On GPS positioning and integrity monitoring

The paper reinvestigates the measurement model associated with Global Positioning System (GPS) signal processing. It is argued that the GPS positioning model is better formulated as a linear equation with errors in both the data matrix and measurement variables. Furthermore, depending on the nature of the measurement errors, the model is categorized into unstructured and structured perturbation cases. In the former, the total least squares method is proposed for position fixing and clock bias determination. In the latter, an iteration method is developed to search for the optimal solution. In addition to the position update, both the total least squares and optimization methods provide estimates of the model mismatch which leads to a measure of GPS receiver autonomous integrity monitoring. Two new GPS fault detection metrics are then proposed and discussed. The first integrity test statistic is the norm of the residual vector in the total least squares estimate. Statistical properties of this test statistic are obtained for integrity monitoring. The second metric is a two-dimensional vector that characterizes the norm of the residual vector and mismatch matrix, both are outcomes of the total least squares method or the optimization method. The positioning and integrity monitoring schemes are verified using simulated examples.