Algorithm 1 Implementation of Kalman Filtering

Input:  $data$: Received Multiple Signal Sets, m: Number of Signal Sets, n: Signal Length Output: $signal$: Filtered Signals 1:function kalmanfilter($data,m,n$) 2:    for $i=1$ to n do 3:        $s\leftarrow data[1:m,i]$ 4:        $D\leftarrow 1$ 5:        $k\leftarrow 1$ 6:        $x\left[k\right]\leftarrow s\left[k\right]$ 7:        $\mathbf{A}\leftarrow eye\left(D\right)$ 8:        $\mathbf{P}\leftarrow eye\left(D\right)$ 9:        $\mathbf{Q}\leftarrow c\ast eye\left(D\right)$ 10:      $R\leftarrow d$ 11:      for $k=2$ to m do 12:           $x\left[k\right]\leftarrow \mathbf{A}\ast x[k-1]$ 13:           $\mathbf{P}\leftarrow \mathbf{A}\ast \mathbf{P}\ast {\mathbf{A}}^{\top }+\mathbf{Q}$ 14:           $\mathbf{H}\leftarrow eye\left(D\right)$ 15:           $K\leftarrow \mathbf{P}\ast {\mathbf{H}}^{\top }/(\mathbf{H}\ast \mathbf{P}\ast {\mathbf{H}}^{\top }+R)$ 16:           $x\left[k\right]\leftarrow x\left[k\right]+K\ast \left(s\right[k]-\mathbf{H}\ast x[k\left]\right)$ 17:           $\mathbf{I}\leftarrow eye\left(D\right)$ 18:           $\mathbf{P}\leftarrow (\mathbf{I}-K\ast \mathbf{H})+\mathbf{P}$ 19:        end for 20:        $signal\left[i\right]\leftarrow x\left[m\right]$ 21:    end for 22:end function