Split Happens! Imprecise and Negative Information in Gaussian Mixture Random Finite Set Filtering

Abstract

In object tracking and state estimation problems, ambiguous evidence such as imprecise measurements and the absence of detections can contain valuable information and thus be leveraged to further refine the probabilistic belief state. In particular, knowledge of a sensor's bounded field-of-view can be exploited to incorporate evidence of where an object was not observed. This paper presents a systematic approach for incorporating knowledge of the field-of-view geometry and position and object inclusion/exclusion evidence into object state densities and random finite set multi-object cardinality distributions. The resulting state estimation problem is nonlinear and solved using a new Gaussian mixture approximation based on recursive component splitting. Based on this approximation, a novel Gaussian mixture Bernoulli filter for imprecise measurements is derived and demonstrated in a tracking problem using only natural language statements as inputs. This paper also considers the relationship between bounded fields-of-view and cardinality distributions for a representative selection of multiobject distributions, which can be used for sensor planning, as is demonstrated through a problem involving a multi-Bernoulli process with up to one-hundred potential objects.

Trajectory Optimization for Multi-Sensor Multi-Target Search and Tracking with Bearing-Only Measurements

“…According to Equations ( 5) and (23), because the detection range of the onboard sensor is limited, the posterior intensity of undetected targets is related to the positions of the UAVs. As shown in Figure 2, the intensity of unknown targets in the sensor field of view decreases significantly after the update, while the intensity maintains the prior value in the uncovered area.…”

“…Note that utilizing Equation ( 23) in the update of λ u k|k yields a non-Gaussian distribution of the posterior undiscovered target intensity, which cannot be used in the recursion of JPDA-based multi-target tracking filters. This problem can be tackled by the mean-based partition method in [23,24]. In this approach, the prior intensity distribution of undetected targets is split into multiple Gaussian components, and the components with their means inside the sensor FOV are deleted in the posterior intensity, while the others are preserved.…”