A Modified LSR Algorithm Based on the Critical Value of Characteristic Slopes for RAIM

Utilizing the least squares residuals (LSR) algorithm to detect the faulty satellite, the faulty satellite with a large characteristic slope will bring a high miss detection risk (MDR) and that with a small characteristic slope will bring a high false alert risk (FAR). However, the magnitude of characteristic slopes whether large or small is currently indefinite. In this paper, analyzing the MDR whether exceeding its allowable value or not, we propose the critical value of characteristic slopes to define the magnitude of a characteristic slope. The slope with the value larger than the critical one can be defined as a large slope whereas the slope with a value smaller than the critical one can be defined as a small slope. To reduce the fault detection risk of the LSR algorithm, including the MDR caused by a large slope faulty satellite and the FAR caused by a small slope faulty satellite, a modified LSR algorithm based on the critical value of characteristic slopes is proposed. In the modified algorithm, the most potential faulty satellite is determined via correlation analysis. Then, a subset fault detection methodology will be used to reduce the MDR when the most potential faulty satellite owns a large slope, whereas a threshold amplification fault detection methodology will be used to reduce the FAR when the most potential faulty satellite owns a small slope. The performance evaluation simulations of the modified LSR algorithm show that both the MDR caused by a large slope faulty satellite and the FAR caused by a small slope faulty satellite could be effectively reduced.