Intelligence-Aware Batch Processing for TMA with Bearings-Only Measurements

This paper develops a framework to track the trajectory of a target in 2D by considering a moving ownship able to measure bearing measurements. Notably, the framework allows one to incorporate additional information (e.g., obtained via intelligence) such as knowledge on the fact the target’s trajectory is contained in the intersection of some sets or the fact it lies outside the union of other sets. The approach is formally characterized by providing a constrained maximum likelihood estimation (MLE) formulation and by extending the definition of the Cramér–Rao lower bound (CRLB) matrix to the case of MLE problems with inequality constraints, relying on the concept of generalized Jacobian matrix. Moreover, based on the additional information, the ownship motion is chosen by mimicking the Artificial Potential Fields technique that is typically used by mobile robots to aim at a goal (in this case, the region where the target is assumed to be) while avoiding obstacles (i.e., the region that is assumed not to intersect the target’s trajectory). In order to show the effectiveness of the proposed approach, the paper is complemented by a simulation campaign where the MLE computations are carried out via an evolutionary ant colony optimization software, namely, mixed-integer distributed ant colony optimization solver (MIDACO-SOLVER). As a result, the proposed framework exhibits remarkably better performance, and in particular, we observe that the solution is less likely to remain stuck in unsatisfactory local minima during the MLE computation.

A Likelihood Approach to Bornhuetter–Ferguson Analysis

A new Bornhuetter–Ferguson method is suggested herein. This is a variant of the traditional chain ladder method. The actuary can adjust the relative ultimates using externally estimated relative ultimates. These correspond to linear constraints on the Poisson likelihood underpinning the chain ladder method. Adjusted cash flow estimates were obtained as constrained maximum likelihood estimates. The statistical derivation of the new method is provided in the generalised linear model framework. A related approach in the literature, combining unconstrained and constrained maximum likelihood estimates, is presented in the same framework and compared theoretically. A data illustration is described using a motor portfolio from a Greek insurer.