Enhanced approximation of labeled multi-object density based on correlation analysis

Multi-object density is a fundamental descriptor of a point process and has ability to describe the randomness of number and values of objects, as well as the statistical correlation between objects. Due to its comprehensive nature, it usually has a complicate mathematical structure making the set integral suffer from the curse of dimension and the combinatorial nature of the problem. Hence, efficient and accurate approximations of multi-object density is a key research theme in point process theory or finite set statistics. Conventional approaches usually discard part or all of statistical correlation mechanically in return for computational efficiency, without regard for the actual statistical correlation between objects. In this paper, we propose an enhanced approximation of labeled multi-object (LMO) density by adaptively factorizing the LMO density into densities of several independent subsets according to the actual statistical correlation between object states. Besides, to get a tractable factorization of LMO density, we derive the set marginal density of any subset suitable for the universal labeled RFS, such as the generalized labeled multi-Bernoulli RFS family and its subclasses. The numerical studies show that the proposed method takes into account the simplification of the complicate structure of LMO density and the reservation of necessary correlation at the same time.