pedestrian dead reckoning— a solution to navigation in ... - CiteSeerX

G

E

O

M

A

T

I

C

A

PEDESTRIAN DEAD RECKONING— A SOLUTION TO NAVIGATION IN GPS SIGNAL DEGRADED AREAS? Oleg Mezentsev and Gérard Lachapelle Department of Geomatics Engineering, University of Calgary, Calgary, Alberta Jussi Collin, Institute of Digital and Computer Systems Tampere University of Technology, Tampere, Finland

This paper presents an analysis of the performance of medium-accuracy Pedestrian Dead Reckoning (PDR) systems. Such PDR systems, based on self-contained sensors, are well suited for indoor use and in urban canyons where GPS signals are degraded or not available with an adequate geometry. An analysis of major error contributors to the PDR system position errors, namely the step length error and the heading error, is performed. The importance of accurate PDR initialization is also discussed. A new method to estimate the 2-D position accuracy of stand-alone PDR navigation is proposed. Several stochastic models to represent the major PDR error source for a medium-grade PDR system namely, the step length estimation error, are presented and analyzed. A quantitative analysis of the upper-bound horizontal position error for a given quality PDR system is performed for the case of a straight walk, which represents the worst case of PDR horizontal error propagation. Using this analysis, the requirements for a PDR system and the initialization accuracy can be estimated for a desired accuracy of navigation as a function of time. The feasibility analysis is tested with a field experiment. Cet article présente une analyse du rendement des systèmes de navigation piétonnière à l’estime (NPE) à exactitude moyenne. De tels systèmes de NPE, basés sur des détecteurs autonomes conviennent bien pour une utilisation à l’intérieur et dans les canyons urbains où les signaux GPS sont dégradés ou ne peuvent fournir une géométrie adéquate. Une analyse des principaux facteurs ayant un apport dans les erreurs de position du système de NPE, notamment l’erreur de la longueur du pas et l’erreur de la direction est présentée. L’analyse discute aussi de l’importance de l’initialisation adéquate du NPE. Les auteurs proposent une nouvelle méthode pour évaluer l’exactitude de la position en 2D de la navigation autonome du système de NPE. L'article présente et analyse aussi plusieurs modèles stochastiques pour représenter les sources principales d’erreurs des NPE pour un système de NPE de qualité moyenne, notamment l’erreur de l’estimation de la longueur du pas. Une analyse quantitative de la limite supérieure de l’erreur de la position horizontale pour un système de NPE d’une qualité donnée est effectué pour le cas d’une marche en droite ligne ce qui représente le pire cas de propagation de l’erreur horizontale du NPE. À l’aide de cette analyse, les exigences d’un système de NPE et de l’exactitude de l’initialisation peuvent être estimés pour obtenir l’exactitude désirée de la navigation en fonction du temps. L’analyse de faisabilité est mise à l’essai à l’aide d'une expérience sur le terrain.

Introduction Recently, intense research has been done in the area of seamless outdoor/urban canyons/indoor personal navigation. Most of the proposed systems aimed at this application fall in one of the following groups: • Radionavigation systems (GPS/Cellular networks) • Indoor-to-indoor systems (Pseudolites, WLAN, UWB) • Self-contained sensor based systems (INS, PDR). This list is neither complete nor sets any priority towards the selection of a particular pedestrian

navigation system for a certain purpose, but shows the main systems that are used for indoor navigation. Each class in the list above has its pros and cons, some of which will be mentioned and discussed in the sequel. The focus of this paper will be on the analysis of the last class, which is self-contained sensor based PDR systems. The use of GPS indoor has recently been made more realistic by the development of so-called High Sensitivity (HS) receiver GPS technology that allows for the acquisition and tracking of weak signals. This technology is based on a longer integration of GPS signals that allows the tracking of signals GEOMATICA Vol. 59, No. 2, 2005, pp. 175 to 182

G

…magnetic compasses are subject to strong magnetic disturbances such as power lines, computers and various metal/steel objects and structures.

