Adaptative pedestrian displacement estimation with a smartphone

2013 International Conference on Indoor Positioning and Indoor Navigation, 28-31th October 2013

Adaptative pedestrian displacement estimation with a smartphone Valerie Renaudin, Vincent Demeule, Miguel Ortiz GEOLOC Laboratory IFSTTAR Bouguenais 44344, FRANCE [email protected]

Abstract— Pedestrian dead reckoning is one of the most promising processing strategies of inertial signals collected with a smartphone for autonomous indoor personal navigation. When the sensors are held in hand, step length models are usually used to estimate the walking distance. They combine stride frequency with a finite number of physiological and descriptive parameters that are calibrated with training data for each person. But even under steady conditions, several physiological conditions are impacting the walking gait and consequently these parameters. Frequent calibration is needed to tune these models prior to relying on free inertial navigation solutions in indoor locations. Two hybridization filters are proposed for calibrating the step length model and estimating the navigation solution. They integrate either GNSS standalone positions or GNSS Doppler depending on the coupling level. A data collection performed with four test subjects show the variations of these parameters for the same person during his journey and effectiveness of the calibration for improving the estimation of walking distances. Thanks to the new filters, the error on the travelled distance gets reduced to 7% with the loosely coupled filter and 2% with the tightly coupled filter. Keywords-component; Pedestrian navigation, dead reckoning, step length model, MEMS

I.

INTRODUCTION

Observing and analysing the displacements of persons and crowds is of prime importance for the development of future transport solutions targeting the soft modes of personal mobility. Walking and biking belong to the category of the soft modes of transport. Facing the ageing phenomenon, understanding and encouraging the walk might reduce the health costs but it will also support the goals of reducing the transport energy costs and improve the transport safety and comfort. Autonomous (i.e. independent from terrestrial infrastructure) pedestrian geolocalisation systems and methods are needed to conduct this task. Existing solutions principally rely on WiFi signals that are processed with fingerprinting algorithms and coupled with data emitted by GNSS (Global Navigation Satellites Systems) for geolocating people [1, 2]. They rely on terrestrial infrastructure network broadcasting WiFi, 3G, LTE or other electromagnetic signals. The drawback of these technologies is that their

performance levels depend on the availability and density of local infrastructures. Consequently a person walking in an environment without these signals or leaving a covered zone will face an accuracy loss in its position solution, which may be very large up to several tens of metres, or even solution loss. In light of these limitations, research on using inertial sensors for assisting personal mobility is booming. Not only does it discard the use of additional terrestrial infrastructure but its implementation gets facilitated by the fact that low cost inertial sensors are now largely embedded in daily life equipment. Processing the signals collected with inertial sensors, magnetometers and barometers embedded in smartphones offers an alternative since these measurements don’t rely on opportune telecommunication signals for computing the footpaths of pedestrian. This approach is a very attractive but also very challenging leading to numerous innovations for computing the tracks travelled by pedestrians. Pedestrian Dead Reckoning (PDR) is one of the most promising processing strategies for addressing the quest of personal navigation systems based on signals collected with smartphones. By definition, a PDR process combines a measurement of distance and direction for determining a change in position relative to a known starting location. This technique is attractive since it offers an autonomous and seamless outdoor/indoor navigation solution, which doesn’t depend on the existence of a dedicated and expensive infrastructure. Nevertheless this attractive solution raises many scientific challenges due to the low quality of the sensors embedded in smartphones and the complex nature of hand motions performed by mobile phone users during their journey. These two elements are complicating the estimation of walking directions and distances that are necessary to propagate the pedestrian’s position in a PDR processing scheme. Contrary to using units rigidly attached to the body (foot or waist), the difficulty of inferring step lengths with handheld sensors is increased because the walking pattern (Fig. 1) is not directly sensed. To cope with this issue, novel parametric models have recently been developed. They combine stride frequency with a finite number of physiological and descriptive parameters that are calibrated with training data for each person. It has been observed that human walking gait presents

2013 International Conference on Indoor Positioning and Indoor Navigation, 28-31th October 2013 fluctuations even under apparently steady conditions. Fatigues, weight of a carried bag or small injuries are changing conditions that affect the walking gait. Under these circumstances, the hypothesis of repetitive patterns only holds for relatively short periods of time (several hours). This observation underlines the importance of performing frequent parameters calibration for improving the performance of free inertial PDR in indoor space. Free inertial PDR means a navigation process that does not rely on available opportune radio signals.

