Distributed processing of multiple sensor data has advantages over centralized processing because of lower bandwidth
for communicating data and lower processing load at each site. However, distributed fusion has to address dependence
issues not present in centralized fusion. Bayesian distributed fusion combines local probabilities or estimates to generate
the results of centralized fusion by identifying and removing redundant common information. Approximation of
Bayesian distributed fusion provides practical algorithms when it is difficult to identify the common information.
Another distributed fusion approach combines estimates with known means and cross covariances according to some
optimality criteria. Distributed object tracking involves both track to track association and track state estimate fusion
given an association. Track state estimate fusion equations can be obtained from distributed estimation equations by
treating the state as a random process with measurements that are accumulated over time. For objects with deterministic
dynamics, the same fusion equations for static states can be used. When the object state has non-deterministic dynamics,
reconstructing the centralized estimate from the local estimates is usually not possible, but fusion equations based on
means and cross covariances are still optimal with respect to their criteria. It is possible to fuse local estimates to
duplicate the results of centralized tracking but the local estimates are not locally optimal and the weighting matrices
depend on covariance matrices from other sensors.
This paper compares the performance of several algorithms for estimating relative sensor biases when two sets of sensor
tracks from two sensor systems are to be fused to form system tracks. The primary focus of this paper is the algorithms'
performance, particularly in terms of the mean-square estimation error criterion. The efficiency of the algorithms is not
our focus for this study. We are especially interested in three estimation algorithms: (1) the joint track-association/
relative-bias-estimation maximum a posteriori (MAP)
algorithm; (2) the marginal MAP probability density estimation algorithm; and (3) the minimum-variance (MV)
estimation algorithm. Those algorithms rely on the capability of generating and evaluating multiple significant track-to-track
association hypotheses, which may be obtained by any of the recently developed k-best bipartite data assignment
algorithms. Several other algorithms that have been considered in the past will also be discussed.
This paper discusses the problem of numerically evaluating multi-frame, data-association hypotheses in multiple-target
tracking in terms of their a posteriori probabilities. We describe two approaches to the problem: (1) an approach based
on K-best multi-frame data association hypothesis selection algorithms, and (2) a more direct approach to calculating a
posteriori probabilities through Markov-chain-Monte-Carlo (MCMC) or sequential Monte Carlo (SMC) methods. This
paper defines algorithms based on those two approaches and compares their performance, and it discusses their relative
effectiveness, using simple numerical examples.
This paper is generally concerned with multiple target tracking with possibly unresolved or merged measurements, and is motivated by recent advances in signal processing, particularly radar signal processing, that enable the extraction of two or more targets from a single merged detection, under certain conditions. The output of such signal processing can be viewed as a result of a process of estimating an unknown number of objects with no particular meaningful ordering, i.e., mathematically best characterized as a simple finite point process or, equivalently, a random finite set, and a priori and a posteriori statistics can be described as a set of Janossy measures. However, since a sensor generally observes only a subspace of a target state space, it may not be possible to express the target detection results as a full-dimensional probability distribution on a target state space. In this paper, we will try to extend the concept of the Janossy measure density function to express information pertaining only to an instantaneously observable part of target state space, to formulate what we tentatively called the generalized Janossy density function, which may be viewed as an unnormalized or improper probability distribution. Based on this concept of the generalized Janossy measure, or the likelihood function concept, a tracking process can be formulated as a process of recursively updating, by the measurement likelihood functions, the a posteriori probability distribution expressed as a set of Janossy measure density functions.
It can be shown that sufficient statistics maintained by a multiple-hypothesis algorithm for a multiple-target tracking problem are expressed as a set of a posteriori Janossy measures. This fact suggests a new class of multiple target tracking algorithms without generating and evaluating data-to-data association hypotheses. Under a certain set of assumptions, including target-wise independent detection and measurement errors, a Janossy measure representation can be considered to be the symmetrization or scrambling of a posteriori joint target state distribution under a specific data association hypothesis. This paper explores the possibility of using Janossy measures directly to represent a posteriori joint target state distributions, instead of the product expression of the a posteriori joint target state distributions. By doing so, it becomes possible to combine any two data association hypotheses sharing the same number of detected targets they assume, thereby providing an effective method for combining data association hypotheses. When using Janossy measures as a method of representation, we are not forced to maintain the product structure, and hence, at least theoretically, we can combine two data association hypotheses without any approximation. Since we do not require track-wise independence under any hypothesis, this method allows us to treat split or merged measurements in a unified way.
This paper discusses the evaluation of data association hypotheses for a general class of multiple target tracking problems. We assume that the number of targets is unknown, and that given the number of targets, the joint target state distributions form a system of independent, identically distributed (i.i.d.) probability distributions. We are particularly interested in the case where the prior probability distribution of the number of targets is not necessarily Poisson. We will show that the Poisson assumption is not only sufficient but also necessary for the commonly used standard multiplicative hypothesis evaluation formula. Consequently, we claim that the use of the standard multiplicative hypothesis evaluation formula implies, either explicitly or implicitly, the Poisson assumption. We will also examine the Poisson assumption on the number of false alarms in each measurement set.
A general theory of multi-object state-estimation problems, also known as multi-target tracking problems, is presented, using explicit random-set formalism. Probability density functions of random sets, as well as Choquet's capacity functionals, are used to represent random sets, in pursuit of the possibility of such a theory becoming a theoretical foundation of data fusion theory. The theoretical and algorithmic developments over the past three decades in this area are also re-examined in the light of this new formalism, as well as the recent development of correlation-free algorithms that utilize random-set formalism explicitly.
This paper is generally related to analytic methods for evaluating tracking performance, in particular
for predicting track accuracy in dense target environments. A very simple analytic expression
is derived to predict the effects of mis-associations on track accuracy. The paper analyzes an optimal
track-to-measurement assignment algorithm in track continuation phases, i.e., when tracks are well