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 significantbias in the number of targets. To reduce the cardinality bias, anovel multi-Bernoulli approximation to the multi-target Bayes recursionis derived. Under the same assumptions as the MeMBerrecursion, the proposed recursion is unbiased. In addition, a sequentialMonte Carlo (SMC) implementation (for generic models)and a Gaussian mixture (GM) implementation (for linear Gaussianmodels) are proposed. The latter is also extended to accommodatemildly nonlinear models by linearization and the unscentedtransform.