Figure 1. Gait cycle

The investigation of the estimation of pedestrian step length using a parametric model, which is based on walking gait analysis, and on-the-fly calibration of this model with GNSS measurement prior to penetrating indoor are proposed in this paper. Novel algorithms are enabling the coupling of GNSS signals and walking gait features for performing opportune calibration prior to penetrating indoors. After a state of the art on existing pedestrian dead reckoning strategies, the design of two hybridization filters is presented in section III. They perform an adaptive estimation of pedestrian displacement thanks to a loosely coupling with GNSS positions and a tightly coupling with Doppler measurements. Section IV presents the experimental assessment performed with several test subjects walking with different carrying modes of the mobile unit. Finally section V draws the conclusion. II.

pedestrian dead reckoning exploiting the kinematics of human gait, is preferred. The acceleration data is no longer integrated for inferring the velocity but the user’s position is propagated based on both the outcomes of gait analysis and the estimated walking distances and directions. A. Gait analysis In the context of pedestrian navigation, the gait analysis consists in a pre-processing phase for principally identifying the user’s motion state and step event/frequency. Many different algorithms have been developed for characterizing the motion that a pedestrian is undergoing while waking or running. Originally developed in the medical context, gait signal processing and analysis has been extended to security and navigation applications. Globally, motion recognition techniques are applied to inertial signals recorded with body fixed sensors for inferring the repetitive gait patterns [7, 8]. In the case of handheld device, the analysis must compensate for the different positions and orientations that the mobile unit experiences. Therefore the list of recognized motion states is completed with mobile unit carrying modes. They are the texting, swinging, phoning and irregular carrying modes [9, 10]. Step events are finally detected knowing the motion/carrying state. Fig. 2 shows the main features of a gait analysis for pedestrian navigation applications [11]. The robustness of these methods is however often affected by the rapid hand variations and the variety of user’s gait. A frequency analysis can be combined with a time domain analysis for improving the robustness of the analysis and extracting step frequency independently from step events.

EXISTING PEDESTRIAN DEAD RECKONING METHODS AND SYSTEMS

Two main processing strategies may be chosen for estimating pedestrian navigation solutions with inertial sensors. The first one follows classical Inertial Navigation System mechanization where the measurements are integrated over time to produce the attitude angles of the mobile unit and its successive changes in positions [3, 4]. Largely affected by the errors inherent to the low cost nature of the sensors, this strategy requires frequent sensor calibrations, which are possible thanks to external measurement sources (WiFi, UWB, RFID, etc.) or during particular phases of the human gait. In the context of free inertial pedestrian navigation (i.e. solely based on inertial sensors), these calibrations are mainly possible during the stance phase of the gait cycle during which the foot is flat on the ground. Thanks to units rigidly attached to the foot, it is possible to sense these static phases and mitigate the sensors errors assuming zero velocity and/or zero angular rate states [5, 6]. When the unit is held in hand, the problem becomes more complex since zero motion states can hardly be observed. Consequently another processing strategy,

Figure 2. Gait analysis for pedestrian navigation appications with handheld device [11]

B. Step length estimation Two categories of step length estimation processes have been proposed. Classical INS mechanization can be applied for directly estimating the foot to foot step length. As detailed earlier, this method is not effective for handheld device since the PDR errors can hardly be bounded in hand. The second

2013 International Conference on Indoor Positioning and Indoor Navigation, 28-31th October 2013 category relates sensors’ measurements to the step length through a model. Many models have been proposed for body fixed sensors. In [12], an assessment of four acceleration based step length estimators with a device located in the trouser pocket is proposed. These models no longer hold for handheld units since the hand motion may not reflect the global displacement of the user and more robust modelling is required. Biomechanical research has shown that step length is related to the walking speed and therefore step frequency. First frequency based model have been adopted for navigating with mobile computing device. [13] propose a linear relationship with the step frequency that needs to be tuned for each individual in order to estimate step length. A more complete model base on step frequency and the user height has recently been proposed [14] and showed a 5.7% error over the travelled distance for 10 test subjects:

