Algorithm 1 Kalman filtering using the recommended measurement noise variance.

Input:       $S[1:length]$: a numeric sequence of sensor data;       $f_R\left(\right)$: a function for a measurement noise variance recommendation;       w: a window size used for computing the measurement noise variance; Output:       $S^{\prime }[1:length]$: a filtered sequence by the Kalman Filter; begin       (1) $i:=1$       (2) $S^{\prime }[1:w]:=S[1:w]$;                   // Use the first w entries of S for $S^{\prime }$ as it is.       (3) while $i+w-1\le length$ do       (4)       $R:=f_R\left(S[i:i+w-1]\right)$;     // Determine R by using the w entries.       (5)       $i:=i+w$;                              // Increase i by w.       (6)       $S^{\prime }[i:i+w-1]:=$ KalmanFilter$\left(S\right[i:i+w-1],R)$;                  // Adjust the next w entries by applying R to the Kalman filter.       (7) end       (8) return $S^{\prime }[1:length]$; end