Marginal multi-Bernoulli filters: RFS derivation of MHT, JIPDA and association-based MeMBer

Recent developments in random finite sets (RFSs) have yielded a variety of tracking methods that avoid data association. This paper derives a form of the full Bayes RFS filter and observes that data association is implicitly present, in a data structure similar to MHT. Subsequently, algorithms are obtained by approximating the distribution of associations. Two algorithms result: one nearly identical to JIPDA, and another related to the MeMBer filter. Both improve performance in challenging environments.Comment: Journal version at http://ieeexplore.ieee.org/document/7272821. Matlab code of simple implementation included with ancillary file

A Gaussian inverse Wishart PHD Filter using Stochastic Partitioning for Multiple Extended Object Tracking

This thesis deals with the object tracking problem of multiple extended objects. For instance, this tracking problem occurs when a car with sensors drives on the road and detects multiple other cars in front of it. When the setup between the senor and the other cars is in a such way that multiple measurements are created by each single car, the cars are called extended objects. This can occur in real world scenarios, mainly with the use of high resolution sensors in near field applications. Such a near field scenario leads a single object to occupy several resolution cells of the sensor so that multiple measurements are generated per scan. The measurements are additionally superimposed by the sensor’s noise. Beside the object generated measurements, there occur false alarms, which are not caused by any object and sometimes in a sensor scan, single objects could be missed so that they not generate any measurements. To handle these scenarios, object tracking filters are needed to process the sensor measurements in order to obtain a stable and accurate estimate of the objects in each sensor scan. In this thesis, the scope is to implement such a tracking filter that handles the extended objects, i.e. the filter estimates their positions and extents. In context of this, the topic of measurement partitioning occurs, which is a pre-processing of the measurement data. With the use of partitioning, the measurements that are likely generated by one object are put into one cluster, also called cell. Then, the obtained cells are processed by the tracking filter for the estimation process. The partitioning of measurement data is a crucial part for the performance of tracking filter because insufficient partitioning leads to bad tracking performance, i.e. inaccurate object estimates. In this thesis, a Gaussian inverse Wishart Probability Hypothesis Density (GIW-PHD) filter was implemented to handle the multiple extended object tracking problem. Within this filter framework, the number of objects are modelled as Random Finite Sets (RFSs) and the objects’ extent as random matrices (RM). The partitioning methods that are used to cluster the measurement data are existing ones as well as a new approach that is based on likelihood sampling methods. The applied classical heuristic methods are Distance Partitioning (DP) and Sub-Partitioning (SP), whereas the proposed likelihood-based approach is called Stochastic Partitioning (StP). The latter was developed in this thesis based on the Stochastic Optimisation approach by Granström et al. An implementation, including the StP method and its integration into the filter framework, is provided within this thesis. The implementations, using the different partitioning methods, were tested on simulated random multi-object scenarios and in a fixed parallel tracking scenario using Monte Carlo methods. Further, a runtime analysis was done to provide an insight into the computational effort using the different partitioning methods. It emphasized, that the StP method outperforms the classical partitioning methods in scenarios, where the objects move spatially close. The filter using StP performs more stable and with more accurate estimates. However, this advantage is associated with a higher computational effort compared to the classical heuristic partitioning methods

Efficient approximations of the multi-sensor labelled multi-Bernoulli filter

In this paper, we propose two efficient, approximate formulations of the multi-sensor labelled multi-Bernoulli (LMB) filter, which both allow the sensors' measurement updates to be computed in parallel. Our first filter is based on the direct mathematical manipulation of the multi-sensor, multi-object Bayes filter's posterior distribution. Unfortunately, it requires the division of probability distributions and its extension beyond linear Gaussian applications is not obvious. Our second filter is based on covariance intersection and it approximates the multi-sensor, multi-object Bayes filter's posterior distribution using the geometric mean of each sensor's measurement-updated distribution. This filter can be used for distributed fusion under non-linear conditions; however, it is not as accurate as our first filter. In both cases, we approximate the LMB filter's measurement update using an existing loopy belief propagation algorithm, which we adapt to account for object existence. Both filters have a constant complexity in the number of sensors, and linear complexity in both number of measurements and objects. This is an improvement on an iterated-corrector LMB filter, which has linear complexity in the number of sensors. We evaluate both filters' performances on simulated data and the results indicate that the filters are accurate