Edwin A. Bloem

Probabilistic data association avoiding track coalescence

For the problem of tracking multiple targets, the joint probabilistic data association (JPDA) approach has shown to be very effective in handling clutter and missed detections. The JPDA, however, tends to coalesce neighboring tracks and ignores the coupling between those tracks. Fitzgerald (1990) has shown that hypothesis pruning may be an effective way to prevent track coalescence. Unfortunately, this process leads to an undesired sensitivity to clutter and missed detections, and it does not support any coupling. To improve this situation, the paper follows a novel approach to combine the advantages of JPDA coupling, and hypothesis pruning into new algorithms. First, the problem of multiple target tracking is embedded into one filtering for a linear descriptor system with stochastic coefficients. Next, for this descriptor system, the exact Bayesian and new JPDA filters are derived. Finally, through Monte Carlo simulations, it is shown that these new PDA filters are able to handle coupling and are insensitive to track coalescence, clutter, and missed detections.

Exact Bayesian and particle filtering of stochastic hybrid systems

The standard way of applying particle filtering to stochastic hybrid systems is to make use of hybrid particles, where each particle consists of two components, one assuming Euclidean values, and the other assuming discrete mode values. This paper develops a novel particle filter (PF) for a discrete-time stochastic hybrid system. The novelty lies in the use of the exact Bayesian equations for the conditional mode probabilities given the observations. Therefore particles are needed for the Euclidean valued state component only. The novel particle filter is referred to as the interacting multiple model (IMM) particle filter (IMMPF) because it incorporates a filter step which is of the same form as the interaction step of the IMM algorithm. Through Monte Carlo simulations, it is shown that the IMMPF has significant advantage over the standard PF, in particular for situations where conditional switching rate or conditional mode probabilities have small values

Particle filtering for stochastic hybrid systems

The standard way of applying particle filtering to hybrid systems is to make use of hybrid particles, where each particle consists of two components, one assuming Euclidean values, and the other assuming discrete mode values. This paper develops a novel particle filter for a discrete-time stochastic hybrid system. The novelty lies in the use of the exact Bayesian equations for the conditional mode probabilities given the observations. Therefore particles are needed for the Euclidean valued state component only. The novel particle filter is referred to as the interacting multiple model (IMM) particle filter because it has a switching/interaction step which is of the same form as the switching/interaction step of the IMM algorithm. Through Monte Carlo simulations, it is shown that the IMM particle filter has significant advantage over the standard particle filter, in particular for situations where conditional switching rate or conditional mode probabilities have small values.

Combining IMM and JPDA for tracking multiple maneuvering targets in clutter

The paper combines IMM and JPDA for tracking of multiple possibly maneuvering targets in case of clutter and possibly missed measurements while avoiding sensitivity to track coalescence. The effectiveness of the filter is illustrated through Monte Carlo simulations.

Joint IMMPDA particle filter

For the problem of tracking multiple manoeu- vering targets in clutter and missing measurements the pa- per develops a Joint IMMPDA type of particle filter and compares this with other IMMJPDA based filters through Monte Carlo simulation for a simple example.

Bayesian tracking of two possibly unresolved maneuvering targets

The paper studies the problem of maintaining tracks of two targets that may maneuver in and out formation flight, whereas the sensor and measurement extraction chain produces false and possibly unresolved or missing measurements. If the possibility of unresolved measurements is not modelled then it is quite likely that either the two tracks coalesce or that one of the two tracks diverges on false measurements. In literature a robust measurement resolution model has been incorporated within an interacting multiple model/multiple hypothesis tracking (IMM/MHT) track maintenance setting. A straightforward incorporation of the same model within an IMM and probabilistic data association (PDA)-like hypothesis merging approach suffers from track coalescence. In order to improve this situation, the paper develops a track-coalescence avoiding hypotheses merging version for the two target problem considered. Through Monte Carlo simulations, the novel filters are compared with applying hypotheses merging approaches that ignore the possibility of unresolved measurements or track-coalescence.

Exact Bayesian filter and joint IMM coupled PDA tracking of maneuvering targets from possibly missing and false measurements

This paper represents the problem of tracking multiple maneuvering targets from possibly missing and false measurements as one of filtering for a jump-linear descriptor system with stochastic i.i.d. coefficients. This particular representation serves as an instrument in the characterization of the exact Bayesian filter. Subsequently, novel finite dimensional filter algorithms are developed through introducing approximations to the exact Bayesian solution. One filter approximation assumes conditionally Gaussian density of the joint target state given the joint target maneuver mode and the algorithm is referred to as joint IMM coupled PDA (JIMMCPDA). The specialty of this filter algorithm is that both the IMM step and the PDA step are performed jointly over the modes and states of all targets. Subsequently, the CPDA track-coalescence-avoiding hypothesis pruning approach of [Blom & Bloem (2000). Probabilistic data association avoiding track coalescence. IEEE Transactions of Automatic Control, 45, 247-259] is extended to bring the joint target modes into account. The resulting filter algorithm is referred to as track-coalescence-avoiding joint IMM coupled PDA. The two novel algorithms are compared to IMMJPDA and IMMPDA through Monte Carlo simulations.

Tracking multiple maneuvering targets by joint combinations of IMM and PDA

For the problem of tracking multiple maneuvering targets in false and missing measurements the paper develops a characterization of the exact Bayesian equations of the conditional density. Since in these exact equations both IMM and PDA are jointly performed over all targets, we also develop two joint IMMPDA types of filters and compare them with other combinations of IMM and JPDA through Monte Carlo simulation for a simple example.

Joint Integrated PDA Avoiding Track Coalescence under Non-Homogeneous Clutter Density

Joint PDA has proven to be effective in tracking multiple targets from measurements amidst clutter and missed detections. Joint IPDA has built upon this by including the probability of target existence as a track quality measure to enable automatic tracking and track maintenance. Both JPDA and JIPDA suffer from the problem of track coalescence of near target tracks. JPDA* is an extension of JPDA which avoids coalescence by pruning specific permutation hypotheses prior to hypothesis merging. Following JPDA*s descriptor system derivation, this paper developes JIPDA*, an extension of JIPDA which avoids track coalescence. JIPDA* updates the probability of target existence as the track quality measure. An initial simulation study corroborates the effectiveness of this approach for tracking crossing targets in heavy clutter

JIPDA: Automatic target tracking avoiding track coalescence

Joint integrated probabilistic data association (JIPDA) is effective in automatic multitarget tracking in an environment of false and missing measurements. However, JIPDA suffers from coalescence of closely spaced tracks. This paper develops a coalescence-avoiding version of JIPDA, which is named JIPDA. To accomplish this, the descriptor system approach is used that has previously been used for the development of JPDA, i.e., a coalescence-avoiding JPDA version. The effectiveness of JIPDA is demonstrated through simulations.