In this paper we examine the role of very simple and noisy sensors for the tracking problem. We propose a binary sensor model, where each sensor’s value is converted reliably to one bit of information only: whether the object is moving toward the sensor or away from the sensor. We show that a network of binary sensors has geometric properties that can be used to develop a solution for tracking with binary sensors and present resulting algorithms and simulation experiments. We develop a particle filtering style algorithm for target tracking using such minimalist sensors. We present an analysis of a fundamental tracking limitation under this sensor model, and show how this limitation can be overcome through the use of a single bit of proximity information at each sensor node. Our extensive simulations show low error that decreases with sensor density. 1.

Optimal estimation problems for non-linear non-Gaussian state-space models do not typically admit analytic solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online manner, i.e. recursively as observations become available, and are now routinely used in fields as diverse as computer vision, econometrics, robotics and navigation. The objective of this tutorial is to provide a complete, up-to-date survey of this field as of 2008. Basic and advanced particle methods for filtering as well as smoothing are presented.

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Abstract. An important issue in tracking is how to incorporate an appropriate degree of adaptivity into the observation model. Without any adaptivity, tracking fails when object properties change, for example when illumination changes affect surface colour. Conversely, if an observation model adapts too readily then, during some transient failure of tracking, it is liable to adapt erroneously to some part of the background. The approach proposed here is to adapt selectively, allowing adaptation only during periods when two particular conditions are met: that the object should be both present and in motion. The proposed mechanism for adaptivity is tested here with a foreground colour and motion model. The experimental setting itself is novel in that it uses combined colour and motion observations from a fixed filter bank, with motion used also for initialisation via a Monte Carlo proposal distribution. Adaptation is performed using a stochastic EM algorithm, during periods that meet the conditions above. Tests verify the value of such adaptivity, in that immunity to distraction from clutter of similar colour to the object is considerably enhanced. 1

This tutorial provides an introduction to Simultaneous Localisation and Mapping (SLAM) and the extensive research on SLAM that has been undertaken over the past decade. SLAM is the process by which a mobile robot can build a map of an environment and at the same time use this map to compute it’s own location. The past decade has seen rapid and exciting progress in solving the SLAM problem together with many compelling implementations of SLAM methods. Part I of this tutorial (this paper), describes the probabilistic form of the SLAM problem, essential solution methods and significant implementations. Part II of this tutorial will be concerned with recent advances in computational methods and new formulations of the SLAM problem for large scale and complex environments.

Particle filters are used extensively for tracking the state of non-linear dynamic systems. This paper presents a new particle filter that maintains samples in the state space at dynamically varying resolution for computational efficiency. Resolution within statespace varies by region, depending on the belief that the true state lies within each region. Where belief is strong, resolution is fine. Where belief is low, resolution is coarse, abstracting multiple similar states together. The resolution of the statespace is dynamically updated as the belief changes. The proposed

Wireless sensor networks produce a large amount of data that needs to be processed, delivered, and assessed according to the application objectives. The way these data are manipulated by the sensor nodes is a fundamental issue. Information fusion arises as a response to process data gathered by sensor nodes and benefits from their processing capability. By exploiting the synergy among the available data, information fusion techniques can reduce the amount of data traffic, filter noisy measurements, and make predictions and inferences about a monitored entity. In this work, we survey the current state-of-the-art of information fusion by presenting the known methods, algorithms, architectures, and models of information fusion, and

This work addresses the problem of tracking multiple moving targets by recursively estimating the joint multitarget probability density (JMPD). Estimation of the JMPD is done in a Bayesian framework and provides a method for tracking multiple targets which allows nonlinear target motion and measurement to state coupling as well as non-Gaussian target state densities. The JMPD technique simultaneously estimates both the target states and the number of targets in the surveillance region based on the set of measurements made. We give an implementation of the JMPD method based on particle filtering techniques and provide an adaptive sampling scheme which explicitly models the multitarget nature of the problem. We show that this implementation of the JMPD technique provides a natural way to track a collection of targets, is computationally tractable, and performs well under difficult conditions such as target crossing, convoy movement, and low measurement signal-to-noise ratio (SNR).

The aim is to model "activity" performed by a group of moving and interacting objects (which can be people or cars or different rigid components of the human body) and use the models for abnormal activity detection. Previous approaches to modeling group activity include co-occurrence statistics (individual and joint histograms) and Dynamic Bayesian Networks, neither of which is applicable when the number of interacting objects is large. We treat the objects as point objects (referred to as "landmarks") and propose to model their changing configuration as a moving and deforming "shape" (using Kendall's shape theory for discrete landmarks). A continuous state Hidden Markov Model (HMM) is defined for landmark shape dynamics in an activity. The configuration of landmarks at a given time forms the observation vector and the corresponding shape and the scaled Euclidean motion parameters form the hidden state vector. An abnormal activity is then defined as a change in the shape activity model, which could be slow or drastic and whose parameters are unknown. Results are shown on a real abnormal activity detection problem involving multiple moving objects.

In the last decade, sequential Monte-Carlo methods (SMC) emerged as a key tool in computational statistics (see for instance Doucet et al. (2001), Liu (2001), Künsch (2001)). These algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to a weighted population of particles. These particles and weights are generated recursively according to elementary transformations: mutation and selection. Examples of applications include the sequential Monte-Carlo techniques to solve optimal non-linear filtering problems in state-space models, molecular simulation, genetic optimization, etc. Despite many theoretical advances (see for instance Gilks and Berzuini (2001), Künsch (2003), Del Moral (2004), Chopin (2004)), the asymptotic property of these approximations remains of course a question of central interest. In this paper, we analyze sequential Monte Carlo methods from an asymptotic perspective, that is, we establish law of large numbers and invariance principle as the number of particles gets large. We introduce the concepts of weighted sample consistency and asymptotic normality, and derive conditions under which the mutation and the selection procedure used in the sequential Monte-Carlo build-up preserve these properties. To illustrate our findings, we analyze SMC algorithms to approximate the filtering distribution in state-space models. We show how our techniques allow to relax restrictive technical conditions used in previously reported works and provide grounds to analyze more sophisticated sequential sampling strategies. Short title: Limit theorems for SMC. 1