# Multi-object Tracking in Unknown Detection Probability with the PMBM Filter

## TL;DR

This paper introduces an adaptive method for joint multi-object tracking and detection probability estimation using the PMBM filter, addressing uncertainties in detection probability in dynamic scenarios.

## Contribution

It develops a novel approach to estimate detection probability online within the PMBM filter framework, with closed-form solutions for improved accuracy.

## Key findings

- Effective detection probability estimation demonstrated in simulations
- Outperforms existing methods in accuracy and robustness
- Closed-form solutions enable practical implementation

## Abstract

This paper focuses on the joint multi-object tracking (MOT) and the estimate of detection probability with the \emph{Poisson multi-Bernoulli mixture} (PMBM) filter. In a majority of multi-object scenarios, the knowledge of detection probability is usually uncertain, which is often estimated offline from the training data. In such cases, online filtering is not allowed or believable, otherwise, significate parameter mismatch will result in biased estimates (state and cardinality of objects). Consequently, the ability of adaptively estimating the detection probability is essential in practice. In this paper, we detail how the detection probability can be estimated accompanied with the state estimates. Besides, closed-form solutions to the proposed method are derived by approximating the intensity of Poisson random finite set (RFS) to a Beta-Gaussian mixture form and density of Bernoulli RFS to a single Beta-Gaussian form. Simulation results show the effectiveness and superiority of the proposed method.