Notes on the Product Multi-Sensor Generalized Labeled Multi-Bernoulli Filter and its Implementation

We previously presented the product multi-sensor generalized labeled multi-Bernoulli filter, which constitutes a multi-object filter for centralized and distributed multi-sensor systems with centralized estimator. It implements the Bayes parallel combination rule for generalized labeled multi-Bernoulli densities, simplifying the NP-hard multidimensional k-best assignment problem of the multi-sensor multi-object update to a polynomial-time k-shortest path problem. This way, the filter allows for efficient, parallelizable, and distributed calculation of the multi-sensor multi-object update, while showing excellent performance. However, the derivation of the filter formulas relies on a well-established approximation of the fundamental multi-sensor Gaussian identity, which was inadvertently not labeled as such in our original article. Thus, on the one hand, we clarify this mistake, discuss its consequences, and present a mathematically clean derivation of the filter yet to establish the claim of Bayes-optimality. On the other hand, we discuss implementation details and present extensive evaluations, that complete the previous publication of the filter.