Residual and stratified branching particle filters

A class of discrete-time branching particle filters is introduced with individual resampling: If there are Nn particles alive at time n, N0 = N , an ≤ 1 ≤ bn, L̂n+1 is the current unnormalized importance weight for particle i and An+1 = 1 N Nn ∑ i=1 L̂n+1, then weight is preserved when L̂n+1 ∈ (anAn+1, bnAn+1). Otherwise, ⌊ L̂in+1 An+1 ⌋ +ρn offspring are produced and assigned weight An+1, where ρn is a Bernoulli of parameter L̂in+1 An+1 − ⌊ L̂in+1 An+1 ⌋ . The algorithms are shown to be stable with respect to the number of particles and perform better than the bootstrap algorithm as well as other popular resampled particle filters on both tracking problems considered here. Moreover, the new branching filters run significantly faster than these other particle filters on tracking and Bayesian model selection problems.