the error margin of the accelerometer triad is 0.3% of gravitational acceleration.

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Figure 5. Six-axis translation and rotation platform. Table 2. Calibrated parameters of the accelerometer triad.

Axis

Scale Factor (ratio)

Bias (V)

x y z

0.9968 0.9991 1.0025

0.0506 0.0006 0.0019

Nonorthogonal Angle (°) αx αy αz

Figure 5. Six-axis translation and rotation platform. 1.015 Table

−0.0207 0.0004 −0.0505

2. Calibrated parameters of the accelerometer triad. Default

Axis

Bias (V)

0.9968 0.9991 1.0025

0.0506 0.0006 0.0019

1.01

Acceleration (g)

x y z


Nonorthogonal Angle (°) Calibrated αx αy αz

Reference

−0.0207 0.0004 −0.0505

1.005 1.015 Default Calibrated Reference

1 1.01

Acceleration (g)

0.995 1.005 0.99 1

0

20

40

60

80 100 Sample

120

140

160

Figure 6. The calibration results of the total acceleration measured from the accelerometer triad. Figure 6. The calibration results of the total acceleration measured from the accelerometer triad. 0.995

3.3. Gyroscope CalibrationTable 2. Calibrated parameters of the accelerometer triad. The calibration of the gyroscope triad can Bias also (V) be accomplished by applyingAngle scalar(˝calibration to Axis Scale Factor (ratio) Nonorthogonal ) 0.99 a rotation platform. In this study, a single-axis rotation platform was utilized to perform the 0 0.9968 20 40 60 0.0506 80 100 120 α 140 160 x ´0.0207 x Sample calibration ofy the gyroscope 0.9991 triad. The platform held the sensor triad in a desired0.0004 orientation and 0.0006 αy 1.0025 αz reference value ´0.0505 performed a zspecified rotation with a constant 0.0019 angular rate; thus, the of the rotating 6. The calibration results of the total the accelerometer sensor Figure triad was able to be determined. For thisacceleration study, themeasured specifiedfrom angular rate was set triad. to 300 deg/s during the calibration. Moreover, the accuracy biases of the gyroscope triad were first determined by 3.3. Gyroscope Calibration 3.3. Gyroscope Calibration keeping the platform in a static condition. After the biases were determined, the remaining unknown The calibration of the gyroscope triad can also be accomplished by applying scalar calibration to a parameters were reduced six, and this six different the platform with The calibration of the to gyroscope triadrequired can alsoat beleast accomplished byrotations applyingof scalar calibration to rotation platform. In this study, a single-axis rotation platform was utilized to perform the calibration constant platform. angular rate to apply least squares optimization. gyroscope a rotation In this study,the a single-axis rotation platform The was results utilizedoftothe perform the of the gyroscope triad. The platform held the sensor triad in a desired orientation and performed a calibration of with procedure areThe shown in Table 3. the In addition, Figure shows the errors ofand the thethis gyroscope triad. platform held sensor triad in a7 desired orientation specified rotation with a constant angular rate; thus, the reference value of the rotating sensor triad gyroscope triad, with an error margin lower than 0.2% of thethus, reference angular rate. performed a specified rotation with a constant angular rate; the reference value of the rotating was able to be determined. For this study, the specified angular rate was set to 300 deg/s during the sensor triad was able to be determined. For this study, the specified angular rate was set to 300 deg/s calibration. Moreover, the accuracy biases of the gyroscope triad were first determined by keeping the during the calibration. Moreover, the accuracy biases of the gyroscope triad were first determined by platform in a static condition. After the biases were determined, the remaining unknown parameters keeping the platform in a static condition. After the biases were determined, the remaining unknown were reduced to six, and this required at least six different rotations of the platform with a constant parameters were reduced to six, and this required at least six different rotations of the platform with angular rate to apply the least squares optimization. The results of the gyroscope calibration with this a constant angular rate to apply the least squares optimization. The results of the gyroscope procedure are shown in Table 3. In addition, Figure 7 shows the errors of the gyroscope triad, with an calibration with this procedure are shown in Table 3. In addition, Figure 7 shows the errors of the error margin lower than 0.2% of the reference angular rate. gyroscope triad, with an error margin lower than 0.2% of the reference angular rate.

Table 3. The calibrated parameters of the gyroscope triad.

Axis


Bias (V)

1.0138 0.9702 1.0031

0.2920 0.2486 0.1029

Angular rate(deg/s)

Gz(deg/s)

Gy(deg/s)

Gx(deg/s)

x y ISPRS Int. J. Geo-Inf. 2016, 5, 70 z

Nonorthogonal Angle (°) αx αy αz

0.0014 0.0207 −0.0090

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500 0 -500

0

20

40

60

80

100

120

0

20

40

60

80

100

120

0

20

40

60

80

100

120

0

20

40

60 80 Sample

100

120

500 0 -500 500 0 -500 300.5 300 299.5

Figure 7. The calibration results of of thethe total from the thegyroscope gyroscopetriad triad (the Figure 7. The calibration results totalrotation rotationmeasured measured from (the redred lineline is the reference). is the reference).

