Uphill resampling for particle filter and its implementation on graphics processing unit.

We introduce a new resampling method, named Uphill, that is free from numerical instability and suitable for parallel implementation on graphics processing unit (GPU). Common resampling algorithms such as Systematic suffer from numerical instability when single precision floating point numbers are used. This is due to cumulative summation over the weights of particles when the weights differ widely or the number of particles is large. The Metropolis and Rejection resampling algorithms do not suffer from numerical instability as they only calculate the ratios of weights pairwise rather than perform collective operations over the weights. They are more suitable for the GPU implementation of the particle filter. However, they undergo non-coalesced global memory access patterns which cause their speed deteriorate rapidly as the number of particles gets large. Uphill also does not suffer from numerical instability but, experiences the same non-coalesced global memory access problem with Metropolis and Rejection. We introduce its faster version named Uphill-Fast which eliminates this problem. We make comparisons of Uphill and Uphill-Fast with the Systematic, Metropolis, Metropolis-C2 and Rejection resampling methods with respect to quality and speed. We also compare them on a highly non-linear system. Uphill-Fast runs faster and attains similar quality, in terms of RMSE, in comparison with Metropolis and Rejection when the number of particles is very large. Uphill-Fast runs with roughly same speed as Metropolis-C2 with better variance and MSE when the number of particles is very large.