176

E

O

M

A

T

attenuated by as much as 25 dB as compared to the nominal GPS signal power requirement of -157 dB. The performance of HSGPS indoors has been reported in several recent papers [e.g. Lachapelle et al. 2003] and it shows superior availability indoors compared to conventional GPS, but with a poorer accuracy. The major reason against the pseudolitebased and building dependent positioning systems (WLAN) is the obvious requirement of building dependent infrastructure. The aim of the building dependent communication/location systems is the location of a person or asset on a specific floor or in a specific room. The simplest way to achieve this goal is through the use of radio beacons on every floor or inside every room, and to equip the assets to be located with low cost tags such as RF ID tags. This service however is of no use when seamless location is required over large areas encompassing buildings and streets. The pseudolite-based indoor positioning systems are also limited in their use due to severe multipath and losses in propagation through concrete/brick walls. This causes significant positioning errors and very limited applicability when high accuracy indoor navigation is required [e.g. Klukas et al. 2004]. The use of unaided traditional Inertial Navigation Systems (INS) for navigation indoor is also very limited. To limit the position error to a reasonable value, say 50 metres after one hour of self-contained navigation, either a very accurate navigation-grade INS or very frequent zero velocity updates (ZUPTs) with a medium-grade system are required [e.g. Petovello et al. 2003]. These facts, along with the high cost and size of current navigation-grade INS, make their use in traditional mechanization schemes for self-contained navigation rather impractical. In this paper, an analysis of PDR systems based on a medium-accuracy Inertial Measurement Unit (IMU) is presented. The PDR algorithms exploit the kinematics of human walking, thus using IMU data in a different way than the classical double integration of acceleration in INS [Levi and Judd 1999]. It will be shown that if long-term accurate self-contained navigation is required, a certain quality IMU must be chosen and utilized in a PDR mechanization mode and an accurate PDR initialization has to be performed. The variance analysis derived clearly shows that, in long missions without external updates, PDR mechanization should be used instead of INS mechanization. No other systems of the same quality and, most importantly, cost can compete with accurate PDR systems under these conditions. The paper begins with an overview of PDR systems, their architecture and algorithms. Aspects and the importance of PDR initialization are dis-

I

C

A

cussed. Significant emphasis is put on the analysis of major PDR error sources, i.e. the step length estimation error and heading error. Several simulations are run to illustrate that PDR mechanization is superior to classical INS schemes during long periods without updates. The analysis is also illustrated with real data.

Pedestrian Dead Reckoning PDR mechanization exploits the kinematics of human walking. The main idea of PDR mechanization is to use accelerometer signals to detect steps, estimate step length and propagate position using a measured heading (such mechanization requires that possible means of transportation other than walking are excluded). Heading can be computed using gyroscopes or a levelled compass. The PDR system utilizing a magnetic compass is not the best choice for urban navigation because magnetic compasses are subject to strong magnetic disturbances such as power lines, computers and various metal/steel objects and structures. Those disturbances, being of sporadic time/space nature, are hard to detect and are even harder to correct without external correction signals. When a magnetic compass is coupled with a gyro triad, the magnetic disturbances can potentially be detected and corrected but the tuning of such a filter is extremely difficult. The later usually requires ad hoc assumptions of the time length and magnitude of possible magnetic disturbances. Therefore, if accurate navigation is required, the system has to rely on other means to determine heading, such as gyros. The gyros are a major component of inertial navigation systems. In classical inertial mechanization schemes, the gyro accuracy limits the overall positioning accuracy of any inertial system since it introduces a third order position error that grows with time. With such fast error growth, a mediumgrade INS in a stand-alone mode with classical mechanization will be practically useless after more than five minutes unless special care is taken, such as very frequent ZUPTs [Petovello et al. 2003]. In any case, it will be shown that PDR mechanization using a medium-grade IMU (from now on, medium-grade IMUs will refer to IMUs with a 1 deg/hour bias gyros – see Appendix) outperforms a classical INS even with a large step length estimation error, the latter being the major error contributor in this case. PDR and INS mechanizations are relative navigation systems and thus their output accuracy is always dependent on the initialization accuracy. Initialization requires a highly accurate, preferably DGPS-level, position information. Thus, it is

