Efficient Radio Map Construction Based on Low-Rank Approximation for Indoor Positioning

Algorithm 1

The algorithm of smoothing low-rank completion model.

Input:

   The sparse measurement matrix 𝐵;

   The estimated rank of the measurement matrix 𝐾;

   The model weights 𝜆 and 𝜂;

   The error threshold for the iteration 𝜀;

Output:

   The constructed measurement matrix 𝑋;

 (1) Initialize 𝐿, 𝑅 randomly, denoted by 𝐿₀, 𝑅₀.

 (2) Calculate the objective function 𝐹(𝐿₀,𝑅₀).

 (3) Fix 𝐿 and optimize 𝑅, the result is denoted by 𝑅₁.

 (4) Fix 𝑅 and optimize 𝐿, the result is denoted by 𝐿₁.

 (5) Calculate the objective function 𝐹(𝐿₁,𝑅₁).

 (6) If |𝐹(𝐿₁,𝑅₁)−𝐹(𝐿₀,𝑅₀)|/|𝐹(𝐿₁,𝑅₁)|>𝜀,

    set 𝐿₀=𝐿₁, 𝑅₀=𝑅₁ and go to (2).

 (7) return 𝑋=𝐿𝑅^𝑇.