3.4. Multi-Sensor Fusion Algorithm Table 3. The calibrated parameters of the gyroscope triad. For the step-and-heading-based dead reckoning method, the accuracy of the estimated step Axislength, and Scale (ratio) Bias (V) (˝ ) count, the the Factor heading were determined by the quality Nonorthogonal of the measured Angle acceleration and the angular rate. In order to enhance the quality of the measurements for the sensors and acquire x 1.0138 0.2920 αx 0.0014 information multi-sensor fusion algorithm was applied by using a second-order y from them, a0.9702 0.2486 αy 0.0207 z 1.0031 0.1029 αz the calibrated´0.0090 complementary filter [33]. This multi-sensor fusion algorithm then output acceleration, calibrated angular rates, and the estimated attitude, which is the roll and pitch angles, to the Dead Reckoning Algorithm part. 3.4. Multi-Sensor Fusion Algorithm The preprocessing of the multi-sensor fusion algorithm consisted of acquiring the raw data from For the step-and-heading-based the accuracy of thethe estimated the sensor module, performing the dead sensorreckoning calibration,method, data filtering, and obtaining attitude step estimation fromand the accelerometer. The applied data filtering used was aof low-pass filter withacceleration a 5 Hz count, the length, the heading were determined by the quality the measured cutoff frequency, was applied to the the outputs of theofaccelerometer triad. The cutoff and and the angular rate.andInitorder to enhance quality the measurements forselected the sensors frequency was based on the frequencies of different movements, between 0.4 and 5 Hz, for regular acquire information from them, a multi-sensor fusion algorithm was applied by using a second-order human daily activity [34,35]. The direct outputs of the sensors are the acceleration and angular rate complementary filter [33]. This multi-sensor fusion algorithm then output the calibrated acceleration, of the target object, but these signals are not enough to describe the motion of the human body while calibrated angular rates, and the estimated attitude, which is the roll and pitch angles, to the Dead walking. In order to extract more information about pedestrian activities, the multi-sensor fusion Reckoning Algorithm part.to derive the reliable orientation of the sensor module. The orientation is algorithm was applied The preprocessing of used the multi-sensor algorithmofconsisted of acquiring the raw data information that can be to indicate the fusion spatial condition the target object when performing from various the sensor module, performing the sensor calibration, data filtering, and obtaining the attitude daily activities, such as walking, jogging, or cycling. In this study, the estimated attitude of estimation the accelerometer. applied filtering and usedgyroscopes was a low-pass with a the userfrom is estimated by fusing theThe outputs of thedata accelerometer with the filter secondfilter. The basic ideato of the the complementary is to fuse the roll and 5 Hzorder cutoffcomplementary frequency, and it was applied outputs of the filter accelerometer triad. Thepitch selected derivedwas from the gyroscope outputs through a high-pass filter, and between those derived from5the cutoffangles frequency based on the frequencies of different movements, 0.4 and Hz, for accelerometer through a low-pass filter, to obtain the estimated attitude, thus compensating for the and regular human daily activity [34,35]. The direct outputs of the sensors are the acceleration drift of the gyroscope and the slow dynamics and high noise of the accelerometer. The cutoff angular rate of the target object, but these signals are not enough to describe the motion of the frequencies of the adopted low-pass and high-pass filters were both set to 0.1 Hz. This number was human body while walking. In order to extract more information about pedestrian activities, the determined by test data and was based on the frequencies of different movements of regular human

multi-sensor fusion algorithm was applied to derive the reliable orientation of the sensor module. The orientation is information that can be used to indicate the spatial condition of the target object when performing various daily activities, such as walking, jogging, or cycling. In this study, the estimated attitude of the user is estimated by fusing the outputs of the accelerometer and gyroscopes with the second-order complementary filter. The basic idea of the complementary filter is to fuse the roll and pitch angles derived from the gyroscope outputs through a high-pass filter, and those derived from the accelerometer through a low-pass filter, to obtain the estimated attitude, thus compensating for the drift of the gyroscope and the slow dynamics and high noise of the accelerometer. The cutoff frequencies of the adopted low-pass and high-pass filters were both set to 0.1 Hz. This number was determined by test data and was based on the frequencies of different movements of regular human


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daily activity to recognize stationary from moving activity. The estimated attitudes would thus have to recognize stationary from moving activity. The estimated attitudes would thus have both daily short-activity and long-term accuracy. both shortand long-term accuracy.roll and pitch angles from different methods while the subject is Figure 8 presents the estimated Figure 8 presents the estimated roll and pitch angles from different methods while the subject is walking. The data denoted as “acc,” ‘’gyro,” and “CF” are the roll and pitch angles derived from the walking. The data denoted as “acc,” ‘’gyro,” and “CF” are the roll and pitch angles derived from the accelerometer, the gyroscope, and the complementary filter methods, respectively. The data reveal that accelerometer, the gyroscope, and the complementary filter methods, respectively. The data reveal the accelerometer suffers suffers from high during highhigh dynamic motion, thethe gyroscope that the accelerometer fromnoise high noise during dynamic motion, gyroscopesuffers suffers from drift, from and only the complementary filter can perform well in both the short and long terms. This drift, and only the complementary filter can perform well in both the short and long terms. Thisfigure also shows thatshows the estimated roll androll pitch from from the CF areare more reliable figure also that the estimated andangles pitch angles themethod CF method more reliablethan thanthose from two the other two estimation methods. Theofdrift the pitch is larger drift in roll from those the other estimation methods. The drift the of pitch angleangle is larger thanthan the the drift in the rollreason angle. The for this issue be that theangle pitch angle contains larger errors in bias andinitial angle.theThe for reason this issue could becould that the pitch contains larger errors in bias and value. Moreover, results reflect that a walking is fairly complicated consists of value.initial Moreover, the resultsthe reflect that a walking motionmotion is fairly complicated and and consists of regular regular vertical and horizontal motion. vertical and horizontal motion. 30 acc gyro CF

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4. Pedestrian Dead Reckoning Algorithm

4. Pedestrian Dead Reckoning Algorithm

The proposed PDR in this study is based on the step-and-heading-based dead reckoning

The proposed PDR in thisisstudy is from based on the step-and-heading-based dead reckoning method. method. A current location derived a previous location by adding the displacement estimated A current location is derived fromTherefore, a previous the displacement estimated from step length and heading. thelocation accuracybyofadding the estimated step count, length, and from headingand is critical to the performance of the PDR. In this study, since measurement of heading the step length heading. Therefore, the accuracy of the estimated step the count, length, and magnetometer triad was influenced by In both natural man-made sources of magnetism in the is critical to the performance of the PDR. this study,and since the measurement of the magnetometer environment, the magnetometer triad was not adopted to aid with heading estimation. The triad indoor was influenced by both natural and man-made sources of magnetism in the indoor environment, Step Counting block detects a user’s periodic motion while moving, and it outputs the detected steps the magnetometer triad was not adopted to aid with heading estimation. The Step Counting block and step time to the Knowledge-Based SLE block. The Knowledge-Based SLE block calculates step detects a user’s periodic motion while moving, and it outputs the detected steps and step time strength and frequency using estimated step count and step time. With an estimated step strength to the Knowledge-Based SLE block. The Knowledge-Based SLE block calculates step strength and and frequency, the Knowledge-Based SLE block then uses the FL method to estimate every step frequency estimated count step time. With step strengththe and frequency, lengthusing of a user. A user’sstep heading orand the direction they facean is estimated estimated by integrating angular the Knowledge-Based block then the to estimate every stepdistance, length of a user. rates in the HeadingSLE Estimation block.uses Based onFL an method initial position, a user’s traveling and A user’s headingheading or the information, direction they face is estimated bytime integrating thetoangular ratesby in the thePDR Heading continuous a user’s location at any is thus able be estimated algorithm. Estimation block. Based on an initial position, a user’s traveling distance, and continuous heading information, a user’s location at any time is thus able to be estimated by the PDR algorithm. 4.1. Step Counting

