Recursive Batch Smoother with Multiple Linearization for Single-Beacon Navigation Problem

Abstract

A problem of single-beacon navigation of an autonomous underwater vehicle (AUV) is considered. It is solved in terms of the Bayesian approach and belongs to the class of problems with essential nonlinearity, the posterior probability density function (PDF) of which changes from multi-extremal to single-extremal during its evolution. As a rule, traditional recursive Kalman-type algorithms do not work in this case. To solve the single-beacon navigation problem, an algorithm based on the combined use of recursive and nonrecursive data processing schemes, called a recursive batch smoother with multiple linearization, has been designed. Its main essence lies in the simultaneous use of a bank of batch algorithms – recursive iterative smoothing linearized filters, which allows identifying the point of time at which the PDF becomes single-extremal. After this moment is identified, it becomes possible to switch from the problem solution using a bank of batch algorithms to the solution with a single recursive iterative Kalman filter, thus decreasing the computational complexity. The possibilities of reducing computational complexity by applying methods used in factor graph optimization algorithms are discussed. The advantages of the proposed algorithm are shown by the simulation.