Robust estimation of model parameters of the probability integral method based on CA-rPSO

This paper introduces a framework for robustly estimating the parameters of the probability integral method (PIM). According to the framework, the initial robust estimates of the PIM parameters are firstly obtained by combining the cultural algorithm and rand particle swarm optimisation (CA-rPSO) with the LTS method. As a byproduct, an initial standard deviation can be calculated and used to determine the initial weights of the measurements according to the Institute of Geodesy and Geophysics (IGGIII) down-weighting scheme. Meanwhile, a modified CA-rPSO (referred to as CA-rPSO-IGGIII) is constructed, where the IGGIII scheme is introduced to alleviate the adverse influence of outliers. Then, the initial robust estimates and the standard deviation can act as a priori information for the CA-rPSO-IGGGIII to search for the optimal estimates. Experiments with simulated and real data demonstrate that the proposed method can robustly estimate the PIM parameters.