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Table of Contents
Intro; Preface; Contents; Acronyms; 1 Introduction and Book Objectives; 1.1 GNSS for Safety of Life Applications; 1.2 The Concept of Integrity in Satellite Navigation; 1.3 From Aviation to the Railway Transportation Domain; 1.4 Objectives; References; Part I GNSS Integrity; 2 Review of Common Navigation Algorithms and Measurements Errors; 2.1 Methods for Position Velocity and Time (PVT) Computation; 2.1.1 Least Square Solution; 2.1.2 Geometric Interpretation of Least Square Solution Using Orthogonal Subspaces; 2.1.3 Weighted Least Square Solution and Subspace Projection.
2.1.4 Covariance Matrix2.1.5 Errors Due to the Receiving Hardware and Local Environment; References; 3 Fundamentals of Integrity Monitoring; 3.1 Evaluation of the Confidence Interval in an AWGN Model; 3.1.1 PL of a Single Coordinate, in Case of Zero-Mean Gaussian Position Error; 3.1.2 Verification of the AWGN Model; 3.1.3 Introduction to RAIM; 3.2 Fault Detection in the Range Domain; 3.2.1 Range Residual Method; 3.2.2 Parity Method; 3.2.3 Computation of the Decision Threshold for the AWGN Model; 3.3 Fault Detection and Exclusion in the Position Domain.
3.3.1 Solution Separation with a Single Fault3.3.2 Bias Estimator; 3.3.3 Solution Separation Test with a Generic Number of Faults; 3.4 Comparison Between Methods in the Range and in the Position Domains; 3.5 Residual and Solution Separation Tests: Geometric Interpretation and Efficient Implementation; 3.5.1 Efficient Implementation in Single Fault Case; 3.5.2 Efficient Implementation in Double Fault Case; 3.6 Conclusions; References; 4 Evaluation of the Confidence Intervals; 4.1 Confidence Interval in the Case of a Single Fault; 4.1.1 Alert Limit, Integrity Risk, and Protection Level.
4.1.2 The Effect of Bias in a Single Satellite4.1.3 Confidence Interval Computation in a Slope-Based RAIM; 4.1.4 Fault Detection Algorithms in a Slope-Based RAIM; 4.2 Method to Evaluate an Upper Bound for PL; 4.2.1 Nominal and Faulty Conditions: Binary Hypothesis Case; 4.2.2 Hypothesis mathscrHa: Error Model Based on Non Zero Mean Gaussian PDF; 4.2.3 Confidence Interval in the Case of Multiple Faults; 4.2.4 Estimation of the Mean of the Gaussian Error Model; 4.2.5 Modelling of the Variance of the Gaussian Error Model; 4.2.6 Fault Tree; 4.3 Stanford Plot; 4.4 Final Remarks on RAIM Algorithms.
2.1.4 Covariance Matrix2.1.5 Errors Due to the Receiving Hardware and Local Environment; References; 3 Fundamentals of Integrity Monitoring; 3.1 Evaluation of the Confidence Interval in an AWGN Model; 3.1.1 PL of a Single Coordinate, in Case of Zero-Mean Gaussian Position Error; 3.1.2 Verification of the AWGN Model; 3.1.3 Introduction to RAIM; 3.2 Fault Detection in the Range Domain; 3.2.1 Range Residual Method; 3.2.2 Parity Method; 3.2.3 Computation of the Decision Threshold for the AWGN Model; 3.3 Fault Detection and Exclusion in the Position Domain.
3.3.1 Solution Separation with a Single Fault3.3.2 Bias Estimator; 3.3.3 Solution Separation Test with a Generic Number of Faults; 3.4 Comparison Between Methods in the Range and in the Position Domains; 3.5 Residual and Solution Separation Tests: Geometric Interpretation and Efficient Implementation; 3.5.1 Efficient Implementation in Single Fault Case; 3.5.2 Efficient Implementation in Double Fault Case; 3.6 Conclusions; References; 4 Evaluation of the Confidence Intervals; 4.1 Confidence Interval in the Case of a Single Fault; 4.1.1 Alert Limit, Integrity Risk, and Protection Level.
4.1.2 The Effect of Bias in a Single Satellite4.1.3 Confidence Interval Computation in a Slope-Based RAIM; 4.1.4 Fault Detection Algorithms in a Slope-Based RAIM; 4.2 Method to Evaluate an Upper Bound for PL; 4.2.1 Nominal and Faulty Conditions: Binary Hypothesis Case; 4.2.2 Hypothesis mathscrHa: Error Model Based on Non Zero Mean Gaussian PDF; 4.2.3 Confidence Interval in the Case of Multiple Faults; 4.2.4 Estimation of the Mean of the Gaussian Error Model; 4.2.5 Modelling of the Variance of the Gaussian Error Model; 4.2.6 Fault Tree; 4.3 Stanford Plot; 4.4 Final Remarks on RAIM Algorithms.