Distributed Asynchronous Fusion Algorithm for Sensor Networks with Packet Losses

Algorithm 1

(1) Initialization: 𝑀^𝑖_𝑘=𝑀₀, 𝑥^𝑖_𝑘+1=𝑥₀.

(2) Obtain local measurements 𝑧_𝑘^𝑖,𝑝.

(3) Broadcast message 𝑚_𝑘^1,𝑖={𝑧_𝑘^𝑖,𝑝} (𝑝=1,2,…,𝑛^𝑖_𝑘) to neighbors.

(4) Receive messages 𝑚_𝑘^1,𝑙, 𝑙∈𝒩_𝑖, from neighbors.

(5) Compute 𝑌^𝑖_𝑘, 𝐻^𝑖_𝑘, 𝑅^𝑖_𝑘, and 𝑉^𝑖_𝑘 by using (9)–(19).

(6) Calculate the local estimate 𝑥^𝑖_𝑘 by using Theorem 1.

(7) Broadcast message 𝑚_𝑘^2,𝑖={𝑀^𝑖_𝑘,𝑥^𝑖_𝑘} to neighbors.

(8) Receive messages 𝑚_𝑘^2,𝑙, 𝑙∈𝒩_𝑖, from neighbors.

(9) Calculate the fusion estimate 𝑥^𝑖_𝑘 by using Theorem 4 and (25).