Optimal estimation of vehicle position in an acoustic transponder navigation system

In an Acoustic Transponder Navigation System the vehicle position is determined in relation to the transponders by the use of ranges to the transponders and the distances between the transponders. The vehicle position determined is usually inaccurate due to the timing error and the inaccuracy of the sound velocity assumed in obtaining the range data. This paper develops computational algorithms for the optimal estimation of the vehicle position with given erroneous range data. The development begins with the formulation of a least-squares error criterion. Computational algorithms are then developed to best estimate the vehicle position by minimizing the least-squares error criterion. For the moving vehicles, optimal filtering algorithms are developed which sequentially update the vehicle position based on the knowledge of the vehicle dynamics and the range measurements. Computational results for one illustrative example in the application of the optimal filtering algorithms are presented.