Algorithm 1 IR-RLS scheme

Input: Measurement data ($r_{i1}$, ${\phi }_i$), error threshold ($\epsilon$),

$$ norm value (p)

Output: Optimal solution ($\widehat{\mathbf{u}}$)

1: Initialization Obtain ${\widehat{\mathbf{u}}}_1$ using Equation (17)

2: while new data is measureddo

3:      Obtain ${\widehat{\mathbf{u}}}_i$ using Equation (21)

4:      while ${\mathbf{e}}^T\mathbf{e}\ge \epsilon$do

5:            Obtain ${\mathbf{C}}_i\left(j\right)$ using Equation (14)

6:            Obtain ${\widehat{\mathbf{u}}}_i\left(j\right)$ using Equation (15)

7:            $j=j+1$

8:      end while

9:      ${\mathbf{B}}_{i+1}={\left[{\mathbf{B}}_i{\mathbf{b}}_{i+1}\right]}^T$

10:      ${\mathbf{w}}_{i+1}={\left[{\mathbf{w}}_i{w}_{i+1}\right]}^T$

11:      $i=i+1$

12: end while