Iterative Mixture Component Pruning Algorithm for Gaussian Mixture PHD Filter

Algorithm 1

Iterative pruning algorithm.

(1)  normalize 𝑤₁,…,𝑤_𝑀 by formula (20).

(2)   𝑡=0.

(3)   𝑡=𝑡+1.

(4)  for   𝑖=1,…,𝑛   do

(5)         for   𝑗=1,…,𝑀   do

(6)         compute 𝜔_𝑗𝑧_𝑖 by formula (28).

(7)         end for

(8)  end for

(9)  for   𝑗=1,…,𝑀   do

(10)   compute 𝜔_𝑗 by formula (31).

(11) end for

(12) for   𝑗=1,…,𝑀   do

(13)   compute 𝑤_𝑗 by formula (34).

(14) end for

(15) for   𝑗=1,…,𝑀   do

(16)       if   𝑤_𝑗<0   do

(17)       for   𝑙=𝑗,…,𝑀−1   do

(18)       𝑤_𝑙=𝑤_𝑙+1.

(19)       𝑚^(𝑙)=𝑚^(𝑙+1).

(20)       𝑃^(𝑙)=𝑃^(𝑙+1).

(21)       end for

(22)       𝑗=𝑗−1.

(23)       𝑀=𝑀−1.

(24)       else  do

(25)       compute 𝑚^(𝑗) by formula (35).

(26)       compute 𝑃^(𝑗) by formula (36).

(27)       end if

(28) end for

(29) normalize 𝑤₁,…,𝑤_𝑀;

(30) compute 𝜆 by formula (27);

(31) if   log𝑝(𝜃(𝑡)∣𝑍)−log𝑝(𝜃(𝑡−1)∣𝑍)>𝜀⋅log𝑝(𝜃(𝑡−1)∣𝑍)   do

(32)   goto step  3;

(33) end if.