4.1. Step Counting Step detection and counting are fundamental with regard to knowing the displacement of a user. Accelerometers are widely used to fundamental detect a user’swith steps,regard and various methods achieve this have Step detection and counting are to knowing thetodisplacement of a user. been presented in many studies, with peak detection and zero-crossing detection widely applied to Accelerometers are widely used to detect a user’s steps, and various methods to achieve this have waist-mounted and handheld PDRs [10,16,36]. The objective of the Step Counting block is to been presented in many studies, with peak detection and zero-crossing detection widely applied to waist-mounted and handheld PDRs [10,16,36]. The objective of the Step Counting block is to recognize each step and to detect its duration and strength. In order to increase the accuracy and reliability of the


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step counting method, in this study a static state detection method was applied to detect whether a Int. J. Geo-Inf. 2016, 5, 70 of 21 user ISPRS is moving or not. The Signal Vector Magnitude (SVM) is calculated every epoch as a 10 feature of a user’s movement. When a user is static, the detected SVM is approximately 1 g. If the SVM value recognize each step and to detect its duration and strength. In order to increase the accuracy and deviates from of 1 gthe and exceeds a pre-selected threshold, in thisstate casedetection 0.1 g, then that user is considered reliability step counting method, in this study a static method was applied to to bedetect moving. For the kth epoch, SVM(k) is defined as the root square of the sum of theepoch squared whether a user is moving or not. The Signal Vector Magnitude (SVM) is calculated every acceleration signal eachmovement. axis: as a feature of a of user’s When a user is static, the detected SVM is approximately 1 g. If the SVM value deviates from 1 g and exceeds ab pre-selected threshold, in this case 0.1 g, then that user is 2 pkq considered to be moving. For the kth epoch, the root square of the sum of the (4) SV M pkq “ SVM(k) a2x pkq `isa2ydefined pkq ` aas z squared acceleration signal of each axis:

where a x , ay , and az denote the measured acceleration in the x-axis, y-axis, and z-axis, respectively, of 𝑆𝑉𝑀(𝑘) = √𝑎𝑥2 (𝑘) + 𝑎𝑦2 (𝑘) + 𝑎𝑧2 (𝑘) (4) the accelerometer triad at the kth epoch. Peak zero crossing detection are the most common step detection methods. where detection 𝑎𝑥 , 𝑎𝑦 , andand 𝑎𝑧 denote the measured acceleration in the x-axis, y-axis, and z-axis, respectively, However, the results of some walking experiments, as shown in Figure 9, have indicated that the raw of the accelerometer triad at the kth epoch. accelerometer contain noise and inconsistences each step, in the y- and Peak data detection andsignificant zero crossing detection are the mostfor common stepespecially detection methods. z-axes. This reflects the fact that walking human experiments, walking creates a reaction force whenindicated the feet that hit the ground, However, the results of some as shown in Figure 9, have the raw accelerometer contain noise and of inconsistences for each in the y- and which in technicaldata terms is thesignificant heel strike phase the gait cycle. The step, highespecially noise of the acceleration z-axes. This reflectsthe the accuracy fact that human walking creates a reaction forceon when thepeak feet hit the ground, information degrades of step detection methods based either detection or zero which in technical terms is the heel strike phase of the gait cycle. The high noise of the acceleration crossing detection. As shown in Figure 9, the acceleration in the x-axis is more regular and stable than information degrades the accuracy of step detection methods based on either peak detection or zero that in the other two axes, and the x-axis acceleration is consistent with the forward displacement crossing detection. As shown in Figure 9, the acceleration in the x-axis is more regular and stable than of the user when walking. Therefore, a step detection method was proposed in this study by using that in the other two axes, and the x-axis acceleration is consistent with the forward displacement of the periodic characteristics in the x-axis velocity, which represents forward and backward velocity. It the user when walking. Therefore, a step detection method was proposed in this study by using the is denoted ascharacteristics Vx and is integrated from the x-axis acceleration. When aand pair of peaks and valleys periodic in the x-axis velocity, which represents forward backward velocity. It is in the x-axis velocity is detected, one step will be recognized in the Step Counting block. The detecting denoted as Vx and is integrated from the x-axis acceleration. When a pair of peaks and valleys in the process of peaks and valleys (minima) is doneinbythe determining theblock. local extrema of Vx in x-axis velocity(maxima) is detected, one step will be recognized Step Counting The detecting real time. Inofthis study, two thresholds set toisdetermine whether the maximaoforVx minima process peaks (maxima) and valleyswere (minima) done by determining the local local extrema in time. InOne this was study, thresholds were setpresent to determine local maxima minima were real reckoned. thetwo difference between Vx andwhether nearbythe extremum, and or this threshold wasThe the other difference presentbetween Vx and nearby extremum, valuewere wasreckoned. set at 0.05One m/s. was between the difference the present time and andthis thethreshold time when a value was set at 0.05 m/s. The other was the difference between the present time and the time when previous extremum was detected, and its value was set at 0.15 s. The contention is that this threshold a previous extremum was detected, and its value was set at 0.15 s. The contention is that this threshold can prevent the influence of noise on step counting. The determination of these two thresholds was can prevent the influence of noise on step counting. The determination of these two thresholds was made according to the test data measured from different subjects. When these two thresholds were made according to the test data measured from different subjects. When these two thresholds were achieved at the same time, the local maxima or minima were determined. Theoretically, step time is achieved at the same time, the local maxima or minima were determined. Theoretically, step time is equalequal to thetotime of two walking signals. In this study, we used two two continuous valley signals the time of repeated two repeated walking signals. In this study, we used continuous valley in thesignals x-axisinvelocity to velocity calculate step time. Figure shows the rollthe angle, pitch pitch angle, and the the x-axis to the calculate the step time. 10 Figure 10 shows roll angle, angle, x-axisand velocity. Thevelocity. green dotted line of the top presents thepresents results of state the x-axis The green dotted lineplot of the top plot thestatic results of detection, static state and the zero valueand represents static state. The red asterisks bottomofplot indicate the steps that detection, the zero the value represents the static state. Theof redthe asterisks the bottom plot indicate the steps that are detected. are detected.