G

E

preferable that a PDR or INS navigation mission starts outdoors. For the INS mechanization, the initial values needed are three attitude, three position, and three velocity components and, possibly, estimates for all six sensor biases. Minimum requirements for a two-dimensional PDR initialization are two position components and a heading. However, if a 1 deg/hour heading accuracy is required, a full 3D gyro system is needed and its operation requires all attitude parameters as in the case of traditional INS mechanization [Collin et al. 2003a]. In addition, there is another PDR parameter that requires initial calibration, namely the user’s average step-length. This parameter can be calibrated with either DGPS or with a specific RF foot-to-foot range measuring technique [e.g. Brand and Phillips 2003]. In any case, the PDR mechanization requires less initial values and is less sensitive to errors in these initial values. The importance of PDR initialization and of various accuracies achievable with initialization data, such as carrier phase DGPS or HSGPS, is described and analyzed in Collin et al. [2003b]. Also, the largest drawback of PDR systems is that their orientation with respect to a body needs to be known. In order to maintain orientation with respect to the body, the unit has to be rigidly mounted on it. Otherwise, it may introduce significant heading errors that eliminate the advantage of using an accurate IMU and the results of an accurate initialization. In this paper, the effect of heading and step length errors on PDR position accuracy that are partially due to the initialization errors is analyzed, with emphasis on long-term pedestrian navigation.

Analysis of PDR Performance This section presents a theoretical performance analysis of medium accuracy PDR navigation systems. The main error sources in such systems are the heading error and the step length estimation error. Those two errors are analyzed in the following section. Then, the effect of the two combined errors on the resulting position accuracy is studied. Step Length Error Modeling The step length error is modeled herein as one of the following three stochastic error models: • Gaussian noise – random Gaussian uncorrelated error in each step length with variance σ2 • Constant bias – constant random error in each step with initial variance σ2 (in this case, the random noise component of the error estimate is negligible for long term navigation) • Gauss-Markov – the error in each step is assumed to follow a 1st order Gauss-Markov process.

O

M

A

T

I

C

A

The random noise models (Gaussian noise or Gauss-Markov process) contribute to small step size variations due to environmental factors. The random constant error is due to an initially incorrect assumption of the step size or an incorrect initialization with poor data. In many applications, the stochastic error models are derived using continuous-time processes as the underlying truth, which are then sampled at discrete times. A PDR system is a discrete-time system in nature and, thus, this transformation is not necessary. This is the reason why time is omitted from the following error models and the step count is used as a varying parameter. Gaussian Random Noise Step Error Model Let us suppose that the step length error is modeled as a Gaussian random noise error as Si = S + ωi ωi ~ N (0,σ2)

(1)

where Si is the true ith step length, S is the constant modeled step length, ωi is the ith step length error, and σ2 is the variance of the Gaussian noise. Then, the step errors are uncorrelated during a walk and the distance error variance after N steps is

σ2s = Var

N k=1

ωk =

N

E(ω2k) = N σ2

(2)

k=1

where N is the step count and σ2 is the variance of the input Gaussian noise. In this case, the error variance is just the step count multiplied by the variance of the driving noise. No assumptions are made when the steps occur. Constant Bias Step Error Model Let us suppose the step length error is modeled as a random constant bias as Si = S + c c ~ N (0,σ2)

(3)

where Si is the true ith step length, S is the constant modeled step length, c is the step length error (random over time but constant for every step length), and σ2 is the variance of the Gaussian noise. In this case, the error is constant for all steps and thus the distance error variance after N steps is

σ2s = Var

N

ck = Var (Nc) = N 2 σ2

(4)

k=1

where N is the step count and σ2 is the initial variance of the constant step length error. In this case, 177

G

E

O

M

A

T

the error variance is proportional to the square of the step count and the variance of the initial constant error. Also, no assumptions when the steps occur are made. Gauss-Markov Step Error Model If the step length error is modeled as a GaussMarkov process, the step length can be written as Si = S + xi = S + xi-le-β + ωi (5)

ωi ~ N(0,σ2) where Si is the true ith step length, S is the constant modeled step length, xi-l is the (i-1) step length error, 1/β is the correlation coefficient, and σ2 is the variance of the Gaussian driving noise. A discrete Gauss-Markov process is essentially an autoregressive process due to its correlation with the previous value. Thus, the autocorrelation function of xi-l can be expressed as – βh r(h) = σ2 e (6) 1 – e– 2 β where h ≥ 0. Thus, the distance error variance after N steps is equal to the variance of the integrated AR process and is equal to N–1

N σ2 + 2σ2 (7) (N – m)e– βm 1 – e– 2 β 1 – e– 2 β m = 1 where N is the step count and σ2 is the initial variance of the driving noise of the Gauss-Markov process. The error growth properties of the above model are in between those of the random constant and the random noise models. In this paper, examples of GMprocess error growth are not given. The proper value

