The interference of noise

the unreasonable distribution of receivers and target

and the number of receivers all affect the coefficient matrix in the multi-station passive positioning model based on time difference of arrival (TDOA) and frequency difference of arrival (FDOA). Therefore

the coefficient matrix may be ill-conditioned in the actual solution process

which will affect the positioning accuracy to a large extent. A closed-form analytical method based on regularized constrained total least squares (RCTLS) was proposed to further improve the positioning accuracy when the coefficient matrix was ill-conditioned. The method was divided into two steps. In the first step

the positioning model based on RCTLS method was established to solve the positioning problem using TDOA and FDOA

and the regularization parameter was solved based on the criterion of minimizing mean square error. Then

the closed-form analytical solution of the model could be obtained by mathematical operation. The second step was to establish the equation of the estimation error obtained from the first step utilizing the constraint conditions

which was then solved. Finally

the obtained solution was used to modify the estimation results of the first step. Simulation results show that the root mean square error (RMSE) of the proposed method was lower than those of two-stage weighted least squares (TSWLS) and constrained total least squares (CTLS) methods through sacrificing unbiasedness

and the positioning performance was more stable than those of TSWLS and CTLS methods in the case of ill-conditioned coefficient matrix.