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Figure 9. Acceleration signals in each axis and the Signal Vector Magnitude (SVM) value of the user.


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4.2. Knowledge-Based SLE Algorithm Based on Fuzzy Logic

4.2. Knowledge-Based SLE Algorithm Based on Fuzzy Logic There are several step length estimation methods that have been proposed for different

There are in several step length estimationof methods that have been forthedifferent applications the past [21–23]. A comparison several popular methods has proposed revealed that one applications in the past [21–23]. A comparison of several popular methods has revealed that proposed by Weinberg et al. is best suited for a waist-mounted IMU [16,26]. This method adopts an the one approximation proposed by Weinberg et al. is best suited for a waist-mounted IMU [16,26]. This method adopts of the inverted pendulum model described by Zijlstra et al. [24], yet it is a model that an approximation the inverted pendulum model described by Zijlstra et al. [24], yet it is equation, a model that does not requireofinformation about the user’s leg length. This approach applies an empirical estimates the step length, L, from theleg vertical displacement of the pelvis.an From data gained doeswhich not require information about the user’s length. This approach applies empirical equation, from empirical equation be approximated which estimates theexperiments, step length,the L, from the can vertical displacementas:of the pelvis. From data gained from empirical experiments, the equation can be𝐿 approximated = 𝐾 4√𝑎 − 𝑎 as: (5) 𝑚𝑎𝑥

𝑚𝑖𝑛

? 4 are the maximum minimum L “ Kand amax ´ amin vertical acceleration during a step, (5)

where 𝑎max and 𝑎min respectively. K is a constant value that needs to be adjusted for different subjects. This empirical equation has abeen adopted in this study in order to compare its performance with that of the method where amax and min are the maximum and minimum vertical acceleration during a step, respectively. proposed herein. The applied values for each test subject were obtained by usingequation different has K is a constant value that needsconstant to be adjusted for different subjects. This empirical step lengths measured by said test subjects. Therefore, the constant values of the adopted empirical been adopted in this study in order to compare its performance with that of the method proposed equation will be changed based on the difference between the maximum and minimum vertical herein. The applied constant values for each test subject were obtained by using different step lengths acceleration. measured by said test subjects. Therefore, the constant values of the adopted empirical equation will The fuzzy rules adopted in this study are the Mamdani-type, also called the max-min inference be changed onvariables the difference theone maximum anddefuzzification minimum vertical acceleration. method, based and the are twobetween inputs and output. The strategy is the centerThe fuzzy rules adopted in this study are the Mamdani-type, also called the max-min inference of-gravity method [37]. The input variables of the adopted FL are step frequency and strength, and method, and value the variables are two output. The defuzzification strategy is the its output is the estimated stepinputs length.and The one step frequency is derived from the step time, and center-of-gravity method [37]. The input variables of the adopted FL aresubtraction, step frequency and strength, the step strength is based on the summation signal magnitude calculated by the SVM from the magnitude of theThe gravitational field. The step frequency and strength and subtracting its output value is the estimated step length. step frequency is derived from the step time, and of the nth stepisare determined as follows: of signal magnitude subtraction, calculated by subtracting the step strength based on the summation

the SVM from the magnitude of the gravitational field.1 The step frequency and strength of the nth step 𝑓𝑟𝑒𝑞(𝑛) = , and (6) are determined as follows: 𝑡𝑛 1 f req pnq “ E , and (6) (7) 𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ(𝑛) = ∑ tn (𝑆𝑉𝑀(𝑘) − 𝑔) 𝑘=1

E ÿ

where 𝑡𝑛 represents the step time of nth step, and E pSV is the Strength pnq “ Mdetected pkq ´ gqepochs in the duration of the nth (7) step. k“1 The FL design is based on the results of a metrical analysis of a set of walking experiments. The where tn represents the step time of nth step, and E is the detected epochs in the duration of the target subject was asked to walk at different step lengths, 30, 60, and 90 cm, and different frequencies, nth step. 1, 1.5, 2, and 2.5 Hz. The adopted step lengths of the subjects were controlled by drawing markers on Theground FL design is based the results of aanalyzing metrical the analysis of adata, set of experiments. the for each given on step length. After resulting thewalking membership functionsThe target subject was asked to walk at different step lengths, 30, 60, and 90 cm, and different frequencies, of the frequency and strength inputs that were adopted are five and seven triangular functions, 1,

1.5, 2, and 2.5 Hz. The adopted step lengths of the subjects were controlled by drawing markers on the ground for each given step length. After analyzing the resulting data, the membership functions of the frequency and strength inputs that were adopted are five and seven triangular functions, respectively.


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The range of the membership functions for the frequency input is from 0.6 to 3 Hz, and for the strength the membership functions for the frequency input is from 0.6 to 3 Hz, and inputrespectively. is from 2 toThe 25 range g. Theofadopted membership functions of the estimated step length output are for the strength input is from 2 to 25 g. The adopted membership functions of the estimated step ISPRS Int. J. Geo-Inf. 2016, 5, 70 12 of 21 applied seven triangular functions, and its range is from 20 to 105 cm. There are thus 35 rules in the length output are seven triangular functions, and its range is from 20 to 105 cm. There are thus 35 FL, and the output surface of the FIS is shown in Figure 11. DueintoFigure the differences in height, weight, rules in the applied FL, and themembership output surface of thefor FISthe is shown Due0.6 toto the differences respectively. The range of the functions frequency input is11. from 3 Hz, and and leg length between every subject, the design of the FL, including the membership functions and infor height, weight, andisleg length every subject, the design ofofthe including the strength input from 2 to 25between g. The adopted membership functions theFL, estimated step the the rule table,output varied the subjects. Forrange each design of each the needed membership functions and thedifferent rulefunctions, table, varied the different subject, length areamong seven triangular and among its issubject, from 20 the tosubjects. 105 cm. For There areFL thus 35 theto be adjusted according the data. rules in FL,test and theadjusted output surface of the shown in Figure 11. Due to the differences design ofthe theapplied FLto needed to be according toFIS theistest data. in height, weight, and leg length between every subject, the design of the FL, including the membership functions and the rule table, varied among the different subjects. For each subject, the design of the FL needed to be adjusted according to the test data.

