Critical analysis of the particle flow filter

The particle flow filter (PFF) has been claimed to have superior performance in terms of accuracy and computational speed compared with existing nonlinear filters. We carefully examine the PFF algorithm and homotopy used in the PFF. We find three problems in the formulation of the PFF. First, homotopy used in the PFF violates the definition of homotopy. Second, a posterior probability density function (pdf) p(x, λ), is used in the Fokker-Planck equation (FPE) with respect to a parameter λ. A prediction pdf should be used in the FPE, not a posterior pdf. Third, a given measurement is processed a number of times in a loop over the parameter λ and the correlation between a particle state and measurement noise is ignored. We analyze the PFF using the range-azimuth nonlinear filtering problem and calculate the cross-correlation coefficients between the particle states and measurement noise to show high values of cross-correlation coefficients.