Hans Driessen

Brief Hybrid state estimation: a target tracking application

In this paper we present a framework in which the general hybrid filtering or state estimation problem can be formulated. The problem of joint tracking and classification can be formulated in this framework as well as the problem of multiple model filtering with additional mode observations. In this formulation the state vector is decomposed into a continuous (kinematic) component and a discrete (mode and/or class) component. We also suppose that there are two types of measurements. Measurements that are related to the continuous part of the state (e.g. bearing and range measurements in a radar application) and measurements that are related to the discrete part of the state (e.g. radar cross-section measurements). We will derive an optimal filter for this problem and will show how this filter can be implemented numerically.

Mixed Labelling in Multitarget Particle Filtering

The so-called mixed labelling problem inherent to a joint state multitarget particle filter implementation is treated. The mixed labelling problem would be prohibitive for track extraction from a joint state multitarget particle filter. It is shown, using the theory of Markov chains, that the mixed labelling problem in a particle filter is inherently self-resolving. It is also shown that the factors influencing this capability are the number of particles and the number of resampling steps. Extensive quantitative analyses of these influencing factors are provided.

A particle-filter-based detection scheme

In this paper, we present a new result that can be used for detection purposes. We show that when estimating the a posteriori probability density of a possible signal in noise by means of a particle filter, the output of the filter, i.e., the unnormalized weights, can be used to approximately construct the likelihood ratio, which arises in many different detection schemes.

Particle filter-based track before detect algorithms

In this paper we will give a general system setup, that allows the formulation of a wide range of Track Before Detect (TBD) problems. A general basic particle filter algorithm for this system is also provided. TBD is a technique, where tracks are produced directly on the basis of raw (radar) measurements, e.g. power or IQ data, without intermediate processing and decision making. The advantage over classical tracking is that the full information is integrated over time, this leads to a better detection and tracking performance, especially for weak targets. In this paper we look at the filtering and the detection aspect of TBD. We will formulate a detection result, that allows the user to implement any optimal detector in terms of the weights of a running particle filter. We will give a theoretical as well as a numerical (experimental) justification for this. Furthermore, we show that the TBD setup, that is chosen in this paper, allows a straightforward extension to the multi-target case. This easy extension is also due to the fact that the implementation of the solution is by means of a particle filter.

Integrated tracking and classification: an application of hybrid state estimation

In this paper we present a framework in which the general hybrid filtering or state estimation problem can be formulated. The problem of joint tracking and classification can be formulated in this framework as well as the problem of multiple model filtering with additional mode observations. In this formulation the state vector is decomposed into a continuous (kinematic) component and a discrete (mode and/or class) component. We also suppose that there are two types of measurements. Measurements that are related tot eh continuous part of the state (e.g. bearing and range measurements in a radar application) and measurements that are related to the discrete part of the state (e.g. radar cross section measurements). We will derive an optimal filter for this problem and will show how this filter can be implemented numerically.

Results on the modified Riccati equation: target tracking applications

The modified Riccati equation is studied in this paper. This equation has been associated with tracking a target under measurement origin uncertainty. We consider the case of tracking a target with a detection probability less than one. This case has received attention recently, especially in relationship with Cramer Rao bounds. Results on this equation have been derived. We compare these results and point out their importance for performance assessment for target tracking.

The mixed labeling problem in multi target particle filtering

In this paper the so called mixed labeling problem inherent, or at least thought to be inherent to a joint state multi target particle filter implementation is treated. The mixed labeling problem would be prohibitive for track extraction from a joint state multi target particle filter. It is shown and proven using the theory of Markov chains, that the mixed labeling problem is inherently self-resolving in a particle filter. It is also shown that the factors influencing this capability are the number of particles and the number of resampling steps.

On tracking performance constrained MFR parameter control

An efficient Multi Function Radar (MFR) parameter control for single target tracking would minimize the amount of radar resources required for meeting the requirements on tracking performance. In this paper the problem of finding this eficient MFR parameter control is formulated as a constrained minimization problem. No explicit analytical solution to the resulting constrained minimization problem is available (yet). Instead, the resource scheduling and tracking pe rformance results are presented that result from solving it numerically. The two examples for which numerical results are given illustrate the wide range of constraints on tracking performance that can be applied. The insight that can be gained from using this method will in turn be of use in designing, improving, or validating practical algorithms for MFR parameter control.

Multitarget Tracking With Multiscan Knowledge Exploitation Using Sequential MCMC Sampling

Exploitation of external knowledge through constrained filtering guarantees improved performance. In this paper we show how multiscan processing of such information further enhances the track accuracy. This can be achieved using a Fixed-Lag Smoothing procedure, and a proof of improvement is given in terms of entropy reduction. Such multiscan algorithm, i.e., named KB-Smoother (“Fixed-lag smoothing for Bayes optimal exploitation of external knowledge,” F. Papi , Proc. 15th Int. Conf. Inf. Fusion, 2012) can be implemented by means of a SIR-PF. In practice, the SIR-PF suffers from depletion problems, which are further amplified by the Smoothing technique. Sequential MCMC methods represent an efficient alternative to the standard SIR-PF approach. Furthermore, by borrowing techniques from genetic algorithms, a fully parallelizable multitarget tracker can be defined. Such approach, i.e., named Interacting Population (IP)-MCMC-PF, was first introduced in “Multitarget tracking with interacting population-based MCMC-PF” (M Bocquel , Proc. 15th Int. Conf. Inf. Fusion, 2012). In this paper, we propose and analyze a combination of the KB-Smoother along with the IP-MCMC-PF. As will be shown, the combination of the two methods yields an improved track accuracy while mitigating the loss of particles diversity. Simulation analyses for single and multitarget tracking scenarios confirm the benefits of the proposed approach.

Threat-based sensor management for target tracking

A sensor management scheme that focuses on managing the uncertainty in the threat level of targets is proposed. The scheme selects the best sensing mode such that the uncertainty in the threat level of targets is minimized. The main advantage of the proposed scheme is that it opens the possibility for incorporation of the operational context when performing Bayes-optimal sensor management. Different aspects of threat can be meaningfully aggregated making this flexible approach a favorite choice for multifunctional systems. The proposed scheme is demonstrated in simulated scenarios, both simple and advanced, where the data association problem is taken into account. In the multitarget example, the proposed scheme outperforms the other schemes considered in this manuscript, both naive and adaptive. The proposed scheme can be used in target tracking applications, such as air traffic management or area surveillance.