s  h   af  b   c 





where s is the estimated step length, h is the user height, f is the step frequency and K={a,b,c} is a set of individual parameters. This model, which is adopted for the rest of the paper, is less perturbed by instantaneous hand motions since it depends only on global user locomotion parameters including the user’s height. The set of three parameters K is generally tuned for each individual during specific training phases. Let us note that (1) has been developed for the context of general public applications where a limited use of personal data such as height, gender, weight or clothes, is targeted for ethical reasons. This prohibits the use of a more complex modelling. Depending on the physical profiles, the type of shoes, the health status and the motion mode, these parameters will change. Therefore once calibrated, the set of parameters has to be updated frequently enough to take into account factors like tiredness, injuries, etc. Novel calibration is proposed using GNSS observations tracked by the handheld receiver before entering the building. Optimum calibration of the step length model is sought before entering the building and relying on a free inertial PDR navigation process. III.

PEDESTRIAN NAVIGATION FILTER

Two filters are proposed for calibrating the step length model and computing the walking path. They use GNSS measurements following two strategies: a loosely and tightly hybridization schemes. This section first describes the loosely coupled filter integrating GNSS positions and whose number of state parameters has been minimized for coping with observability issues. The tightly coupled filter is then presented. It uses GNSS Doppler measurements instead of GNSS positions.

A. Pedestrian dead reckoning/GNSS positions filter The first calibration algorithm of the step length model (1) is a loosely coupled Kalman filter where the observations are the GNSS positions collected with the handheld device. 1) System model: Even if the determination of the attitude angles of an handheld unit has recently been improved, especially using magnetometers data [15], it remains an issue for PDR navigation especially since the unit may not be aligned with the walking direction. Consequently, it has been chosen not to integrate heading data in the state vector. Only GNSS coordinates in the local level frame are considered in the loosely coupled PDR/GNSS system model. The state vector comprises four elements that are: 

x  f

a b c 



f is the pedestrian step frequency. The dynamic model of the step length is given by (1) and the three parameters (a,b,c) are modelled as constant random variables. 2) Measurement model: The observations considered in the loosely coupling scheme are standalone positions (PGNSS) computed by the handheld GNSS receiver and the step frequency estimated by the gait analysis phase. Step frequency and step instants, calculated in the gait analysis (section II.A), are fused with these geographical coordinates for extracting GNSS step lengths (sGNSS). Because in a real time processing strategy, when a step occurs at time t, only previous GNSS positions (PGNSSt-i with i  1, , i  1 ) are available, an extrapolation is applied for predicting GNSS step length at the filter epoch t. 

sGNSS  PGNSS,t - PGNSS,t-1 



The step frequency estimated by the gait analysis, following the method described in [11], is directly related to the first element of the state vector. The relationship between the GNSS step length and the state vector being nonlinear, an Extended Kalman Filter (EKF) is adopted.

δz = Hδx + w 

 1  h  f

0 0 0  δx + w h  b h 1 



where the process noise w is assumed to be white. The later can be estimated from a residuals analysis of a least squares adjustment conducted over a straight line whose length is known. 3) Trajectory estimation The loosely coupled EKF does not provide directly the positioning solution. Instead it is derived from the step lengths estimated with the calibrated model (1) and walking directions derived from the series of GNSS positions. In the experimental assessment (section IV), the walking directions (θ) are derived from the post-processed phase differential GNSS solution. Finally, a standard PDR mechanization is applied for determining the pedestrian trajectory in the horizontal plane.

