Enhanced Approximation of Labeled Multi-object Density based on Correlation Analysis
For researchers in point process theory and finite set statistics, this work offers a more nuanced approximation that retains necessary correlations while reducing computational complexity, though it is an incremental improvement over existing factorization methods.
The paper proposes an enhanced approximation of labeled multi-object density that adaptively evaluates object correlations and factorizes the density into independent subsets, balancing computational tractability with correlation preservation. The method derives set marginal densities for GLMB RFS families to achieve tractable factorization.
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 suffering from the curse of dimension and the combinatorial nature of the problem. Hence, the approximation of multi-object density is a key research theme in point process theory or finite set statistics (FISST). Conventional approaches usually discard part or all of statistical correlation mechanically in return for computational efficiency, without considering the real situation of correlation between objects. In this paper, we propose an enhanced approximation of labeled multi-object (LMO) density which evaluates the correlation between objects adaptively and factorizes the LMO density into densities of several independent subsets according to the correlation analysis. Besides, to get a tractable factorization of LMO density, we derive the set marginal density of any subset of the universal labeled RFS, the generalized labeled multi-Bernoulli (GLMB) RFS family and its subclasses. 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.