Algorithm 1: DOA estimation via the improved URM algorithm.

Input: The received data X

1. The initial covariance matrix $\widehat{\mathit{C}}$ is calculated according to (9).

2. The initial angle set ${\widehat{\theta }}^{\left(0\right)}=[{\widehat{\theta }}_1^{\left(0\right)},{\widehat{\theta }}_2^{\left(0\right)},\dots ,{\widehat{\theta }}_K^{\left(0\right)}]$ are calculated by (13).

Start iteration

3. Update the array manifold $\widehat{\mathit{A}}$ according to Equation (15).

4. Calculate the non-ideal terms by Equations (19) and (20).

5. Update the covariance matrix $\widehat{\mathit{C}}$ according to (22).

6. Update the new angle set $\left\{{\widehat{\theta }}_1^{\left(l\right)},{\widehat{\theta }}_2^{\left(l\right)},\dots ,{\widehat{\theta }}_K^{\left(l\right)}\right\}$ according to the updated covariance matrix $\widehat{\mathit{C}}$.

7. ${\sum }_{k=1}^K{\parallel {\widehat{\theta }}_k^{(l-1)}-{\widehat{\theta }}_k^{\left(l\right)}\parallel }_2^2$ is less than the preset constant.

Terminate iteration

Output: ${\widehat{\theta }}^{\left(l\right)}=[{\widehat{\theta }}_1^{\left(l\right)},{\widehat{\theta }}_2^{\left(l\right)},...,{\widehat{\theta }}_K^{\left(l\right)}]$