Evaluating set measurement likelihoods in random-finite-set SLAM

The use of random finite set (RFS) in simultaneous localization and mapping (SLAM) has many advantages over the traditional random-vector-based approaches. These include the consideration of detection and clutter statistics and the circumvention of data association and map management heuristics in the estimator. However, the equations involved in the RFS-SLAM formulation are computationally more complex compared to the vector-based formulation. The evaluation of the set measurement likelihood is one of the computationally complex steps, as it is necessary to consider the likelihood of all possible landmark to measurement correspondences. In general, a brute-force approach in calculating a set measurement likelihood is computationally intractable, and such an approach prevents a RFS-SLAM algorithm to perform in real time. This paper presents a collection of methods for efficiently computing and approximating the set measurement likelihood. The proposed methods are validated in both simulations and using real experimental data.