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Online Bayesian Estimation for Indoor Localization and Positioning


Leila Pishdad


July 23, 2015 at  12:00 AM
McConnell Engineering Room 603

Abstract

The increasing prevalence of pervasive computing and ubiquitous systems has led to the requirement for more accurate and more precise localization systems. For outdoor scenarios, the existing satellite positioning and navigation systems can provide the required precision and accuracy. However, for indoor systems this is more challenging. Specifically, due to the characteristics of indoor environments such as the presence of multi-path fading and non-line-of-sight conditions, the existing indoor location systems cannot provide the required localization accuracy and precision. Furthermore, these requirements are more stringent for indoor applications. Hence, to provide better location estimation, post-processing the location information gathered from the indoor sensors is vital. In this dissertation, by using the state-space representation for localization problems we apply Bayesian estimation techniques to improve the location estimation accuracy and precision for mobile targets indoors. Bayesian techniques provide recursive methods for predicting and updating the posterior distribution, which is defined as the probability distribution function of being at a certain location given the available measurements. Since the noise processes in the indoor environment are non-Gaussian, optimal Gaussian Bayesian estimation techniques such as Kalman filter cannot provide good estimations. Hence, we apply approximate methods, namely particle filters and Gaussian sum filters.

Particle filters use a set of particles and their associated weights to represent the posterior. The particles or samples are taken from an importance function. Hence, the choice of this importance function can change the performance of the filter significantly. Moreover, a better selection of the importance function can decrease the degeneracy of particles and remove the requirement for resampling. Hence, in the first part of this dissertation we use particle filters with the optimal importance functions for indoor location estimation. To enable this, we propose motion and sensor models that not only are general enough to address a wide range of mobile targets and sensors, but also allow the evaluation and use of the optimal importance function. Specifically, we use Gaussian mixtures (GM) to represent the noise distributions. By evaluating and using the optimal importance function, we decrease the degeneracy of particles and resolve the sample impoverishment. In the second part of this dissertation we use parallel Kalman filters or the Gaussian sum filter (GSF) to estimate the components of the GM posterior. By taking advantage of the low-computational complexity of Kalman filters, we are able to use a finer approximation of the noise distributions. In other words, we can use GMs with more components with a lower computational complexity when compared with particle filters. However, GSF can suffer from an exponentially increasing number of filters and requires reduction schemes to maintain its bank size. Hence, to overcome this problem we propose an approximate minimum-mean-square-error (AMMSE) filter. This filter minimizes the trace of the combined covariance matrix of the filter as opposed to minimizing the trace of the individual filters covariance matrices in GSF. Consequently, the proposed filter is more robust to removing its components and can be used with the simplest reduction schemes. As another contribution of the second part of this thesis we propose a low-computational complexity reduction scheme based on removing components.

Finally, we propose analytic upper and lower bounds on the MMSE, as the MMSE itself is not analytically tractable, and GSF can only provide the MMSE estimation. Moreover, the general analytic bounds for dynamic systems are not tractable for GM noise statistics. We provide two analytic upper bounds which are the mean-square errors (MSE) of implementable filters. Additionally, we show that depending on the GM noise distributions in the system, one of the proposed upper bounds provides a tighter bound and can be selected based on the shape of the GM noise distributions. We also show that for highly multimodal GM noise distributions, the bounds and the MMSE converge.