Algorithm 1: The AOA-based localization method based on bias compensation

Step 1: Set $B_1$ as an identity matrix and solve the optimization problem using (10). A rough value $\theta$ can be obtained.

Step 2: Reformulate the weighting matrix W with the rough value $\theta .$

Step 3: Construct constraints based on the (13)–(15).

Step 4: Get the closed-form ${\tilde{u}}_0$ of the localization problem using (16) based on the SDP method.

Step 5: Based on the closed-form solution, construct a constrained optimization equation based on the Taylor expansion as (25) shows.

Step 6: Use Lagrange multiplier technology to get the bias $∆u$ as (27) shows.

Step 7: Revise the result using (29) and an improved result can be obtained.