Performance bounds analysis for hybrid estimation

Abstract

The Cramér-Rao lower bound, CRLB, is important for the performance analysis of a filter. The theoretical CRLB for hybrid estimation requires enumeration of all possible model sequences. In the current paper a computationally tractable estimation of CRLB for hybrid estimation is proposed, which makes use of a subset of sequence hypotheses to approximate the theoretical bound. This approach provides a trade-off between computation and tightness of the estimated CRLB. Thus, the bound is an improvement of the simple ‘conservative’ bound, which only includes a correct model sequence. To compute the estimation of the Cramér-Rao bound for a non-linear system, a Monte Carlo approximate method is introduced. The subset of model sequence hypotheses is achieved through sampling and the expectation integrals are approximated by means of sampling based on Monte Carlo simulation of the particle filtering. The bound is shown a tighter bound than the ‘conservative’ bound for the state estimation by simulation.