Abstract: The robust estimation based on equivalent weights keeps the outstanding properties of Least Squares (LS) adjustment in processing normal observations. Nevertheless, its robustness is highly related to the initial values. If the LS estimates, which are insensitive to outliers, are used as initial values it will certainly impact the robust characteristics of equivalent weight robust estimates. Comparatively, the Least Median (LM) estimates are much robust than LS estimates, but they are computed only with parts of observables, and many available observables are not used. In this paper, we put forwards the median parameter robust estimation and present an approximate method to estimate its breakdown point in finite observation cases. By integrating the advantages of median parameter estimation with equivalent weight robust estimation, we take the median parameter estimates as the initial values and carry out equivalent weight robust estimation to compute the final results. The numerical experiments show that our robust estimation method of combined median parameter and equivalent weight is much better than both individual robust estimations.