σ2s =

I

C

A

of β heavily depends on the step measurement technique used as well as environmental factors. The choice of values for the input noise variance for both models, σ2, depends on the uncertainty of the user motion, in particular, the step length consistency during the walk. Such uncertainty can be decreased, and thus the value of σ2, if additional information about the user dynamics is considered in the step length estimation filter [Ladetto 2000]. The gyro errors will be modeled as a random constant bias, thus the heading error will be assumed to be linear in time. This will allow the estimation of the position errors due to the maximum drift errors for a specified IMU. Position Domain PDR Errors It can be shown that the maximum PDR position errors occur in the case of a straight walking path, a constant step length error and continuous walking. Therefore, we will analyze the PDR position errors for this case in order to have upper bound estimates for the 2D position errors. Figure 1 shows the geometrical interpretation of the area of all possible position solutions, assuming the presence of the following major errors: the step length error and the heading error. In Figure 1, point O represents the position computed with the used step length model and no heading error present. Points A and B represent the 1σs region due to the step length error modeled as one of the three described stochastic models. Points A-, O-, B- and A+, O+, B+ represent the positions obtained under maximum drift. The deflection of the solution from the horizontal true path in Figure 1 - errors due to the heading error - is rather small compared to the distance error due to the step length error. Thus, it is proposed to consider the deflection of points O- or O+, from the truth path as a 1σG error caused by the gyro drift and to treat the curve of maximum deflection from a straight line due to the gyro drift as a circle with a very large radius R. Then, the corresponding 1σ error ellipse can be formed. In this case, the measure of the horizontal accuracy could be taken as the Distance Root Mean Square (DRMS) value, computed as DRMS = σ2s + σ2G

Figure 1: Geometry of a pedestrian walking path error in presence of step length and heading errors. 178

(8)

where σ2s is the variance of the distance error due to the step length errors, and σ2G is the variance of the heading error. For the specified walking conditions, i.e. non-stop straight walking, and a constant heading drift, the variance of the error caused by the heading drift, σ2G can be approximated as

G

E

O

M

A

T

I

C

A

L (9) θ σG R (1 – cos θ) where L is the computed distance (distance from start to point O in Figure 1), and θ is the heading drift during the walk time in rad. For example, after one hour of non-stop walking with a constant pace of two steps per second an estimated step length of 0.8m and a 1 deg/hour constant heading drift, the value of σG is equal to 50 metres. This is indeed an upper bound estimate of this type of “error across the walking path” caused by gyro drift. R

Simulated Error Analysis Figures 2 and 3 show the expected upper bound estimates of the DRMS position errors of a medium grade PDR system for several error models in stand-alone navigation. Also, for comparison purposes, the expected performance of the same quality traditional INS mechanization approach is shown. The simulation of the traditional INS mechanization errors is performed assuming accurate initial alignment and absence of ZUPTs. It is clear from the results of Figures 2 and 3 that the PDR navigation mechanization, even in the presence of both the heading and the step length errors, outperforms the traditional INS positioning for long-term unaided navigation. The results of Figure 2 show that the value of the variance for the Gaussian noise step length error does not affect the horizontal position error much. On the contrary, the resulting horizontal position error increases significantly if the uncertainty in the constant step length error increases as shown in Figure 3. If the calibration of the system is performed with carrier-phase DGPS, the resulting error is expected to be Gaussian. Then, the expected DRMS accuracy from such a system after 1 hour is expected to be better than 50 metres. The assumption of straight non-stop walking actually increases the error, but, conservatively, this should be taken as an upper bound estimate. If the initialization has been performed with poor quality GPS data, such as HSGPS, then a constant bias in the step length is expected and the results of Figure 3 should be taken as a guideline for the upper bound estimate of the horizontal DRMS PDR error as a function of time.

Experimental Results In this section, the performance of a mediumgrade PDR for long-term navigation is illustrated with real data. The test was performed with a Honeywell 1700 IMU that is a part of the NovAtel

Figure 2: DRMS PDR errors with the step length error modeled as Gaussian noise.

Figure 3: DRMS PDR errors with the step length error modeled as a constant bias.

