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

TL;DR

This paper introduces a new Gaussian mixture Bernoulli filter that leverages imprecise and negative information, such as field-of-view constraints, to improve multi-object tracking and state estimation.

Contribution

It presents a systematic method for incorporating field-of-view geometry and negative evidence into Gaussian mixture models, including a novel recursive component splitting approach.

Findings

Effective tracking with natural language inputs.

Enhanced multi-object cardinality estimation.

Demonstrated scalability to up to 100 objects.

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 multi-object 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.