Ángel F. García-Fernández

Analysis of Kalman Filter Approximations for Nonlinear Measurements

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 approximation 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.

Two-Layer Particle Filter for Multiple Target Detection and Tracking

The detection and tracking of an unknown number of targets using a Bayesian hierarchical model with target labels is presented. To approximate the posterior probability density function (PDF), we develop a two-layer particle filter (PF). One deals with track initiation, and the other deals with track maintenance. In addition the parallel partition (PP) method is proposed to sample the states of the surviving targets.

Asynchronous particle filter for tracking using non-synchronous sensor networks

This paper deals with the problem of tracking using a sensor network when the sensors are not synchronised. We propose a new algorithm called the asynchronous particle filter that, with much less computational burden than the traditional particle filter, has a slightly poorer performance. Thus, it is a good solution to real-time applications with non-synchronised sensors when high performance is required. The low computational burden of the method lies in the fact that we do not predict and update the state every time a measurement is collected. Its high performance is due to the fact that we account for the time instant at which each measurement was taken.

Bayesian Road Estimation Using Onboard Sensors

This paper describes an algorithm for estimating the road ahead of a host vehicle based on the measurements from several onboard sensors: a camera, a radar, wheel speed sensors, and an inertial measurement unit. We propose a novel road model that is able to describe the road ahead with higher accuracy than the usual polynomial model. We also develop a Bayesian fusion system that uses the following information from the surroundings: lane marking measurements obtained by the camera and leading vehicle and stationary object measurements obtained by a radar-camera fusion system. The performance of our fusion algorithm is evaluated in several drive tests. As expected, the more information we use, the better the performance is.

Posterior Linearization Filter: Principles and Implementation Using Sigma Points

This paper is concerned with Gaussian approximations to the posterior probability density function (PDF) in the update step of Bayesian filtering with nonlinear measurements. In this setting, sigma-point approximations to the Kalman filter (KF) recursion are widely used due to their ease of implementation and relatively good performance. In the update step, these sigma-point KFs are equivalent to linearizing the nonlinear measurement function by statistical linear regression (SLR) with respect to the prior PDF. In this paper, we argue that the measurement function should be linearized using SLR with respect to the posterior rather than the prior to take into account the information provided by the measurement. The resulting filter is referred to as the posterior linearization filter (PLF). In practice, the exact PLF update is intractable but can be approximated by the iterated PLF (IPLF), which carries out iterated SLRs with respect to the best available approximation to the posterior. The IPLF can be seen as an approximate recursive Kullback-Leibler divergence minimization procedure. We demonstrate the high performance of the IPLF in relation to other Gaussian filters in two numerical examples.

Facet Model of Moving Targets for ISAR Imaging and Radar Back-Scattering Simulation

A facet model of targets is proposed to simulate inverse synthetic aperture radar (ISAR) images and radar back-scattering of moving targets with rigid and nonrigid motions. Targets are composed of solid objects which are modeled by triangular facets. It is shown that a facet can be treated as an equivalent point-scatterer whose radar cross section (RCS) and position depend on the shape of the triangle, the frequency, and the angle of incidence. A shadowing algorithm is also developed to detect the facets which actually have influence on the signal received by the radar. Besides, a facet division algorithm is implemented to improve the result of the shadowing algorithm and to have at least one facet per resolution cell. Finally, we apply our simulator to obtain the ISAR images of a ship and a helicopter and to calculate the micro-Doppler signature of a human.

Bayesian Sequential Track Formation

This paper presents a theoretical framework for track building in multiple-target scenarios from the Bayesian point of view. It is assumed that the number of targets is fixed and known. We propose two optimal methods for building tracks sequentially. The first one uses the labelling of the current multitarget state estimate that minimizes the mean-square labeled optimal subpattern assignment error. This method requires knowledge of the posterior density of the vector-valued state. The second assigns the labeling that maximizes the probability that the current multi-target state estimate is optimally linked with the available tracks at the previous time step. In this case, we only require knowledge of the random finite-set posterior density without labels.

Derivation of the PHD and CPHD Filters Based on Direct Kullback–Leibler Divergence Minimization

In this paper, we provide novel derivations of the probability hypothesis density (PHD) and cardinalised PHD (CPHD) filters without using probability generating functionals or functional derivatives. We show that both the PHD and CPHD filters fit in the context of assumed density filtering and implicitly perform Kullback-Leibler divergence (KLD) minimizations after the prediction and update steps. We perform the KLD minimizations directly on the multitarget prediction and posterior densities.

Gaussian MAP Filtering Using Kalman Optimization

This paper deals with the update step of Gaussian MAP filtering. In this framework, we seek a Gaussian approximation to the posterior probability density function (PDF) whose mean is given by the maximum a posteriori (MAP) estimator. We propose two novel optimization algorithms which are quite suitable for finding the MAP estimate although they can also be used to solve general optimization problems. These are based on the design of a sequence of PDFs that become increasingly concentrated around the MAP estimate. The resulting algorithms are referred to as Kalman optimization (KO) methods. We also provide the important relations between these KO methods and their conventional optimization algorithms (COAs) counterparts, i.e., Newtons and Levenberg-Marquardt algorithms. Our simulations indicate that KO methods are more robust than their COA equivalents.

Generalized optimal sub-pattern assignment metric

This paper presents the generalized optimal sub-pattern assignment (GOSPA) metric on the space of finite sets of targets. Compared to the well-established optimal sub-pattern assignment (OSPA) metric, GOSPA is not normalised by the cardinality of the largest set and it penalizes cardinality errors differently, which enables us to express it as an optimisation over assignments instead of permutations. An important consequence of this is that GOSPA allows us to penalize localization errors for detected targets and the errors due to missed and false targets, as indicated by traditional multiple target tracking (MTT) performance measures, in a sound manner. In addition, we extend the GOSPA metric to the space of random finite sets, which is important to evaluate MTT algorithms via simulations in a rigorous way.