2013 International Conference on Indoor Positioning and Indoor Navigation, 28-31th October 2013 

E t 1  E t  ssin  N t 1  N t  s cos 





E and N are the pedestrian’s East and North coordinates expressed in the local level frame. B. Pedestrian dead-reckoning/Doppler filter The second approach consists in tightly coupling GNSS Doppler measurements with the gait analysis output in an Extended Kalman Filter (EKF). With the advance in high sensitivity receivers (HSGNSS), it is now possible to track GNSS observations in obstructed environments, which are strongly perturbed with a low signal to noise ratio. Even if GNSS signals are affected by attenuation, fading and multipath in these challenging spaces, they remain good candidates for providing additional measurements and bound PDR errors. Contrary to pseudoranges, Doppler measurements are less perturbed by the multipath components since they are a function of the receiver’s velocity, which is rather slow for pedestrian navigation applications. Not only can signals with low Career to Noise Ratio (C/N0) be tracked in urban canyon or even indoors but the extracted Doppler, even biased, are useful for bounding the error growth of PDR solutions. [16] and [17] have quantified the positioning gain achieved with indoor GNSS Doppler using a conventional block processing method and an improved direct vector method respectively. Consequently, this paper proposes to investigate the integration of Doppler data only for calibrating the step length model used in the PDR navigation solution (1). 1) System model: Doppler measurement is a function of the receiver’s and satellite’s velocity vectors involving their positions in a Cartesian frame and the heading angle of the mobile receiver. As a consequence, the state of the tightly coupled filter is enhanced with the pedestrian’s walking direction and position for relating the later with Doppler observations. The state vector of the tightly coupled GNSS/PDR filter is therefore: 

x   E N U a b c v u

 ct  



where E, N, U are the coordinates, vu is the vertical velocity and c t is the GNSS receiver clock drift multiplied by the speed of light. In the tightly coupled strategy, the filter calibrates the step length model (K), but it also provides a full estimation of the navigation solution. Following equations give the dynamic of the state vector over one step whose duration is t step :

E   h(af  b)  c  

sin t step

cos  N   h(af  b)  c   t step U  vu

a, b,c, v u ,  and t are modeled with random walk processes. The initial conditions for K are extracted from a universal set of parameters that was trained with 12 different subjects (six men and six women) with an mean error of 5.7% on the distance travelled over the 600 m trajectory [14]. The first walking direction is initialized with past GNSS positions. The vertical velocity is considered as null. The receiver’s clock drift was approximated for the high sensitivity receiver used in the experiment. It was approximated by the asymptote value of ct once the convergence of the proposed filter was achieved and on several datasets. 2) Measurement model. The observations consist in GNSS Doppler collected with a handheld HSGNSS receiver and walking directions that are estimated in a separated attitude filter. a) Doppler Measurements The equation relating Doppler measurements to the receiver velocity is given by

f





where

 L1 is GPS L1 wavelength,

e k is the unit vector along the line of sight between the kth satellite and the GPS receiver, vSV and v r are the satellite’s velocity and pedestrian receiver’s velocity expressed in the ECEF frame respectively and

f is mainly a thermal noise due to the code and carrier loops. The mechanization in (7) is expressed in the navigation frame for facilitating the physical interpretation of the PDR strategy. GNSS observations are expressed in the ECEF frame (Earth-Centered, Earth-Fixed). The observations are related to the state vector thanks the rotation matrix R en , which enables changing between the navigation and the ECEF frames as follows:

 v h sin   vX   v   R e  v cos  n  h   Y  v Z   v U 



  sin    0    e  h(af  b)  c   Rn  cos    0        step   0   v U   

with



1 T 1 e k  v r  vSV   ct  f   L1  L1



  sin  0 R   cos  0   0 e n

 sin 0 cos  0  sin 0 sin  0 cos 0





cos 0 cos  0  cos 0 sin  0     sin 0 

2013 International Conference on Indoor Positioning and Indoor Navigation, 28-31th October 2013 where 0 et  0 are the initial geographical coordinates. Because equation (8) is non-linear with respect to the state vector, it must be linearized. 

δf = Hδx + n 



where n is the noise of the GNSS receiver. The linearization of (9) yields:



   v h sin     v X   v   R e   v cos    n   h  Y  v U   v Z 

IV. 

 R en M 3*5 a b c v u





T

with



M 3x5

 hf sin   t step   hf cos    t step  0  

will not be reflected by the heading change sensed by the handheld GNSS receiver but will impact the PDR implementation. To cope with the imperfection in sensing the misalignment between the hand’s and pedestrian’s headings, white process noise is added to the system (7). The fact that the heading sensed by Doppler data through the receiver velocity vector, is also affected by this discrepancy further justifies the additional process noise contributions.

h sin  t step

sin  t step

h cos  t step

cos  t step

0

0

 v h cos     0  v h sin     1 0   0



Substituting (12) into the linearized form of (8) gives:  e1,x e1,y e1,z   v x   f ,1   t  1  c       f    v y          L1  L1 e m,x e m,y e m,z   v z   f ,m   t    mx1 mx1 1 T    E mx3 R en M 3x5 a b c v u    L1 1 cδt mx1  ηf  L1

