We study wireless indoor positioning systems where multiple synchronized infrastructure devices simultaneously receive signals from an object of interest whose arrival times are measured. The positioning performance is degraded by unresolvable channel multipath and non-line-of-sight (NLOS) reflctions which cause a bias in the time difference of arrival (TDOA) measurements. In order to reduce the negative effect of multi-path, a Multi-Path Map (MPM) method based on spatial domain modeling principle in the reverse positioning framework with good robustness is proposed. Meanwhile, an improved non-linear iterative algorithm with height component constrained which reduces the complexity is introduced to calculate the coordinates so that the performance of the MPM can be verified. By using the MPM measurements as pre-calibration information to compensate the TDOA observed value, the accuracy of the cooperative location based on a UWB device is 6.45 cm, which achieves 63% improvement than that of none MPM used.