Recursive Marine PCS Estimation with Set-valued Observations via Space-based Imaging Constellations

With the continuously increasing amount of imaging satellites and the improving on-orbit computational capability, self-sustained estimation of marine vessels’ position, course and speed (PCS) becomes feasible through constantly imaging relay. To adapt to the low bit-rate (LBR) limited satellite-to-satellite communication, this paper proposed a recursive stochastic approximation type estimation algorithm based on set-valued observations. Wasserstein distance is utilized in innovations to measure the different between the a priori distribution and the set-valued sampling expectation. With the aid of convexity, convergency of the proposed algorithm can be proved, the convergence rate is studied as well. A numerical simulation of practical example with square grid set-valued observations is given to verify the results, and a comparison with mid-value recursive least-squares (RLS) method is also illustrated.