Black Diamond™ system (BDS). The ring laser gyros in this system have biases of 1 deg/hour. To demonstrate the effect of initialization accuracy on the PDR, the initialization was performed with both carrier-phase DGPS and HSGPS data. The equipment was mounted in a rigid backpack carried by a pedestrian. Test Description The test consisted of the following stages: • Static outdoor initialization (~ 20 min) • Walking outdoor (~ 1 min) • Walking indoor (~ 60 min) Indoors, a rectangular track was walked repeatedly performing one ZUPT indoors every loop. Every two loops, one ZUPT was performed outdoor. In total, 10 walking loops were performed. 179

G

E

O

M

A

T

In all results, the PDR system was continuously calibrated while outdoors. No GPS data was used to aid the PDR system after the pedestrian had moved indoor the first time (outside ZUPTs were used for a different purpose, namely to obtain a better reference). During all ZUPTs, the system sensors’ biases were not removed; these short ZUPTs were performed solely for a better assessment of the position accuracy after every loop. At the end of the test, the pedestrian walked to the initial outdoor position for the final position error assessment. During this final

Figure 4: PDR solution initialized with carrier phase DGPS.

Figure 5: PDR solution initialized with carrier phase DGPS: a constant bias of 10 cm is introduced in the step length estimate. 180

I

C

A

stage, no GPS data was used to correct the PDR. The test duration was approximately one hour. The GPS data was post-processed with several software packages developed at the University of Calgary. Carrier-phase results were obtained with FLYKIN+™ that is a differential GPS carrier-phase based processing software package. HSGPS data was processed in epoch-by-epoch least-square mode using C3NAVG2™, a carrier phase-smoothing GPS software package. PDR Initialization with Carrier Phase DGPS Figure 4 shows the PDR results when a carrier phase DGPS solution with fixed ambiguities is used to initialize the PDR system outdoors. The carrier-phase DGPS solution was available until entrance into the building. The final PDR 2-D position error, that is the difference between the start and the end of the run, is less than 10 metres. The ZUPTs were performed at two fixed locations. Thus, the spread of “red” points representing ZUPTs in Figure 4 show the spread of 2-D position errors after each loop. These errors are much smaller than expected from the theoretical analysis shown in Figures 2 and 3. Such a small error is likely due to the fact that the trajectory is looped and repeated several times. Such walking will result in a smaller final 2-D position error compared to straight walking, since some errors might cancel out (the simplest case of looped walking error cancellation occurs in the absence of gyro drift when walking N steps forward with a constant step length error, and N steps back – this will result in a 0 final error!). Along the track, the 2-D position error does not exceed 20 metres. Figure 5 shows the PDR results when using the same procedure as above but with the introduction of a 10-cm constant step length bias in the PDR mechanization algorithm. Due to the reason explained above (the looped test track), the position error at the end of the test is also around 10m and better than expected. The accuracy at the other end of the loops is however degraded. PDR Initialization with HSGPS Figure 6 shows the PDR results when a HSGPS solution is used outdoors to initialize the PDR system. It has been shown previously that PDR initialization with HSGPS can be problematic and may lead to significant position errors [Collin et al. 2003b; Mezentsev et al. 2004]. Here, only the outdoor part of the HSGPS data is used for PDR calibration, revealing that such measurements result in an accuracy level similar to that achievable with DGPS carrier-phase initialization.

G

E

O

M

A

T

I

C

A

Conclusions A stochastic analysis of PDR horizontal errors for long-term unaided navigation missions has been performed. It has been shown that if the step length estimation error follows a Gaussian noise distribution, the 2-D PDR position error is expected to grow proportionally to t . If the step length estimation error is constant for every step, the position error is expected to grow proportionally to t. In any case, due to such error propagation properties, PDR outperforms traditional INS mechanizations. Such analysis makes it possible to estimate the requirements for a PDR system as a function of the mission accuracy required. The experimental field results presented herein are better than the theoretical analysis due to the following reasons: • The pedestrian step lengths were likely more regular due to the transportation of a test backpack. • The test path was repeated many times, which may cancel certain PDR position error sources. The above cases are very possible in real navigation missions, for example in the case of a fire fighter carrying a heavy load and moving indoor within a building of finite dimension for a given period of time. As gyro technology evolves and the cost and size of 1 deg/hour gyros will decrease significantly, the above levels of performance will become feasible for significant market segments.

