L1-norm optimisation of rank deficient GNSS networks by an improved Grey Wolf method

Abstract

An improved grey wolf optimization (GWO) is proposed for direct L1-norm optimization in rank deficient GNSS networks to detect outliers since the standard GWO and the global optimization (GO) algorithms cannot deal with such problems. In contrast to the traditional method for L1-norm minimization which is solved by a cumbersome search of linear programming (LP) problem, in this algorithm, one only requires to input the target function. Furthermore, it has a greater ability to detect gross errors of observables with low reliability compared to traditional methods such as LP. Moreover, it does not consider the correct observables as blunders in contrast to some algorithms such as the iteratively reweighted least-squares (IRLS) method, which may consider them as outliers. The numerical results of real and simulated GNSS networks approve the efficiency of the new algorithm.