GNSS for Rail Transportation : Challenges and Opportunities 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 Matrix 2.1.5 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 Fault 3.3.2 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 Satellite.