References Brand, T. and R. Phillips. 2003. Foot-to-Foot Range Measurement as an Aid To Personal Navigation. Proceedings of ION 59th Annual Meeting and CIGTF Guidance Test Symposium, Albuquerque, New Mexico, Alexandria, VA, USA, Institute of Navigation, pages 113-121. Collin J., O. Mezentsev, and G. Lachapelle. 2003a. Indoor Positioning System Using Accelerometry and High Accuracy Heading Sensors, Proceedings of ION GPS 2003 (9-12 September, Portland, Oregon), Alexandria, VA, USA, Institute of Navigation, pages 1164-1170. Collin J., H. Kuusniemi, O. Mezentsev, G. MacGougan, and G. Lachapelle. 2003b. HSGPS under Heavy Signal Masking - Accuracy and Availability Analysis, 6th Nordic Radio Navigation Conference and Exhibition “NORNA 03”, Stockholm-Helsinki, (available at http://plan.geomatics.ucalgary.ca) Klukas R., O. Julien,L. Dong, M.E. Cannon, and G. Lachapelle. 2004. Effects of Building Materials on

Figure 6: PDR solution initialized with HSGPS.

UHF Ranging Signals, GPS Solutions, 8(1), pages 1-8. Lachapelle G., H. Kuusniemi, D.H.T. Dao, G. MacGougan, and M.E. Cannon. 2003. HSGPS Signal Analysis and Performance Under Various Indoor Conditions, Journal of the U.S. Institute of Navigation, 51(1), pages 29-43. Ladetto Q. 2000. On Foot Navigation: Continuous Step Calibration using Both Complimentary Recursive Prediction and Adaptive Kalman Filtering, Proceedings of ION GPS 2000 (January 26-28, 2000, Anaheim, California), Alexandria, VA, USA, Institute of Navigation, pages 1735-1740. Levi R. and T. Judd. 1999. Dead Reckoning Navigation System Using Accelerometer to Measure Foot Impacts, US patent. Mezentsev O., J. Collin, H. Kuusniemi, and G. Lachapelle. 2004. Accuracy Assessment of a High Sensitivity GPS Based Pedestrian Navigation System Aided by Low-Cost Sensors, Proceedings of 11th Saint Petersburg International Conference on Integrated Navigation Systems, Russia, pages156-164. Petovello M., O. Mezentsev, G. Lachapelle, and M.E. Cannon. 2003. High Sensitivity GPS Velocity Updates for Personal Indoor Navigation Using Inertial Navigation Systems, Proceedings of ION GPS 2003 (September 9-12, Portland, Oregon), Alexandria, VA, USA, Institute of Navigation, pages 2886-2896.

Appendix To apply the results for different gyro types, the gyro bias term “b” can be generalized as follows: let x(t) be a gyro output with a zero input (the 181

G

E

O

M

A

T

gyro is not rotating in inertial space). Then, the gyro is said to have a bias b if 1hr

E

x(t)dt = 0(deg/hour) 0hr

(A1 and A2)

1hr

x(t) = b2 (deg2 /hour2 )

Var Oleg Mezentsev 0hr

Jussi Collin

Equation A1 guarantees that any deterministic bias is removed and Equation A2 assures that the standard deviation of the computed angle error is equal to b deg/hour. Thus, no assumption on the random process of the gyro noise is made. In this paper, the simulations were performed by assuming a random constant process for the gyro noise, but the results apply to other possible random processes with sufficient accuracy.

Authors Dr. Mezentsev graduated with an Engineering degree from Bauman Moscow State Technical

Gérard Lachapelle

182

I

C

A

University, Russia, in 1998. In 2001, he received a Master of Science degree from the Department of Mechanical Engineering at the University of Illinois at Urbana-Champaign, USA. In 2005, he received a PhD degree from the Department of Geomatics Engineering, University of Calgary, Canada. His research interests include pedestrian navigation with High Sensitivity GPS and MEMS sensors in signal-degraded environments. Mr. Collin received a Master of Science degree from the Department of Electrical Engineering, Tampere University of Technology, in 2002. He is currently a research scientist and a PhD candidate at the University of Tampere, Institute of Digital and Computer Systems. His research topic is adaptive integration of radionavigation systems with miniature motion sensors. Professor Gérard Lachapelle holds a CRC/iCORE Chair in wireless location in the Department of Geomatics Engineering, University of Calgary, where he has been a professor since 1988 and department head from 1995 to 2003. He and his team have developed numerous novel algorithms and software related to GPS, Galileo and mobile telephone location that have been licensed worldwide. More information is available on http://plan.geomatics.ucalgary.ca o