Tag Archives: Probabilistic Sensor Model

Substituting the update step of a bayesian filter by a maximum likelihood optimisation in order to use non-linear observation models in a (linear-transition) Kalman framework

Damián Marelli, Minyue Fu, and Brett Ninness, Asymptotic Optimality of the Maximum-Likelihood Kalman Filter for Bayesian Tracking With Multiple Nonlinear Sensors, IEEE Transactions on signal processing, vol. 63, no. 17, DOI: 10.1109/TSP.2015.2440220.

Bayesian tracking is a general technique for state estimation of nonlinear dynamic systems, but it suffers from the drawback of computational complexity. This paper is concerned with a class of Wiener systems with multiple nonlinear sensors. Such a system consists of a linear dynamic system followed by a set of static nonlinear measurements. We study a maximum-likelihood Kalman filtering (MLKF) technique which involves maximum-like-lihood estimation of the nonlinear measurements followed by classical Kalman filtering. This technique permits a distributed implementation of the Bayesian tracker and guarantees the boundedness of the estimation error. The focus of this paper is to study the extent to which the MLKF technique approximates the theoretically optimal Bayesian tracker. We provide conditions to guarantee that this approximation becomes asymptotically exact as the number of sensors becomes large. Two case studies are analyzed in detail.

Analysis of the deterioration of several Kalman Filters depending on the amount of uncertainty in the observations, when the observation model is non-linear

Mark R. Morelande and Ángel F. García-Fernández, Analysis of Kalman Filter Approximations for Nonlinear Measurements, IEEE Transactions on signal processing, vol. 61, no. 22, 2013 DOI: 10.1109/TSP.2013.2279367.

A theoretical analysis is presented of the correction step of the Kalman filter (KF) and its various approximations for the case of a nonlinear measurement equation with additive Gaussian noise. The KF is based on a Gaussian app roximation to the joint density of the state and the measurement. The analysis metric is the Kullback-Leibler divergence of this approximation from the true joint density. The purpose of the analysis is to provide a quantitative tool for understanding and assessing the performance of the KF and its variants in nonlinear scenarios. This is illustrated using a numerical example.

Probabilistic models of several sensors plus a method for distinguishing the different hypotheses from the posterior of a PF

V. Alvarez-Santos, A. Canedo-Rodriguez, R. Iglesias, X.M. Pardo, C.V. Regueiro, M. Fernandez-Delgado, Route learning and reproduction in a tour-guide robot, Robotics and Autonomous Systems, Volume 63, Part 2, January 2015, Pages 206-213, ISSN 0921-8890. DOI: 10.1016/j.robot.2014.07.013

Traditionally, route information is introduced in tour-guide robots by experts in robotics. In the tour-guide robot that we are developing, we allow the robot to learn new routes while following an instructor. In this paper we describe the route recording process that takes place while following a human, as well as, how those routes are later reproduced.

A key element of both route recording and reproduction is a robust multi-sensorial localization algorithm that we have designed, which is able to combine various sources of information to obtain an estimate of the robot’s pose. In this work we detail how the algorithm works, and how we use it to record routes. Moreover, we describe how our robot reproduces routes, including path planning within route points, and dynamic obstacle avoidance for safe navigation. Finally, we show through several trajectories how the robot was able to learn and reproduce different routes.