EXPERIMENTAL ASSESSMENT

A. Data collection During the experiment, four test subjects: one woman and three men, whose heights vary between 1.62 and 1.93 m and ages between 20 and 40, were holding an ADIS 16362 IMU from Analog Device and ublox 6T HSGNSS receiver in hand. The test setup is shown in Fig. 3. A DL-V3 dual frequency GNSS receiver from NovAtel was carried in a backpack and connected to an AntCom G5 GNSS antenna located on the pedestrian’s cap. Another DL-V3 receiver was recording GNSS dual frequency signals on a ground point with known coordinates. The reference trajectories of all test subjects were post-processed in a phase GNSS differential mode based on the two datasets collected with the backpack and base station receivers using GrafNav software from NovAtel. The mean horizontal positioning error is 1.5 cm and the mean height error is 2.5 cm. The pedestrians walked several times along a 350 m test track carrying the mobile unit in a “texting” mode and in a swinging “mode”. These states describe the motion that the hand holding the device is experiencing. Both motions are recognized by the gait analysis, which was introduced in section II.A, and illustrated in Fig. 4.

b) Walking directions The estimation of walking directions and distances in a PDR scheme is often performed in separated filters. Two strategies can be followed for estimating the heading. Either the heading is directly measured by an absolute positioning/navigation system such as GNSS or compass, or the relative heading change between two epochs is sensed by embedded sensors such as gyroscopes and magnetometers [15, 18]. The first strategy is followed in this paper and the heading update is made using GNSS heading (θGNSS) derived from the phase differential GNSS positions as follows: 

 E t  E tstep 1   GNSS  atan  step  N t  N t 1  step  step 

Figure 3. Test setup



The pedestrian’s walking direction in the state vector is directly updated using the GNSS heading estimated in (15). The later corresponds to the heading of the handheld receiver, whereas the heading in the state vector matches the walking direction of the pedestrian. Both parameters will differ due to possible hand motions during a step. Furthermore the torso oscillations occurring during normal walking gait [19]

(a)

(b)

Figure 4. Mobile phone carrying mode. Swinging hand in (a) and texting hand in (b)

2013 International Conference on Indoor Positioning and Indoor Navigation, 28-31th October 2013 The experiment was repeated one month later for analysing the changes of K  a, b,c for the same person but under different physiological conditions (time of the day, clothes, weather, etc.). B. Experimental results 1) Performance comparison of the two PDR/GNSS filters. The performance is evaluated in the positioning domain and by estimating the displacement error on the total travelled distance. The “true” walked distance is estimated using the outcome of the gait analysis (step events instants) that are combined with the post-processed GNSS reference trajectory for extracting step lengths and walking directions. The “true” distance that has been travelled by a pedestrian is the sum of all GNSS differential step lengths over the entire footpath. The PDR travelled distance is the sum of all step lengths that have been computed with the step length model in (1), which has been calibrated with the PDR/GNSS filter. a) Impact of the low HSGNSS positioning accuracy The technology of HSGNSS receiver extends the space where GNSS signals can be tracked; even to light indoor locations, but it is correlated with a positioning accuracy loss. The data have been collected in an open sky environment where only the handheld motions and torso were shadowing the signals propagation. This situation does not reflect the challenge of urban zones where the observed performances would be degraded. Nevertheless the filter was unable to provide reliable solutions for K using HSGNSS positions only. This is further explained with Table 1 and Fig. 5. Fig. 5 shows the different footpaths computed for the four test subjects using the loosely coupled filter and the standard PDR mechanization (5). The initial points, from which the inertial displacement is initiated from, are shown with red dots. The reference solution is shown with a dashed red line. The paths in blue and green correspond to the calibrated and universal parameters respectively. The label “M” corresponds to a man and the label “W” to a woman. HSGNSS standalone positions are depicted with black dots. Table 1 gives the percentage of error computed on the entire travelled path. Even if the step length estimation is improved using the calibrated parameters K instead of the universal ones, the trajectory is globally overestimated. Furthermore only a portion of the dataset could be used for calibrating the step length model. In average only 250 m of walk were used for each test subject over the entire 700 m long travelled distance. Indeed HSGNSS coordinates show large positioning errors that are jeopardizing the calibration of the step length model. For improving the signal processing, Fault Detection and Exclusion (FDE) technique could be applied to discard outliers from the measurements set at the risk of ending without sufficient observations. This approach was not adopted here because with HSGNSS receiver, effective weighting parameters are the C/N0 values and the later were extracted for this dataset. Exploring outliers’ removal strategies is a potential future development.

