This paper considers the fusion of multiple estimates of a spatially extended object, where the object extent is modeled as an ellipse that is parameterized by the orientation and semi-axes lengths. For this purpose, we propose a novel systematic approach that employs a distance measure for ellipses, i.e., the Gaussian Wasserstein distance, as a cost function. We derive an explicit expression for the Minimium Mean Gaussian Wasserstein distance (MMGW) estimate. Based on the concept of a MMGW estimator, we develop efficient methods for the fusion of extended target estimates. The proposed fusion methods are evaluated in a simulated experiment and the benefits of the novel methods are discussed.
In this paper, multiple sensor measurement update is studied for a random matrix model. Four different updates are presented and evaluated: three updates based on parametric approximations of the extended target state probability density function and one update based on a Rao–Blackwellized (RB) particle approximation of the state density. An extensive simulation study shows that the RB particle approach shows best performance, at the price of higher computational cost, compared to parametric approximations. The task of tracking extended objects or (partly) unresolvable group targets raises new challenges for both data association and track maintenance. Due to limited sensor resolution capabilities, group targets (i.e., a number of closely spaced targets moving in a coordinated fashion) may show a similar detection pattern as extended objects, namely a varying number of detections whose spread is determined by both the statistical sensor errors as well as the physical extension of the group or extended object. In both cases, tracking and data association under the “one target-one detection” assumption are no longer applicable. This paper deals with the problem of maintaining a track for an extended object or group target with varying number of detections. Herein, object extension is represented by a symmetric positive definite random matrix. A recently published Bayesian approach to tackling this problem is analyzed and discussed. From there, a new approach is derived that is expected to overcome some of the weaknesses the mentioned Bayesian approach suffers from in certain applications. In extended group target tracking, where the extensions of the targets are estimated, target spawning and combination events might have significant implications on the extensions. This paper investigates target spawning and combination events for the case that the target extensions are modeled in a random matrix framework. The paper proposes functions that should be provided by the tracking filter in such a scenario. The results, which are obtained by a gamma Gaussian inverse Wishart implementation of an extended target probability hypothesis density filter, confirms that the proposed functions improve the performance of the tracking filter for spawning and combination events. In algorithms for tracking and sensor data fusion the targets to be observed are usually considered as point source objects; i.e., compared with the sensor resolution their extension is neglected. Due to the increasing resolution capabilities of modern sensors, however, this assumption is often no longer valid as different scattering centers of an object can cause distinct detections when passing the signal processing chain. Examples of extended targets are found in short-range applications (littoral surveillance, autonomous weapons, or robotics). A collectively moving target group can also be considered as an extended target. This point of view is the more appropriate, the smaller the mutual distances between the individual targets are. Due to the resulting data association and resolution conflicts any attempt of tracking the individual objects within the group seems to be no longer reasonable. With simulated sensor data produced by a partly unresolvable aircraft formation the addressed phenomena are illustrated and an approximate Bayesian solution to the resulting tracking problem is proposed. Ellipsoidal object extensions are modeled by random matrices, which are treated as additional state variables to be estimated or tracked. We expect that the resulting tracking algorithms are also relevant for tracking large, collectively moving target swarms.