Algorithm 2: Sensor Refinement

Input: Snxm matrix of time series for n sensors with m samples each, and a set = {r1, r2,…, rn} of reliable sensors.

Output: Set of dislocated sensors and vector Δ of their dislocations from the majority.

←∅

Δ ← {Δi = 0 | 1 ≤ i ≤ n}

m ← {mi = 0 | 1 ≤ i ≤ n}

Pn×n ← {pi,j = 0 | 1 ≤ i,j ≤ n}

// Compute the average squared pairwise-distance between each two sensors.

for i ← 1 to n − 1 do

for j ← i + 1 to n do

// Adjust the valid readings among the reliable sensors.

u ← { sri,k (sri,k ≠ λ) and (srj,k ≠ λ), 1 ≤ k ≤ m };

v ← { srj,k (sri,k ≠ λ) and (srj,k ≠ λ), 1 ≤ k ≤ m };

pi,j ← pj,i ← mean((u − v)2)

end

end

// Compute the median pairwise-distance for each sensor.

for i ← 1 to n do

mi ← median({pi,j|1 ≤ j ≤ n})

end

// The limit to consider a sensor dislocated.

l ← mean(m)

// The dislocated sensors.

← {i | mi > l}

// Compute the dislocation Δi for each reliable sensor.

for i ← 1 to n do

Δi ← median(pi,j − mi)

end

return ( , Δ)