Algorithm 1 Optimization of TDOA based on MPM.

Input: MPM, initial coordinate, $T_0(x_0,y_0)$, error threshold, $T_e$;

Output: Final positioning coordinate, $T(x,y)$;

1: $n\leftarrow 0$;

2: repeat

3:  Get multipath error ${\left({\rho }_m^{A_i-1}\right)}_n$ by substituting $T_n$ into MPM;

4:  ${\left({\rho }^{A_i-1}\right)}_{n+1}={\left({\rho }^{A_i-1}\right)}_n-{\left({\rho }_m^{A_i-1}\right)}_n$;

5:  Obtain $T_{n+1}(x_{n+1},y_{n+1})$ by substituting ${\left({\rho }^{A_i-1}\right)}_n$ into improved Chan-Taylor algorithm;

6: until $|T_{n+1}-T_n|>T_e$;

7: $T\leftarrow T_{n+1}$;

8: return T;