Particle Filter for Randomly Delayed Measurements with Unknown Latency Probability

. 2020 Oct 6;20(19):5689. doi: 10.3390/s20195689

Algorithm 1. Modified particle filter.

$[{x_{k}^{i}, w_{k}^{i}}_{i = 1}^{N_{s}}] : = SIR [{x_{k - N : k}^{i}, w_{k - 1}^{i}}_{i = 1}^{N_{s}}, \hat{p}, y_{k}]$

for $i = 1 : N_{s}$
- –
  Draw $x_{k}^{i} \sim q (x_{k} | x_{0 : k - 1}^{i}, y_{1 : k})$
- –
  Compute the importance weight $w_{k}^{i}$ according to (13) and (18)
- –
  Normalize the importance weight: $w_{k}^{i} : = w_{k}^{i} / SUM [{w_{k}^{i}}_{i = 1}^{N_{s}}]$
end for
Resample the particles at each step
- –
  $[{x_{k}^{i}, w_{k}^{i}}_{i = 1}^{N_{s}}] : = RESAMPLE [{x_{k}^{i}, w_{k}^{i}}_{i = 1}^{N_{s}}]$