Robust Estimation and Failure Detection

1 Introduction.- 2 Estimation and Failure Detection: An Overview.- 2.1 Introduction.- 2.2 Ever Since Wiener.- 2.2.1 Wiener and Kalman Filters.- 2.2.2 Beyond Linear Least Squares Estimation.- 2.2.3 Kalman Filter and Model Uncertainties.- 2.2.4 Robust Estimation and the Small Gain Theorem.- 2.2.5 Robust Stability and Robust Performance for Estimation.- 2.2.6 Further Discussion on Robust Estimation and Control.- 2.2.7 Risk Sensitive Control and Estimation.- 2.3 Failure Detection and Isolation.- 2.3.1 Kalman Filters in FDI Algorithms: The GLUT.- 2.3.2 Nonadditive Failures.- 2.3.3 Modeling Uncertainties and FDI Algorithms.- 2.3.4 Robust Failure Detection and Isolation.- 2.4 Summary.- 3 Discrete-Time Robust Estimation.- 3.1 Introduction.- 3.2 Plants with an Uncertain Noise Model.- 3.2.1 Problem Formulation.- 3.2.2 Derivation of the Estimator.- 3.2.3 Estimator Properties.- 3.2.4 Estimator Equations and Discussion.- 3.3 Plants with Uncertain Dynamics and Noise Model.- 3.3.1 Problem Formulation.- 3.3.2 Derivation of the Estimator.- 3.3.3 Robust Estimator Equations and Discussion.- 3.4 Extension to Steady State.- 3.5 Robust Fixed-Interval Smoothing.- 3.6 Numerical Examples.- 3.6.1 A Two-State System.- 3.6.2 Attitude Determination.- 3.7 Related Work.- 4 Stochastic Interpretation of Robust Estimation: Risk Sensitivity.- 4.1 Introduction.- 4.2 The Risk Sensitive Optimal Estimation Problem.- 4.2.1 Problem Formulation.- 4.2.2 Equivalence to Game Theoretic Estimation.- 4.3 Extension to Systems with Modeling Uncertainty.- 4.4 Numerical Comparison of Error Density Functions.- 4.5 Summary.- 5 Robust Failure Detection and Isolation.- 5.1 Introduction.- 5.2 Problem Description.- 5.2.1 General Discussion and Notation.- 5.2.2 Problem Formulation.- 5.2.3 The Failure Model.- 5.3 A Likelihood Ratio Test with Robustness Properties.- 5.4 Likelihood Ratio Tests and Plant Uncertainties.- 5.4.1 Examples: Underwater Vehicle with Model Uncertainty.- 5.5 FDI with Robustness to Failure Mode, Noise and Plant Uncertainties.- 5.5.1 The Decision Function.- 5.5.2 Robust Estimator Design.- 5.5.3 Summary of the Algorithm.- 5.6 Summary.- 6 Two Applications.- 6.1 Introduction.- 6.2 Application to an Underwater Vehicle.- 6.2.1 Straight and Level Cruise.- 6.2.2 Maneuvers.- 6.3 Application to Reentry Vehicle attitude Control Systems.- 6.3.1 Problem Description.- 6.3.2 Robust FDI Filter Architecture.- 6.3.3 Results.- 6.3.4 Summary.- A The Kalman Filter.- A.1 Problem Description.- A.2 The One-Step Predictor.- A.3 Measurement Update and the Filtered Estimate.- A.4 Gaussian Disturbance.- A.5 The Innovation Process.- A.6 Linear Time-Invariant Systems.- A.7 The Wiener Filter.- A.8 Smoothing.- A.8.1 Fixed-Interval Smoothing.- A.8.2 Fixed-Point and Fixed-Lag Smoothing.- A.9 The Extended Kaiman Filter (EKF).- A.10 Summary of Equations and Additional Remarks.- B Outputs of Linear Systems and Their Quadratic Forms.- B.1 Moments of Linear Systems Outputs.- B.2 Probability Density Functions of Gaussian Quadratic Forms.- C Continuous-Time Robust Estimation.- C.1 Introduction.- C.2 Problem Formulation.- C.3 Derivation of the Estimator.- C.4 Related Work.- D Application Data.- D.1 Underwater Vehicle Application.- D.1.1 The Plant.- D.1.2 Description of Robust Filter Design.- D.2 Reentry Vehicle Application.- D.2.1 The Plant.- D.2.2 The Filters.