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The test results of theFigure FL designed for adesign selected target subject are shown in Figure 12. The subject 11. Rule table of the proposed PDR system.

The test50 results of theunconstrained FL designedspeed, for a selected target subject are shown in Figure 12. The subject walked steps with and the desired step length was 61 cm. The ground truth The test results of the FL designed for aand selected subject shown in Figure 12. The walked 50 steps with unconstrained speed, thetarget desired stepare length was 61 cm. The ground of the traveled distance was measured via a laser range finder. The results show that thesubject detectedtruth walked steps with unconstrained speed, and the desired step length was 61tocm. The ground truth count50matches thewas truemeasured count, and the estimated step lengths are close theshow desired length. The of thestep traveled distance via a laser range finder. The results that the detected of thealso traveled distance was measured via a laser range finder. The results show that the detected results show that the first few steps have greater errors than the others. The probable reason for The step count matches the true count, and the estimated step lengths are close to the desired length. step count matches the true count, andfrom the estimated step lengths and are close to the desired length. The not this is that the subject started to walk a standing position, the first few steps were thus results results also show that that the the first few steps have greater errors than the others. The probable reason for also showerror first few stepsstep havelengths greateriserrors thanand the the others. The probable reason for cm. stable. The mean of the estimated 1.36 cm, standard deviation is 4.27 this is that the subject started to walk from a standing position, and the first few steps were this is that the subject started to walk from a standing position, and the first few steps were thus notthus not stable. stable. The mean errorerror of the estimated lengthsisis1.36 1.36 the standard deviation is 4.27 cm. The mean of the estimatedstep step lengths cm,cm, andand the standard deviation is 4.27 cm. 10

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ISPRS Int. J. Geo-Inf. 2016, 5, 70 ISPRS Int. J. Geo-Inf. 2016, 5, 70

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4.3. Heading Estimation

the Heading Heading Estimation block of Figure 1, the the estimated estimated heading heading of the the sensor sensor module module was was In the from the integration of the calibrated angular rate measured measured from from the the gyroscope. gyroscope. In order to derived from improve the accuracy of the heading estimation, the coordinate frame frame of of the the calibrated calibrated angular rates were transferred transferredfrom from sensor to horizontal local horizontal theangles attitude angles were thethe sensor bodybody to local framesframes by usingbytheusing attitude estimated estimated from the multi-sensor fusion algorithm. The heading estimated is determined by(8): Equation from the multi-sensor fusion algorithm. The estimated isheading determined by Equation (8): ´. . ¯ ψK “ ψK´1 ` ψK̇ ´ ψḃ ∆t (8) (8) 𝜓𝐾 = 𝜓𝐾−1 + (𝜓𝐾 − 𝜓𝑏 )Δ𝑡 . . . where ψ𝜓̇isisthe theangular angularrate rateofofthe theheading headingangle anglein inaalocal localhorizontal horizontalframe, frame,and andψ𝜓̇𝑏isisthe thebias biasofofψ.𝜓̇. where b Due totothe thedrifting drifting problem of gyroscope, the gyroscope, wastovital to determine biases of the Due problem of the it wasitvital determine the biasesthe of the gyroscope gyroscope triad. The determination of the biases was carried out using the static condition of the triad. The determination of the biases was carried out using the static condition of the sensor module sensor module before the user started to walk. The initialization of the estimated heading angles before the user started to walk. The initialization of the estimated heading angles was to averagewas the to average the heading angles of the first few steps when a user walks straightly. Figure 13 presents heading angles of the first few steps when a user walks straightly. Figure 13 presents the results of the results of heading estimation, revealsisthat walking is partially composed ofmotion the swinging heading estimation, and it reveals and that it walking partially composed of the swinging of the motion of the body when the subject walks in a straight line. After walking 50 steps, the subject faces body when the subject walks in a straight line. After walking 50 steps, the subject faces the same the same direction as when they started to walk. The accumulative heading error of this test is within direction as when they started to walk. The accumulative heading error of this test is within 1 deg 1 degthe after the subject walked fors.40The s. The results demonstrate short-termaccuracy accuracyofofthe the heading heading after subject walked for 40 results demonstrate thethe short-term estimation. In map-matching method cancan be be adopted to correct the estimation. Interms termsofoflong-term long-termaccuracy, accuracy,the the map-matching method adopted to correct heading errors [9,10]. Another way to reduce the accumulating error of heading is to use more the heading errors [9,10]. Another way to reduce the accumulating error of heading is to use more accurate gyroscopes, gyroscopes, which which can can be be high-performance high-performance fiber-optic fiber-optic gyroscopes. gyroscopes. It accurate It should should be be noted noted that, that, in Figure 13, the swinging motion in heading is caused by the pelvic motion when the subjects were in Figure 13, the swinging motion in heading is caused by the pelvic motion when the subjects were walking [38]. [38]. walking

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Figure 13. Estimated heading of a user walking 50 steps. steps.

60 5. Experiment ExperimentResults Resultsand andDiscussion Discussion 40

Twotypes typesof ofexperiments experimentswere wereconducted conductedininthis thisstudy study verify performance and accuracy Two toto verify thethe performance and accuracy of 20 of the proposed system. Onea was a step estimation length estimation experiment, and was the aother was a the proposed PDRPDR system. One was step length experiment, and the other pedestrian pedestrian experiment. navigation 0experiment. The step estimation experiment conducted by asking the navigation The step estimation experiment was conductedwas by asking the subjects to walk 0 5 10 15 20 25 30 35 40 45 50 subjects walk at specific step lengths. of was this to first experiment was to and examine the at specifictostep lengths. The objective of thisThe firstobjective experiment examine the reliability accuracy Step reliability and accuracy of the proposed SLE method based on multi-sensor fusion and FL algorithms. of the proposed SLE method based on multi-sensor fusion and FL algorithms. The second experiment, Thepedestrian second experiment, pedestrianwas navigation experiment, was conducted examine theof longthe navigationthe experiment, conducted to examine the long-termtoperformance the term performance the proposed SLE a PDR system. In the step experiment, ten4 subjects proposed SLE for aofPDR system. In thefor step length experiment, ten length subjects (6 male and female) (6 male and 4 female) took part. ranged from28.0 21 to 40 years 28.0 years), their body took part. Their ages ranged fromTheir 21 toages 40 years (mean: years), their(mean: body masses ranged from 48 masses 48 toand 80 kg (mean: 61.7ranged kg), and their heights from166.5 157 tocm). 177 One cm (mean: to 80 kgranged (mean:from 61.7 kg), their heights from 157 to 177ranged cm (mean: of the 166.5subjects cm). One of selected the maleassubjects wassubject selected target subject and the on FL male was the target for as allthe experiments, andfor theall FLexperiments, was calibrated based was calibrated based on the testing data of this individual. The height and body mass of the target the testing data of this individual. The height and body mass of the target subject were 170 cm and subject were 170 cm and 65 kg, respectively. 65 kg, respectively.


