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

It is shown analytically that the multi-target multi-Bernoulli (MeMBer) recursion, proposed by Mahler, has a significant bias in the number of targets. To reduce the cardinality bias, a novel multi- Bernoulli 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.