Auto-adjust lag particle filter smoothing algorithm for non-linear state estimation

Abstract

A novel particle filter smoothing algorithm for non-linear state estimation is proposed. The key point of this algorithm is that the length of the interval of the particle filter smoothing can be dynamically computed by the difference between the particle and the signal observations, which effectively suppress the phenomenon of increasing error of the system state estimation caused by the particles' weight redistribution when using the fixed smoothing interval method. By considering the signal and the heat bath as an abstract universe based on the particle filter/resampling, a physical analogy is made between the particle filter and the abstract universe, which obeys the second law of thermodynamics. That is to say, when there is no new observation, no matter where the initial state is from, the entropy of the whole system will increase. However, with the coming of the observations this law can be violated. The particle filter behaves like a Maxwellian demon in this physical analogy, returning energy to the heat bath which thus causes entropy to decrease. This is possible due to the steady supply of new information. Then the length of the smoothing interval can be dynamically corrected based on the change of the entropy, so the weight assignments of the particles is optimized, and the performance of the particle filter can be improved. The estimation accuracy of the approach which is verified by simulations is better than the traditional smoothing methods with an affordable computation burden.