Solution Separation Versus Residual-Based RAIM

Abstract

Future multi-constellation Global Navigation Satellite Systems (GNSS) will offer the possibility to fulfill stringent navigation integrity requirements using Receiver Autonomous Integrity Monitoring (RAIM). This paper presents a detailed comparison of residual-based (RB) and solution separation (SS) RAIM. A complete step-by-step derivation of the two methods, which is currently missing in the literature, is given for the detection of single and multi-measurement faults, starting from common definitions of the integrity and continuity risks. In addition, a parity-space representation of SS RAIM is developed. It is shown that the integrity monitoring performance of SS RAIM can be superior to RB RAIM because SS test statistics are tailored to the fault hypotheses, and to the state of interest. However, for practical reasons of computational efficiency in conventional SS implementations, which are fully detailed in the paper, RB RAIM ultimately provides tighter bounds on integrity risk.

Integrity Risk Minimisation in RAIM Part 2: Optimal Estimator Design

“…Of particular significance in this work is the fact that for single-measurement faults, q i can be written in terms of p as (Joerger et al, 2014):…”

“…However, in contrast with Blanch et al (2012), the method described here enables DIRE instead of using Protection Level (PL) equations. DIRE provides tighter integrity risk bounds than PL (Joerger et al, 2014).…”

“…Also, it was shown in Joerger et al (2014) that g 0; i can be written as: g 0; i ¼ σ Δi , where σ Δi is defined in the paragraph above Equation (3). The optimal (n − m) × 1 vector β obtained using the DIRE MDO method is displayed in parity space in Figure 6(a) for the example six-SV geometry introduced in Figure 2.…”

“…It was shown in (Joerger et al, 2014) that the bound Pðjq i j < T i j H i Þ ¼ 1 in the last inequality could be loose. This upper bound is conventionally used in SS RAIM, and is the price to pay to significantly reduce the processing time.…”

Integrity Risk Minimisation in RAIM Part 1: Optimal Detector Design

“…With regard to fault detection, two RAIM algorithms have been widely implemented over the past 25 years: chi-squared (χ 2 ) RAIM (also called parity-based or residualbased RAIM (Sturza, 1988;Brown, 1992)) and Solution Separation (SS) RAIM (Brenner, 1996;Blanch et al, 2007). Fundamental differences between the two algorithms have been pointed out in Joerger et al (2014), but it remains unclear whether SS or χ 2 RAIM provides the lowest integrity risk. In parallel, with regard to estimation, researchers have explored the potential of replacing the conventional LeastSquares (LS) process with a Non-Least-Squares (NLS) estimator to lower the integrity risk in exchange for a slight increase in nominal positioning error (Hwang and Brown, 2006;Lee, 2008;Blanch et al, 2012).…”