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5.1. Step Length Estimation Experiment and Results In order to verify the reliability and accuracy of the proposed methods, the step estimation experiment was conducted by having the subjects walk in a straight line. The target subject was asked to walk 50 steps three different times, with different step lengths of 30.5, 61, and 91.5 cm each time. The ground truth of the traveled distance was measured via a laser range finder. The multi-sensor fusion and SLE algorithms were installed on the sensor module and ran in real time. The target subject walked three times for each different step length. Table 4 shows the results of the step length estimation for the target subject. The step counting results show that only two steps out of 450 were missed and the accuracy of the proposed step counting method is thus 99.5%. Regarding the step length estimation, the maximum mean error of the FL method compared with required step lengths is 1.73 cm, which occurred in Test 7. The standard deviation of the estimated step lengths is from 2.18 to 4.45 cm. The 4th-r denotes the step length estimation of the empirical equation proposed by Weinberg et al. The value of K is determined by training with different step lengths of 30, 60, and 90 cm. The maximum mean error of the empirical equation compared with the required step lengths is 3.87 cm, which occurred in Test 9. The estimated lengths of the empirical equation in Test 2 and 7 are better than the FL method, but the total distance errors of the FL method are less than 1.4% of total reference distance, which is better than the empirical equation. Table 4. The experiment results of the Step Length Estimation (SLE) for the target subject. Test 1. 2. 3. 4. 5. 6. 7. 8. 9.

Sub1-30 cm Sub1-30 cm Sub1-30 cm Sub1-60 cm Sub1-60 cm Sub1-60 cm Sub1-90 cm Sub1-90 cm Sub1-90 cm Total

Step Counting

Estimated Length (cm)

Ref.

FL Std.

4th-r Mean

4th-r Std.

Ref.

FL

4th-r

2.66 2.18 4.45 4.05 4.27 4.09 2.73 3.27 2.28

30.15 30.50 28.96 60.06 59.64 61.57 90.08 87.74 83.77

1.82 3.11 1.80 1.84 2.01 2.19 2.21 5.65 7.73

15.25 15.25 15.25 30.50 30.50 30.50 45.75 45.75 45.75 274.50

15.04 14.65 15.57 30.12 29.82 30.46 44.89 44.81 45.21 270.57

14.77 15.24 14.47 30.03 29.82 30.79 45.04 42.99 41.88 265.03

50 50 50 50 50 50 50 50 50 450

Estimated FL Mean 49 50 50 50 50 50 50 49 50 448

30.70 29.30 31.15 60.25 59.64 60.91 89.77 91.46 90.42

Distance (m)

Since the FL adopted in this study was customized for the target subject, nine other subjects were included to examine the usability of the FL with regard to non-target subjects. The first column of Table 5 denotes the subject number, height, and body mass of the subjects. The last four subjects, Subjects 7 to 10, are female. Table 5 shows the results of the step length estimation using the FL and empirical equation for all of the non-target subjects. The step counting results show that only one step out of 900 were missed, and the accuracy of the proposed step counting method is thus 99.89%. The results also reveal that the estimated step lengths of Subject 2 are close to those of the target subject and that both the height and body mass of the subjects have influences on the estimated step length based on the proposed method. The maximum estimated distance errors measured from the FL were about 0.6% to 12.3%, and the total estimated distance error was about 4.3%. The location errors of non-target subjects were from 0.27 to 2.75 m. These results reveal that the location errors were slightly larger than the accumulated walking distance errors in most tests after the heading errors were introduced. Moreover, the errors of the non-target subjects were larger than the error of the target subject since the FL was trained based on the data gathered from the target subject. Moreover, the estimated step lengths of the female and lighter subjects were larger than the others. Compared to the empirical equation, the FL also had a better performance for the non-target subjects, except for Test 13, 15, and 16.


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Table 5. The results of the step length estimation for non-target subjects. Step Counting

Test 1. Sub2/170/65 2. Sub2/170/65 3. Sub3/177/80 4. Sub3/177/80 5. Sub4/162/60 6. Sub4/162/60 7. Sub5/167/50 8. Sub5/167/50 9. Sub6/170/70 10. Sub6/170/70 11. Sub7/157/48 12. Sub7/157/48 13. Sub8/160/56 14. Sub8/160/56 15. Sub9/163/70 16. Sub9/163/70 17. Sub10/168/53 18. Sub10/168/53 Total


Distance (m)

Ref.

Est.

FL Mean

FL std.

4th-r Mean

4th-r Std.

Ref.

FL

Location Error

4th-r

50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 900

49 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 899

61.55 59.61 63.05 63.60 62.96 63.13 64.36 65.40 61.74 62.22 61.34 61.57 64.89 63.86 68.48 67.71 64.68 65.28

4.52 3.24 4.06 4.02 5.24 5.75 3.81 4.60 6.88 6.57 5.08 2.25 5.38 4.71 4.60 4.88 4.83 5.27

56.77 54.18 55.99 55.00 52.62 50.92 50.23 54.36 51.48 51.77 52.27 56.42 58.83 56.16 65.76 66.29 55.03 54.94

4.72 4.34 5.13 4.35 5.05 5.88 6.16 4.28 4.73 5.09 6.64 4.36 5.10 5.15 1.76 3.06 4.78 5.91

30.50 30.50 30.50 30.50 30.50 30.50 30.50 30.50 30.50 30.50 30.50 30.50 30.50 30.50 30.50 30.50 30.50 30.50 549.00

30.78 29.80 31.53 31.80 31.45 31.57 32.18 32.70 30.87 31.11 30.67 30.78 32.45 31.93 34.24 33.85 32.34 32.64 572.69

0.39 0.81 0.88 1.87 1.49 1.84 1.08 0.90 0.27 0.51 0.56 0.55 1.94 1.85 2.37 2.75 1.42 0.61