(M1)

(M2)

(M3)

(W1) Figure 5. The post-processed differential GNSS solutions is depicted in dashed red. The free inertial solution with universal parameters K={a,b,c} and calibrated parameters K using the loosely coupled filter are in green and blue respectively. The trajectory from the HSGNSS receiver (black dots) is made of standalone positions in (a) and post-processed differential position in (b).

2013 International Conference on Indoor Positioning and Indoor Navigation, 28-31th October 2013 Table 1 shows a mean error of 7.3 % over the travelled distance with the calibrated step length model. This value is rather large as compared to existing PDR navigation systems. Finally the universal parameters are showing a rather small error for the test subject W1 as compared to the other datasets. W1 belonged to the twelve test persons whose data were processed for calculating the universal parameters, which explains this observation. TABLE I.

TABLE II.

ERROR IN % ON THE TRAVELLED DISTANCE WITH THE TIGHTLY COUPLED FILTER Test subject

Nature of parameter

M1

M2

M3

W1

Mean

Universal

6.3 %

11.6 %

13.9 %

11.6 %

10.8 %

Calibrated

-0.8 %

-1.8 %

3.5 %

-2.0 %

2.0 %

ERROR IN % ON THE TRAVELLED DISTANCE WITH THE LOOSELY COUPLED FILTER

Test subject Nature of parameter

M1

M2

M3

W1

Mean

Universal

9.9 %

12.1 %

16.1 %

6.6 %

11.2 %

Calibrated

6.6 %

6.3 %

10.7 %

5.7 %

7.3 %

b) Performance assessment on walking distances estimation Table 2 gives the percentage of error computed on the entire travelled path using the tightly coupled filter for calibrating K. The mean error of 2 %, which is computed using the absolute individual percentages for each test person, outperforms 7.3 % of the loosely coupled approach. The percentages of errors calculated with the universal parameters slightly differ from the ones computed with the loosely coupled filter. The fact that more Doppler observations and globally a longer walking path (about 500 m) could be used for assessing the performances explains these small differences. Fig. 6 summarizes all percentages of error made on the total travelled distance estimated with the free inertial PDR navigation strategy (without GNSS) and the three different solutions for computing K. 

Ku equals the universal set of parameters that has been trained with 12 test subjects [14] from Table 2.



Kl is calibrated using the loosely coupled PDR/GNSS filter.



Kt is calibrated using the tightly coupled PDR/GNSS filter.

This figure confirms that Doppler data are providing sufficient information for calibrating the step length model for each individual. Globally the tightly coupled EKF is more promising for pedestrian navigation applications than the loosely one. In urban and obstructed environments, the number of tracked satellites might not be sufficient for computing GNSS positions, which will lead to the unavailability of observations for correcting the state parameters in a loosely coupling approach. In cities and indoor spaces, which are the most popular surroundings for pedestrian navigation, this problem will even be reinforced. Consequently the rest of the paper concentrates on a detailed analysis of its performances.

Figure 6. Percentage of error on the travelled distance estimated with the free inertial navigation and the step length model using either Ku (universal), Kl calibrated with the GNSS/PDR loosely coupled filter or Kt with the GNSS/PDR tightly coupled filter.

