The Cardinality Balanced Multi-Target Multi-Bernoulli Filter and Its Implementations

TLDR

The study derives a novel multiBernoulli approximation to the multi‑target Bayes recursion to reduce cardinality bias. The authors develop this approximation and implement it with a sequential Monte Carlo method for generic models and a Gaussian‑mixture approach for linear Gaussian models, extended to mildly nonlinear cases via linearization and the unscented transform. Analytical results show that the original MeMBer recursion is biased in target count, whereas the proposed recursion is unbiased under the same assumptions.

Abstract

It is shown analytically that the multitarget multiBernoulli (MeMBer) recursion, proposed by Mahler, has a significant bias in the number of targets. To reduce the cardinality bias, a novel multiBernoulli approximation to the multi-target Bayes recursion is derived. Under the same assumptions as the MeMBer recursion, the proposed recursion is unbiased. In addition, a sequential Monte Carlo (SMC) implementation (for generic models) and a Gaussian mixture (GM) implementation (for linear Gaussian models) are proposed. The latter is also extended to accommodate mildly nonlinear models by linearization and the unscented transform.