28.38 27.09 27.99 27.50 26.31 25.46 25.12 27.18 25.74 25.88 26.14 28.21 29.42 28.08 32.88 33.15 27.51 27.47 499.51

5.2. Pedestrian Navigation Experiment and Results The objective of this experiment was to examine the long-term performance of the proposed PDR system applied to the target subject. Two courses were selected to demonstrate the accuracy and reliability of the proposed system. One was in an indoor environment and the other was in an outdoor environment. In an indoor environment, the subjects walked twice around a selected course, with a total distance of around 116.51 m, which was measured via a laser range finder. Table 6 presents the results of the subjects walking on this course. The first two tests are the results when Subject 2 was asked to walk at a constant step length of approximately 60 cm, and the other two are the results when Subject 1 walked at self-selected step lengths and speeds. These results show that only two steps out of 731 were missed, and the accuracy of the proposed step counting method is thus 99.7%. The maximum distance error of the estimated distance was 1.39 m, which is less than 1.2% of the reference distance, despite the subjects walking at different step lengths and speeds. The total estimated distance error was about 0.17%. The S-E term denotes the distance error between the start and end points of the course, called the loop closure error. Figure 14 presents the test results. The subjects walked around the course twice from the start to end points. The distance errors of the start and end points were less 16 of 21 thanISPRS 2.22Int. m.J. Geo-Inf. 2016, 5, 70

Figure14. 14. The The PDR experiment Figure experimentresults. results. Table 7. The results of the target subject walking on brick pavement. Test 1. Sub1-free 2. Sub1-free

Step Counting Ref. Est. 556 556 542 541

Estimated Length (cm) FL Mean FL SD 69.59 1.80 71.17 2.28

Ref. 385.2 385.2

Distance (m) FL Error (%) 386.93 0.45 385.01 0.05

S-E 5.80 1.49

Heading Error (deg) 0.90 3.60


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Table 6. The results of the subjects walking around selected course. Test 1. Sub2-60 cm 2. Sub2-60 cm 3. Sub1-free 4. Sub1-free Total

Step Counting


Distance (m)

Ref.

Est.

FL Mean

FL SD

Ref.

FL

Error (%)

S-E

192 192 179 168 731

192 191 179 169 731

60.53 60.27 65.16 69.39

2.20 2.30 2.42 3.16

116.51 116.51 116.51 116.51 466.04

116.22 115.12 116.64 117.27 465.25

0.24 1.19 0.11 0.65

0.72 0.73 1.27 2.22 4.94

In the outdoor environment, the target subject walked on a path in a university campus covered with brick pavement for six rounds, with the total distance of each round being around 385.2 m, which was measured using Google Maps, as shown in Figure 15. The biases of the gyroscope were initialized Figure 14. The PDR experiment results. by collecting the values when the sensor module was static prior to every test. The subject took about 5 min to complete each round. thetarget designed subject decided the step lengths Table 7. TheExpect results for of the subjecttrajectory, walking onthe brick pavement. and speed naturally. The results show that the estimated distance errors were from 0.19 to 6.85 m, and Step Counting Estimated Length (cm) Distance (m) Heading the loop Test closure errors were fromFL1.49 to 10.15 m, as shown in Table 7.Error The(%) maximum heading error Error (deg) Ref. Est. Mean FL SD Ref. FL S-E occurred in Test 4 was 4.27 deg. Moreover, the step counting results show that only two steps out 1. Sub1-free 556 556 69.59 1.80 385.2 386.93 0.45 5.80 0.90 2. Sub1-free 542 541 71.17 2.28 385.2 385.01 0.05 1.49 3.60 of 3289 steps was missed, and the accuracy of the proposed step counting method was 99.9%. The 3. Sub1-free 541 70.59 2.17 385.2 378.35 1.78 5.03 maximum distance error of541 the estimated distance was 6.85 m, which is less than 1.78% of the1.95 reference 4. Sub1-free 542 541 70.91 1.92 385.2 383.60 0.41 4.76 4.27 distance, despite the subject walking at different step lengths and speeds on brick pavement. 5. Sub1-free 553 553 70.70 2.33 385.2 390.96 1.50 10.15 4.07 These Sub1-free 557 557 70.34 1.98 385.2 391.82and the 1.72dead reckoning 5.71 1.46 results6. verify the accuracy and reliability of the proposed methods algorithm Total 3291 3289 2311.2 2316.7 31.75 applied to the target subject.

Figure walkingon onbrick brickpavement. pavement. Figure15. 15.The Thetrajectories trajectories of of the the subject subject walking

In the outdoor environment, the target subject walked on a path in a university campus covered with brick pavement for six rounds, with the total distance of each round being around 385.2 m,


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Table 7. The results of the target subject walking on brick pavement. Test 1. 2. 3. 4. 5. 6.

Sub1-free Sub1-free Sub1-free Sub1-free Sub1-free Sub1-free Total

Step Counting


Distance (m)

Ref.

Est.

FL Mean

FL SD

Ref.

FL

Error (%)