2) Details on the calibration of K The analysis of the variations of K, which is proposed in next section, is only conducted with the tightly coupling strategy. a) Comparison between universal and calibrated parameters Fig. 7 shows the trajectories computed following the free inertial PDR navigation strategy applied with both the universal and the calibrated parameters for the four test subjects. This scenario corresponds to the performance of an indoor scenario once the individual parameters set K of the step length model has been calibrated using GNSS Doppler prior to penetrating indoor. The starting position of the walking path is shown with a red dot. As stated in section III.A, three men and one woman participated to the tests. Again the post-processed phase differential GNSS reference footpath is shown in red whereas the free inertial trajectories computed with the calibrated and universal parameters are shown in blue and green respectively. The calibrated solution shows a lower positioning error than the universal one. For the test subject M1 a heading mismatch is observed due to an underestimation of the travelled distance and an anticipated turn as compared to the reference one. All plots are showing two runs corresponding to different carrying modes of the mobile device. The first run was performed with a “texting” state whereas the second was performed with a “swinging” hand. Several walking pace were intentionally performed by the pedestrian. This can be observed in Fig. 8 where the varying step frequency is observed in green. The red dots corresponds to the identified step events plotted on the normalized acceleration norm (blue)

2013 International Conference on Indoor Positioning and Indoor Navigation, 28-31th October 2013

(M1)

Figure 8. Gait analysis output with texting carrying mode. The normalized norm of the acceleration is in blue. The step events are identified with red dots and the step frequency is shown in green.

(M2)

(M3) Figure 9. Convergence of the parameters set K in the tightly coupled PDR/GNSS filter

(W1) Figure 7. Comparison of the free inertial PDR performances in the positioning domain using the universal and the calibrated parameters, shown in blue and green respectively. The reference trajectory is plotted in red.

It can be observed that no degradation of the positioning accuracy is experienced during the second run as compared to the first one. Even if this result is expected as the model is independent from the carrying state, it is a very interesting results since it shows that the performance of the free inertial navigation solution is not affected by a carrying mode change during the pedestrian displacements.

b) Convergence of K The EKF convergence for estimating a, b and c is shown for one dataset in Fig. 9 along with the associated standard deviations (red). It is observed that the filter convergence is quickly achieved. Already after 10 seconds of walk, the asymptote is reached. Globally less than 100 m of walk were sufficient for estimating the parameters set K. This observation highlights the possibility of launching the calibration just before entering in GNSS denied environments in order to get the best possible model before relying only on inertial signals and magnetic field. c) Variations of K for the same person Last assessment aims at understanding how the parameters (K) may change for the same person in time and depending on the physical fitness. Test subjects M1, W1 and M2 participated to a second experiment following the same test procedure but at one month interval. The parameters K have been calculated for all 6 datasets. For all collected data, the errors on the total travelled distance have been computed using the set of

2013 International Conference on Indoor Positioning and Indoor Navigation, 28-31th October 2013 parameters (K) estimated with the appropriate dataset and the set of parameters estimated with the other set of experimental data. All percentages are shown in Fig. 10. Except for one dataset, i.e M2, the use of a step length model that was previously calibrated and fixed for new data collection shows worse performances. Although assessed on a limited number of test persons, this observation support the motivation of the proposed research and filters in performing opportune calibration of step length model for improving pedestrian navigation solution in obstructed environments.

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[8] Figure 10. Convergence of the parameters set K in the tightly coupled PDR/GNSS filter [9]

V.

CONCLUSION

Pedestrian dead reckoning solution in GNSS denied environments rely on the accuracy of estimated distances and walking directions. Since numerous factors (fatigue, hardware type, carrying bag, etc.) may influence the walking gait of pedestrians, two filters have been proposed for tuning the individual parameters of a step length model, which is used to propagate the user’s position following a free inertial navigation process, i.e. without relying on opportune RF signals. Depending on the coupling level, the filters are either using standalone positions of a HSGNSS receiver held in hand or tracked HSGNSS Doppler. It is shown that the quality of the HSGNSS standalone positions is often too low for providing reliable observations to the calibration filter. On the contrary, Doppler data are found to be sufficient for calibrating the parameters needed by the step length model. In average, the tightly coupling of Doppler data and the outcomes of a gait analysis (step instants and frequency) enable to reduce the error on the estimated travelled distance by a factor of 5 as compared with the use of a set of predetermined parameters, called “universal”. The latter are used to set the initial values of the filter and were calibrated in previous work based on numerous data collected with 12 test persons. The experiment conducted with six persons shows also that the convergence of the filter can be achieved in a rather short period of time (about 10 seconds). This validates the strategy of performing opportune calibrations prior to penetrating indoor. Finally the experimental results show that these parameters are effectively varying for the same person

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