Given 𝑖 𝑡 | 𝑡 1 , error covariance, ̂ 𝑥 𝑖 𝑡 | 𝑡 1 , previous estimate, consensus
update parameter 𝜀 , and the window size Δ .
 1. Obtain measurement 𝑦 𝑖 𝑡 = 𝐶 ( 𝛾 𝑖 𝑡 ) 𝑥 𝑡 + 𝜐 𝑖 𝑡 + 𝑧 𝑖 𝑡 , 𝑖 = 1 , , 𝑁 .
 2. For each measurement solve L1-norm optimization problem,
   reject outliers as given in (3.5) and then obtain the trimmed
   measurements: ̂ 𝑦 𝑖 𝑡 = 𝑦 𝑖 𝑡 ̂ 𝑧 𝑖 𝑡 .
 3. Calculate the mode probability P r ( 𝛾 𝑖 𝑡 ̂ 𝑦 𝑖 𝑡 Δ 𝑡 ) .
   Given P r ( 𝛾 𝑖 𝑡 Δ ̂ 𝑦 𝑖 𝑡 Δ ) ,
   For 𝑠 = 𝑡 Δ 𝑡
    Evaluate measurement likelihood for ̂ 𝑦 𝑖 𝑠 .
    Evaluate the Bayesian recursion (3.8)-(3.9).
   End
   Decide the channel mode ̂ 𝛾 𝑖 𝑡 using threshold testing.
 4. Compute contribution term of information state and matrix
   such that
           𝑢 𝑖 𝑡 = ( 𝐶 𝑖 𝑡 ( ̂ 𝛾 𝑖 𝑡 ) ) 𝑇 ( 𝑅 𝑖 ) 1 ̂ 𝑦 𝑖 𝑡 ,
          𝑈 𝑖 𝑡 = ( 𝐶 𝑖 𝑡 ( ̂ 𝛾 𝑖 𝑡 ) ) 𝑇 ( 𝑅 𝑖 ) 1 𝐶 𝑖 𝑡 ( ̂ 𝛾 𝑖 𝑡 ) .
 5. Broadcast message 𝑚 𝑖 𝑡 = ( 𝑢 𝑖 𝑡 , 𝑈 𝑖 𝑡 , ̂ 𝑥 𝑖 𝑡 | 𝑡 1 ) to neighbors in 𝐿 𝑖 .
 6. Collect messages 𝑚 𝑟 𝑡 = ( 𝑢 𝑟 𝑡 , 𝑈 𝑟 𝑡 , ̂ 𝑥 𝑟 𝑡 | 𝑡 1 ) from neighbors.
 7. Aggregate the information states and matrices of neighbors
   including node 𝑖 : 𝐽 𝑖 = 𝐿 𝑖 { 𝑖 } :
          𝑔 𝑖 𝑡 = 𝑟 𝐽 𝑖 𝑢 𝑟 𝑡 , 𝑆 𝑖 𝑡 = 𝑟 𝐽 𝑖 𝑈 𝑟 𝑡 .
 8. Compute the Kalman-Consensus estimate:
           ( 𝑀 𝑖 𝑡 ) 1 = ( Φ 𝑖 𝑡 𝑡 1 ) 1 + 𝑆 𝑖 𝑡 ,
̂ 𝑥 𝑖 𝑡 𝑡 = ̂ 𝑥 𝑖 𝑡 𝑡 1 + 𝑀 𝑖 𝑡 ( 𝑔 𝑖 𝑡 𝑆 𝑖 𝑡 ̂ 𝑥 𝑖 𝑡 | 𝑡 1 𝑀 ) + 𝜀 𝑖 𝑡 1 + 𝑀 𝑖 𝑡 𝑟 𝐽 𝑖 ( ̂ 𝑥 𝑟 𝑡 𝑡 1 ̂ 𝑥 𝑖 𝑡 𝑡 1 ) .
   Prediction stage
Φ 𝑖 𝑡 + 1 𝑡 𝐴 𝑀 𝑖 𝑡 𝐴 𝑇 + 𝑄 ,
           ̂ 𝑥 𝑖 𝑡 + 1 𝑡 𝐴 ̂ 𝑥 𝑖 𝑡 𝑡 .
Algorithm 1: Robust distributed fusion algorithm for node 𝑖 .