Implementation of Kalman Filter with Python Language

International audienceIn this paper, we investigate the implementation of a Python code for a Kalman Filter using the Numpy package. A Kalman Filtering is carried out in two steps: Prediction and Update. Each step is investigated and coded as a function with matrix input and output. These different functions are explained and an example of a Kalman Filter application for the localization of mobile in wireless networks is given

Evaluation of a geometric positioning algorithm for hybrid wireless networks

International audienceIn this paper, we propose a geometric positioning method for hybrid wireless networks, based on a set membership method. Three common types of radio observables are considered for the position estimation: range, difference of ranges and received power. This paper details how to build geometric constraints from observables, and how to merge them to estimate the position. Given a realistic scenario, Monte Carlo simulation shows that the performance of the proposed method in terms of root mean squared error and cumulative density functions outperforms that of a numerically optimized maximum likelihood

PyLayers: An open source dynamic simulator for indoor propagation and localization

International audience— In this paper, we introduce PyLayers a new open source radio simulator built to tackle indoor localization problem. PyLayers has been designed to simulate complete dynamic scenarios including the realistic movement of persons inside a building, the transmission channel estimation for multiple radio access technologies and the position estimation relying on location-dependent parameters originated from the simulated OSI physical layer. The channel is estimated by using a fast graph-based ray tracing method. From these simulated data, location dependent parameters, such as received power or time of arrival, can be deduced. The realistic movement of persons into the building layout is modeled with a virtual forces approach. The simulated data can be directly used with one of the built-in localization algorithms or be exported to various standards extensions. Finally, the accuracies of both the channel estimation and the localization are compared to measurements and show a good match

Enhancing positioning accuracy through direct position estimators based on hybrid RSS data fusion

International audienceIn this paper, localization based on Received Signal Strength (RSS) is investigated assuming a path loss log normal shadowing model. On the one hand, indirect RSS-based estimation schemes are investigated; these schemes are based on two steps of estimation: estimation of ranges from RSS and then estimation of position using weighted least square approximation. We show that the performances of this type of schemes depend on the used estimator in the first step.We suggest that typical median estimator must be replaced by maximum likelihood estimator (mode) to enhance the positioning accuracy. On the other hand, a new direct RSS-based estimation scheme of position is proposed; Monte Carlo simulations show that the new estimator performs better than indirect estimators and can be reliable in future hybrid localization systems

Improved Mobility Modeling for Indoor Localization Applications

International audienceThis paper presents a novel mobility model to perform realistic simulations of human movements and behaviors. The proposed model is based on discrete event simulation and graph theory. The proposed model is implemented in a wireless propagation simulator and used to evaluate various wireless network protocols including: propagation, localization and communication

Hybrid Data Fusion Techniques for Localization in UWB Networks

International audienceIn this paper, we exploit the concept of data fusion in UWB (Ultra Wide Band) localization systems by using different location-dependent observables. We combine ToA (Time of Arrival) and RSS (Received Signal Strength) in order to get accurate positioning algorithms.We assume that RSS observables are usually available and we study the effect of adding ToA observables on the positioning accuracy. The proposed architecture of Hybrid Data Fusion (HDF) is based on two stages: Ranging using RSS and ToA; and Estimation of position by the fusion of estimated ranges. In the first stage, we propose a new estimator of ranges from RSS observables assuming a path loss model. In the second stage, a new ML estimator is developed to merge different ranges with different variances. In order to evaluate these algorithms, simulations are carried out in a generic indoor environment and Cramer Rao Lower Bounds (CRLB) are investigated. Those algorithms show enhanced positioning results at reasonable noise levels

Enhancing Positioning Accuracy Through RSS Based Ranging And Weighted Least Square Approximation

International audienceIn this paper, localization based on Received Signal Strength (RSS) is investigated assuming a path loss log normal shadowing model. RSS-based estimation schemes of ranges are investigated; three different schemes are studied: Mean, median and mode. Estimation of position is performed using weighted least square approximation. We show that the positioning accuracy depends on the used estimator of ranges from RSS observables. We suggest that typical median estimator must be replaced by maximum likelihood estimator (mode) to enhance the positioning accuracy. Monte Carlo simulations show that the estimation scheme based on the mode estimator performs better than those based on the median or the mean estimator; and that the use of Weighted Least square approximation enhances the accuracy comparing to typical unweighted least square approximation

A Maximum Likelihood TOA Based Estimator For Localization in Heterogeneous Networks

International audienceIn this paper, we exploit the concept of data fusion in hybrid localization systems by combining different TOA (Time of Arrival) observables coming from different RATs (Radio Access Technology) and characterized by different precisions in order to enhance the positioning accuracy. A new Maximum Likelihood estimator is developed to fuse different measured ranges with different variances. In order to evaluate this estimator, Monte Carlo simulations are carried out in a generic environment and Cramer Rao Lower Bounds (CRLB) are investigated. This algorithm shows enhanced positioning accuracy at reasonable noise levels comparing to the typical Weighted Least Square estimator. The CRLB reveals that the choice of the number, and the configuration of Anchor nodes, and the type of RAT may enhance positioning accuracy

Evaluation of a geometric positioning algorithm for hybrid wireless networks

International audienceIn this paper, we propose a geometric positioning method for hybrid wireless networks, based on a set membership method. Three common types of radio observables are considered for the position estimation: range, difference of ranges and received power. This paper details how to build geometric constraints from observables, and how to merge them to estimate the position. Given a realistic scenario, Monte Carlo simulation shows that the performance of the proposed method in terms of root mean squared error and cumulative density functions outperforms that of a numerically optimized maximum likelihood

Exploiting the Graph Description of Indoor Layout for Ray Persistency Modeling in Moving Channel

International audienceThis paper proposes a technique based on descrip- tion of the layout using different graphs to obtain a ray signature which is associated with path persistency observed for small displacement of radio link termination of a mobile channel. The algorithm used to derive the signature from the layout graph description and the position of Tx and Rx is described. The mathematical relationship between signature and rays is also presented. A comparison of simulated and measured IR-UWB channel impulse response over a pedestrian trajectory is shown