On Monte Carlo Smoothing in Multi Sensor Indoor Localisation

Frank Ebner, Toni Fetzer and Frank Deinzer

Faculty of Computer Science and Business Information Systems

University of Applied Sciences Würzburg-Schweinfurt

Würzburg, Germany

{frank.ebner, toni.fetzer, frank.deinzer}@fhws.de

Marcin Grzegorzek

Pattern Recognition Group University of Siegen Siegen, Germany {marcin.grzegorzek}@uni-siegen.de

Abstract—

I. Introduction

Determining a position indoors is a challenging task. Besides the complex architecture of many buildings, a high accuracy needs to be achieved, especially for buildings with many small separated areas like shopping malls or office blocks. In recent years, many different systems were presented to meet those requirements. Especially Wi-Fi positioning and pedestrian dead reckoning (PDR) are very popular solutions. Approaches based on PDR try to estimate the current position given the previous position and thus require an initial state. However, this allows for cumulative errors and leads to an erroneous position estimation within a very short period. By incorporating the absolute position information of Wi-Fi this drift can be corrected. Additional improvements can be achieved by using environmental information about walls and obstacles provided by a floor map.

In most cases, probabilistic methods are used to incorporate those highly different sensor types. Here, a probability distribution describes the pedestrian’s possible whereabouts and therefore the uncertainty of the system. Drawing from a probability distribution and finding an analytical solution for densities is in most cases a difficult task, especially in case of time sequential, non-linear and non-Gaussian models. Due to the high complexity of the human movement, we consider indoor localisation as such. A broad class to obtain numerical results instead are the Monte Carlo methods. Here, a set of weighted random samples is used to solve any problem having a probabilistic interpretation. By applying the time sequential hidden Markov process of Bayes filtering, one of the most important Monte Carlo techniques results: particle filtering. A particle filter updates the state estimation recursively in time with every new incoming measurement using the state transition and state evaluation step.

Based on this general methodology, many different approaches for estimating a position in indoor environments have been developed. All these approaches differ mainly in how the dynamics are modelled in the transition step and how a specific sensor measurement can be used for evaluation. For example, recent approaches are using a graph-based structure to consider environmental restrictions (walking through walls) and the characteristics of human movement (walking speed) within the transition model [1]. The evaluation model is mostly separated into any number of sensor models, each representing the probability for a noisy measurement in regard to the current position. For example, a barometer can be used to determine the probability of being on a certain floor [2].

Despite the many advances made in the last years, nearly all systems suffer from more or less the same problems. Of course, every sensor model brings its very own weaknesses. Like mentioned before, PDR suffers from an accumulating bias, the signal of Wi-Fi gets attenuated by walls and the barometric pressure is highly affected by weather patterns and humidity [2]. That is the reason for the use of statistical methods in the first place. Nevertheless, there are even more profound problems regarding the whole position estimation procedure.

Current transition models, which aim to approximate the movement, are still very restrictive and unable to handle unforeseen events. Faulty sensor measurements, like a falsely detected turn, can cause the estimation to lose track. For example by taking a turn too soon and walking into a room instead of another big hallway [1]. Due to this, the filter needs some time to recover, which again takes a while because of the restrictive model (e.g. no walking through walls and only realistic walking speed). This temporal delay worsens the estimate immensely. A solution to recover from such filter divergences faster, is using methods for re-initializing the filtering procedure [?]. However, even this can not completely prevent delays. Another reason for possible time delays are slow sensor updates. For example, most mobile devices restrict the Wi-Fi module to update only every few seconds, to save on battery.

Further critical problems arise from multimodal distributions. Those are caused by multiple possible position estimates. Fig. 1 illustrates an example where a floor gets separated by a wall. Due to inaccurate measurements and a PDR approach for evaluating the movement, the distribution splits apart. Therefore, the most likely position is somewhere inbetween. Only after the pedestrian turns right, the distribution is again unimodal, since moving through walls is prohibited. As one can imagine, this can lead to serious problems in big indoor environments. Such a situation can be improved

Time t  t − 1  t − 2

Fig. 1. An example of the occurrence of a multimodal distribution. At time t − 1 the floor gets separated by a wall and the mode of the distribution (colored circle), representing the current position, splits apart. The most likely position (green line) is estimated somewhere in-between. After a right turn, the distribution slowly starts to recover its unimodality.

by incorporating future measurements (e.g. the right turn) or predictive information (e.g. the most likely path) to the filtering procedure [3]. However, standard filtering methods are not able to use any future information and the possibilities to make a distant forecast are also limited [4]–[6].

Within this work, we ...

II. Related Work III. Recursive State Estimation

IV. Transition V. Smoothing

Test

VI. Experiments

ddd [7] dddd

• Vorwrtsschritt die Ergebnisse und Probleme beschreiben. Zeitlicher Verzug etc.

• Fixed-Interval Smoothing mit beiden Methoden. Was wird besser? Warum?

AUf die schlechte Performance eingehen fr was knnte man es nutzen?

• Fixed-lag Smoothing der beiden Methoden erstmal ergebnisse mit 3 unterschiedlichen lags. 5,

30, 50 oder so Fehlerplot wie beim fusion paper. wo ist der error

besonders hoch, warum? warum wurde er besser? welche anwendungen gibt es da jeweils? plot mit kurven die den fehler bei den unter-

schiedlichen lag lngen angibt.

• Fixed-lag gap einen offset (gap) im smoothing. was bringt es?

sinnvoll?

VII. Conclusion References

[1] F. Ebner, T. Fetzer, L. Köping, M. Grzegorzek, and F. Deinzer, “Multi Sensor 3D Indoor Localisation,” in Indoor Positioning and Indoor Navigation (IPIN), Int. Conf. on, 2015, pp. 1–10.

[2] B. Li, B. Harvey, and T. Gallagher, “Using barometers to determine the height for indoor positioning,” in Indoor Positioning and Indoor Navigation (IPIN), Int. Conf. on, 2013, pp. 1–7.

[3] F. Ebner, T. Fetzer, M. Grzegorzek, and F. Deinzer, “On Prior Navigation Knowledge in Multi Sensor Indoor Localisation,” in On Review, 2016, pp. 1–8.

[4] S. Thrun, W. Burgard, and D. Fox, Probabilistic Robotics. Cambridge, MA, USA: The MIT Press, 2005.

[5] A. Doucet and A. M. Johansen, “A Tutorial on Particle Filtering and Smoothing: Fifteen years later,” in The Oxford Handbook of Nonlinear Filtering, D. Crisan and B. Rozovsky, Eds. Oxford University Press, 2011.

[6] Z. Chen, “Bayesian filtering: From kalman filters to particle filters, and beyond,” Statistics, vol. 182, no. 1, pp. 1–69, 2003.

[7] V. Honkavirta, T. Perl, S. Ali-Lytty, and R. Piche, “A comparative survey of wlan location fingerprinting methods,” Workshop on Positioning, Navigation and Communication, vol. 6, no. 1, pp. 243–251, 2009.