S-E

556 542 541 542 553 557 3291

556 541 541 541 553 557 3289

69.59 71.17 70.59 70.91 70.70 70.34

1.80 2.28 2.17 1.92 2.33 1.98

385.2 385.2 385.2 385.2 385.2 385.2 2311.2

386.93 385.01 378.35 383.60 390.96 391.82 2316.7

0.45 0.05 1.78 0.41 1.50 1.72

5.80 1.49 5.03 4.76 10.15 5.71 31.75

Heading Error (deg) 0.90 3.60 1.95 4.27 4.07 1.46

5.3. Results and Discussion The results of the experiments using the proposed multi-sensor and FL step length estimation algorithms demonstrate the high accuracy and reliability of the SLE method for the PDR system developed in this study. The proposed SLE based on the FL has been shown to have the capability of estimating a wide range of step lengths for a target subject. The results show that the proposed SLE method has a better performance than the empirical equation proposed by Weinberg et al. [26] with the varying constant value K training with three different step lengths, 30, 60, and 90 cm. Moreover, for the non-target subjects, the estimation accuracy of the FL method was better than the empirical equation. In particular, it has been observed that, when the height and body mass of a non-target subject is the same as the target subject, the accuracy of the FL method for those two individuals are similar. The results show that the height and body mass of the subjects both had an influence on the estimated step length based on the FL. The maximum estimated distance errors measured from the FL were about 0.6% to 12.3%, and the total estimated distance error was about 4.3%. The maximum estimated error in this study is thus better than that reported in the study in [16]. From the experiment results of this study, it is revealed that the errors of the non-target subjects were larger than the error of the target subject since the FL was trained based on the data measured from the target subject. This shows the disadvantage of the proposed SLE method, which has a higher accuracy only for the target subject or subjects with similar height and body mass to the target subject. The results of the pedestrian navigation experiment show that the proposed method had the performance with acceptable accuracy. In the indoor environment, the maximum distance error of the walking distance was 1.2% of 116.51 m, and the errors of the loop closure were less than 2.2 m. However, with regard to the drifting problem of the gyroscope, the results of the first course show that the errors of the distance between the start and end points became larger from Test 1 to 4, as seen in Table 6. In the outdoor environment, the test duration of every round was about 5 min. The maximum distance error of the walking distance was 1.78% out of 385.2 m, and the errors of the loop closure were less than 5.8 m. Due to the drifting problem of the gyroscope triad, which has significant influence on the heading estimation, a rigorous process was conducted to determine the biases of the gyroscope triad. The design of this process was based on the experimental results as shown in Figure 16. In this test, the gyroscope triad was kept static for 3 h. After 25 min, the outputs became steady, especially for z axis. Therefore, the tests in Figure 15 were conducted after the gyroscope outputs became steady. Then, the biases of the gyroscope triad were carefully acquired at the beginning of every test when the sensor module was static. With this process, the maximum heading error occurred in Test 4 of the second course and was 4.27 deg. The calibrating procedure adopted in this study was easily able to compensate for the random constant errors, but the time-correlated random process errors, such as the stochastic error and temperature effects [20,39], were not solved. There are many possible ways to solve the drifting problem of the gyroscope, such as using complex compensation-control methods to compensate for the errors of the sensor for one [40], or adopting the map-matching algorithm to the pedestrian navigation systems for another [9,10]. For indoor environments, the radio-frequency beacon-based positioning, such as Wi-Fi or Bluetooth, is a good solution to overcome the drifting problem when the user travels a

the varying constant value K training with three different step lengths, 30, 60, and 90 cm. Moreover, for the non-target subjects, the estimation accuracy of the FL method was better than the empirical equation. In particular, it has been observed that, when the height and body mass of a non-target subject is the same as the target subject, the accuracy of the FL method for those two individuals are similar. The results show that the height and body mass of the subjects both had an influence on the ISPRS Int. J. Geo-Inf. 2016, 5, 70 18 of 21 estimated step length based on the FL. The maximum estimated distance errors measured from the FL were about 0.6% to 12.3%, and the total estimated distance error was about 4.3%. The maximum estimated error this study is thus better than that which reported in the study in [16]. From the experiment long distance. Ain motion-assisted Wi-Fi localization, fused Wi-Fi fingerprint and inertial sensors, results ofstudied this study, is revealedinthat theInerrors non-target subjects were largerand thanreliability, the error has been anditdiscussed [41]. orderoftothe enhance the long-term accuracy of the target subjectare since the FL for wasatrained based on the data measured the of target subject. This the infrastructures required PDR system. Moreover, due to thefrom growth dead reckoning showsdifferent the disadvantage of the proposed SLE and method, whichassessment has a higher accuracy only for the target error, levels of integrity monitoring reliability are required to constrain the subject or subjects similar height and body to the target subject. accumulating errorwith for long-term applications or mass complex environments [42].

Figure 16. 16. Static test test of of the the adopted adopted gyroscope gyroscope triad. triad. Figure

The results of the pedestrian navigation experiment show that the proposed method had the 6. Conclusions performance with acceptable accuracy. In the indoor environment, the maximum distance error of An accurate and usable SLE method for the PDR system with the features of a wide range of step the walking distance was 1.2% of 116.51 m, and the errors of the loop closure were less than 2.2 m. lengths, a self-contained system, and real-time computing, based on the multi-sensor fusion and FL However, with regard to the drifting problem of the gyroscope, the results of the first course show algorithms, has been proposed in this study. In order to achieve a self-contained capability, a portable and wearable inertial sensor module was developed using low-cost inertial sensors, a gyroscope, and an accelerometer, and it was based on the MEMS. Since the low-cost MEMS sensors suffer from various errors, the sensor errors of this module were calibrated with a sensor calibration procedure to improve the accuracy of the inertial sensors. To enhance the reliability and stability of the PDR system, the adopted sensor module selected in this study was waist-mounted. In order to extract more information about pedestrian activities, a multi-sensor fusion algorithm was applied using a second-order complementary filter to derive the reliable orientation of the sensor module. To achieve accurate step counting and step time calculation, a step detection method was adopted that utilized velocity in the x-axis that was derived from acceleration along the x-axis. These results show the accuracy of the step counting method to be 99.5% for all tests. The wide-range SLE method for the PDR system was accomplished by using the FL method. The input variables of the adopted FL were step strength and frequency, and the output value was estimated step length. The FL design was based on the data acquired from the walking experiments of the target subject. The results of the proposed SLE for the target subject, who walked at different step lengths, showed distance errors that were within 1.2% of 116.51 m in the indoor environment, even for the non-target subject with the same height and body mass, and were within 1.78% of 385.2 m in the outdoor environment. The results of the experiment demonstrate that the proposed SLE had good navigation performance when the user was walking in an indoor environment. The SLE method and sensor calibration procedure could be applied to waist-mounted wearable devices with low-cost sensors to enhance the PDR and attitude estimation solutions. From the experiment’s results, the proposed SLE method and the PDR scheme demonstrate the ability to be implemented on waist-mounted wearable devices in real time and are suitable for the indoor and outdoor environments considered in this study without the help of map information or a pre-installed infrastructure.


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Acknowledgments: This study was supported in part by the Ministry of Science and Technology of Taiwan under grant number MOST 103-2221-E-035-067 and MOST 103-2632-E-035-001-MY3. Author Contributions: Ying-Chih Lai developed the calibration procedure, multi-sensor fusion, and fuzzy logic methods for the proposed PDR system. Chin-Chia Chang and Chia-Ming Tsai designed and developed the sensor module and Android app for the experiments. All authors conducted the experiments and participated in discussions and data analyses. Kai-Wei Chiang and Shih-Ching Huang supervised the work and revised the paper. Conflicts of Interest: The authors declare no conflict of interest.

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