An IMM Extension of RBPMF for Terrain-Referenced Navigation Under Radar Return Ambiguity

Terrain-referenced navigation (TRN) relies on nonlinear terrain matching, which can produce multimodal position uncertainty that should be retained during estimation. Accuracy can deteriorate when the relative probabilities of ground and canopy returns vary over time because a fixed measurement model cannot adapt to the changing return regime. To address this problem, an interacting multiple-model (IMM) extension of the Rao-Blackwellized point-mass filter (RBPMF) is developed, yielding an IMM-RBPMF that adapts between measurement hypotheses while retaining the non-Gaussian navigation posterior. The extension uses grid-resolved posterior mixing to remap complete mode-conditioned RBPMF representations onto a common grid; nonlinear-state point masses are combined using global IMM interaction probabilities, whereas conditional Gaussian components are combined using state-dependent local responsibilities. Monte Carlo simulations over rough and rough-flat-rough terrain compare the proposed filter with single-model and fixed-mixture RBPMFs. Relative to the best baseline for each metric, the filter reduces overall horizontal-position root-mean-square error (RMSE) by up to 44% and altitude RMSE by 53%, demonstrating improved robustness to ambiguous radar returns and weakly informative terrain.