Neural Networks in GPS Navigation

Abstract

Neural networks have been proposed as nonlinear filters in a variety of applications that involve nonlinear processing of input signals; examples include blind signal separation, image registration, and blind deconvolution. The Global Positioning System (GPS) navigation equations are nonlinear (quadratic) in nature, and a direct closed form solution of the GPS navigation equations does not exist. This article presents a new approach to solving the GPS pseudorange equations using three-layer neural networks. A three-layer radial basis function (RBF) neural network is designed, which solves the non-linear GPS pseudorange equations directly as opposed to the linear least squares or extended Kalman filter approaches in traditional GPS receivers. For training the neural network, a carefully selected cost function is minimized using a variation of the classical conjugate gradient algorithm such that training time for the neural network is reasonable. Simulations have been performed at SiRF Technology Inc. that show stable behavior even under bad geometry conditions where the traditional recursive least squares and extended Kalman filter approaches show high sensitivity to measurement errors. Under good geometry conditions the neural network solution shows slightly improved noise performance compared to the expected performance of traditional leas squares solution. Simulations have been performed with additive white Gaussian noise and correlated noise models to evaluate the performance of the trained neural network. © 2000 John Wiley & Sons, Inc.