Simulation of multilateration system based on Chan algorithm and conjugate gradient optimisation algorithm

Abstract

In multilateration (MLAT) systems, the traditional Chan algorithm applies the theory of time-difference-of-arrival (TDOA) to solve the target position of the mathematical model. By introducing intermediate variables, the algorithm adopts a two-step weighted least-squares solution. The introduction of intermediate variables results in the target position equation producing a fuzzy solution, this reduces positioning accuracy. The conjugate gradient algorithm (CGA) is one of the most useful methods for solving large linear equations, it avoids solving the inverse of the matrix, whilst it 'speeds up' the solution of the target position. A four stations multi-point-positioning system mathematical model is established, and a new fusion algorithm Chan-CGA is applied to the MLAT system. Finally, the fusion algorithm is evaluated by simulation and compared with the Chan-Taylor algorithm.