A navigation algorithm for single channel low-cost GPS receiver

Abstract

A sequential navigation algorithm for a navigator using the Global Positioning System satellites is developed and tested for both the noise-free and noisy system models. Data from a six-hour flight from California to Hawaii (C5A aircraft) simulates a true user to test the accuracy of the user's position for a sequential navigation system. For the low-cost aspect of the navigation system, the analysis of satellite visibility and selection have led to finding of a fast satellite in-view test and two fast satellite selection procedures (FOS and QS) with the Quadrature System (QS) of satellite selection being 134 times faster than a given optimum satellite selection procedure. Also, a fast criteria for the Geometric Dilution of Precision test is experimentally determined. For the error reduction in the user's position in the sequential navigation system, considering 100 m as a maximum average error tolerated by any low-cost GPS user, an analysis of error sources in the sequential system has led to the use of range-ephemeris rate to translate ranges to a common point in time and to use velocity aiding at the time of a satellite disappearance. To reduce the user's position and velocity errors in a noisy navigation system an “α-β” filter is implemented whose optimum α is obtained experimentally. A user's position error of 73 m at noise ranger error standard deviation of 30.48 m is achieved. A mathematical model of the user error as a function of GDOP and ranger errors is derived. This model is supported by an equation derived for a noisy system from the experimental results.