Study of long baseline optimization positioning algorithms Bbsed on redundancy measurement

Abstract

Generally, underwater vehicles real-time navigation system works through the principle of spherical intersection. The number of array elements required for this method is fixed, but in the case of redundant array elements, they can't be fully utilized. This paper presents two optimization methods based on redundancy measurement. One approach is the steepest descent method and the other is Gauss-Newton method. The former searches for the minimum value of the measurement’s sum of squared residuals along the negative gradient direction, and the later, a non-linear least-squares optimization method that constantly revise regression coefficients through multiple iterations to minimize the sum of squared residuals. Simulation show that both methods are greatly affected by the initial position, the closer the distance between initial position to the target is, the smaller positioning error is. On the same initial position, the Gauss-Newton method has less positioning error than the steepest descent method. The conclusions have been proved to be valid by sea trial.