A Quantitative Analysis on Two RFS-Based Filtering Methods for Multicell Tracking

Algorithm 1

Read image 𝐲_𝑘.

Given the posterior density 𝜔^(𝑖)_𝑘−1,𝑚^(𝑖)_𝑘−1,𝑃^(𝑖)_𝑘−1^𝐽𝑘−1_𝑖=1, the birth density 𝜔^(𝑖)_𝛾,𝑘,𝑚^(𝑖)_𝛾,𝑘,𝑃^(𝑖)_𝛾,𝑘^𝐽𝛾_𝑖=1, and the cell

measurement set 𝐙_𝑘 calculated by detection module.

Step  1. Prediction for birth cells

 𝑖=0.

 for   𝑗=1,…,𝐽_𝛾,𝑘

     𝑖∶=𝑖+1.

     𝜔^(𝑖)_{𝑘∣𝑘−1}=𝜔^(𝑗)_𝛾,𝑘, 𝑚^(𝑖)_{𝑘∣𝑘−1}=𝑚^(𝑗)_𝛾,𝑘, 𝑃^(𝑖)_{𝑘∣𝑘−1}=𝑃^(𝑗)_𝛾,𝑘.

 end

Step  2. Prediction for existing cells

 for 𝑗=1,…,𝐽_𝑘−1

       𝑖∶=𝑖+1

      𝜔^(𝑖)_{𝑘∣𝑘−1}=𝑝_𝑆,𝑘𝜔^(𝑗)_𝑘−1, 𝑚^(𝑖)_{𝑘∣𝑘−1}=𝐹_𝑘−1𝑚^(𝑗)_𝑘−1, 𝑃^(𝑖)_{𝑘∣𝑘−1}=𝑄_𝑘−1+𝐹_𝑘−1𝑃^(𝑗)_𝑘−1𝐹^𝑇_𝑘−1.

 end

  𝐽_{𝑘∣𝑘−1}=𝑖.

Step  3. Construction of update module

  for   𝑗=1,…,𝐽_{𝑘∣𝑘−1}

     𝜂^(𝑗)_{𝑘∣𝑘−1}=𝐻_𝑘𝑚^(𝑗)_{𝑘∣𝑘−1}, 𝑆_𝑘^(𝑗)=𝑅_𝑘+𝐻_𝑘𝑃^(𝑗)_{𝑘∣𝑘−1}𝐻^𝑇_𝑘,

     𝐾_𝑘^(𝑗)=𝑃^(𝑗)_{𝑘∣𝑘−1}𝐻^𝑇_𝑘[𝑆_𝑘^(𝑗)]⁻¹, 𝑃^(𝑗)_{𝑘∣𝑘−1}=[𝐼−𝐾_𝑘^(𝑗)𝐻_𝑘]𝑃^(𝑗)_{𝑘∣𝑘−1}.

 end

Step  4. Update module

 for   𝑗=1,…,𝐽_{𝑘∣𝑘−1}

      𝜔_𝑘^(𝑗)=(1−𝑝_𝐷,𝑘)𝜔^(𝑗)_{𝑘∣𝑘−1}, 𝑚_𝑘^(𝑗)=𝑚^(𝑗)_{𝑘∣𝑘−1}, 𝑃_𝑘^(𝑗)=𝑃^(𝑗)_{𝑘∣𝑘−1}.

 end

 𝑙∶=0.

 for each 𝐳∈𝐙_𝑘

    𝑙∶=𝑙+1.

   for 𝑗=1,…,𝐽_{𝑘∣𝑘−1}

     𝜔^{(𝑙𝐽𝑘∣𝑘−1}_𝑘^+𝑗)=𝑝_𝐷,𝑘𝜔^(𝑗)_{𝑘∣𝑘−1}𝑁(𝐳;𝜂^(𝑗)_{𝑘∣𝑘−1},𝑆_𝑘^(𝑗)), 𝑚^{(𝑙𝐽𝑘∣𝑘−1}_𝑘^+𝑗)=𝑚^(𝑗)_{𝑘∣𝑘−1}+𝐾_𝑘^(𝑗)(𝐳−𝜂^(𝑗)_{𝑘∣𝑘−1}),

     𝑃^{(𝑙𝐽𝑘∣𝑘−1}_𝑘^+𝑗)=𝑃^(𝑗)_𝑘∣𝑘.

   end

    𝜔^{(𝑙𝐽𝑘∣𝑘−1}_𝑘^+𝑗)𝜔∶=^{(𝑙𝐽𝑘∣𝑘−1𝑘+𝑗)}𝜅_𝑘(𝐳)+∑^{𝐽𝑘∣𝑘−1}_𝑖=1𝜔^{(𝑙𝐽𝑘∣𝑘−1}_𝑘^+𝑖), for 𝑗=1,…,𝐽_{𝑘∣𝑘−1}.

 end

Step  5. Pruning and merging module

Output  𝜔_𝑘^(𝑖),𝑚_𝑘^(𝑖),𝑃_𝑘^{(𝑖)𝐽𝑘}_𝑖=1.