Distributed Kalman-Consensus Filtering for Sparse Signal Estimation

Algorithm 1

KCIF-PM.

(1) Set Σ_𝑖,1∣0=𝑃₀⁻¹, 𝑥_𝑖,1∣0=𝜇₀.

(2) for  𝑘=1,2,3, … do

(3)  Compute 𝑢_𝑖,𝑘=𝐻^𝑇_𝑖,𝑘𝑅_𝑖,𝑘𝑦_𝑖,𝑘 and 𝑈_𝑖,𝑘=𝐻^𝑇_𝑖,𝑘𝑅_𝑖,𝑘𝐻_𝑖,𝑘+𝜎_𝑖⁻¹Ω_𝑖,𝑘.

(4)  Send [𝑥_{𝑖,𝑘∣𝑘−1},𝑢_𝑖,𝑘,𝑈_𝑖,𝑘] to node 𝑗∈𝒩_𝑖.

(5)  Receive [𝑥_{𝑗,𝑘∣𝑘−1},𝑢_𝑗,𝑘,𝑈_𝑗,𝑘] from node 𝑗∈𝒩_𝑖.

(6)  Fuse local information using (19) and (20).

(7)  Compute measurement update using (21) and (22).

(8)  Compute time update using (23) and (24).

(9) end for