A novel particle filter with noisy input

In nonlinear systems, system inputs play a critical role in achieving control objectives, yet they are highly susceptible to noise during measurement and execution. Ignoring input noise can cause the standard particle filter (SPF) algorithm to produce biased estimates. To address this issue, this study begins by analyzing how input noise contributes to the deviation in the SPF at first. A novel particle filter (PF) then is proposed, designed to be robust against noisy inputs by incorporating information from both process noise and input noise. This approach constructs a new importance density. Drawing inspiration from Gibbs sampling, the method hierarchically and independently samples input and state variables from the new importance density, which accounts for both input and state randomness. The input random variable is eliminated through Monte Carlo independent resampling of the two variables, yielding the final state estimate. To validate the proposed method, three comparative experiments were conducted, evaluating the SPF, the combined particle filter (CPF), and the auxiliary particle filter (APF) algorithms. The results demonstrate that the new PF outperforms SPF in handling nonlinear, non-Gaussian systems with noisy inputs and effectively mitigates deviations caused by input noise.