Robust Estimation and Failure Detection A Concise Treatment

The series Advances in Industrial Control aims to report and encourage technology transfer in control engineering. The rapid development of control technology impacts all areas of the control discipline. New theory, new controllers, actuators, sensors, new industrial processes, computer methods, new applications, new philosophies ... , new challenges. Much of this development work resides in industrial reports, feasibility study papers and the reports of advanced collaborative projects. The series offers an opportunity for researchers to present an extended exposition of such new work in all aspects of industrial control for wider and rapid dissemination. This monograph brings together two of the most exciting areas of advanced signal processing and control. The first involves the development of optimal estimators for uncertain signal and noise models. The second is the subject of failure detection and isolation, which has considerable potential in a range of applications. The text provides a gradual build-up of ideas moving from traditional Wiener and Kalman fIltering to risk sensitive control and estimation problems.

1 Introduction.- 2 Estimation and Failure Detection: An Overview.- 2.1 Introduction.- 2.2 Ever Since Wiener.- 2.3 Failure Detection and Isolation.- 2.4 Summary.- 3 Discrete-Time Robust Estimation.- 3.1 Introduction.- 3.2 Plants with an Uncertain Noise Model.- 3.3 Plants with Uncertain Dynamics and Noise Model.- 3.4 Extension to Steady State.- 3.5 Robust Fixed-Interval Smoothing.- 3.6 Numerical Examples.- 3.7 Related Work.- 4 Stochastic Interpretation of Robust Estimation: Risk Sensitivity.- 4.1 Introduction.- 4.2 The Risk Sensitive Optimal Estimation Problem.- 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.- 5.3 A Likelihood Ratio Test with Robustness Properties.- 5.4 Likelihood Ratio Tests and Plant Uncertainties.- 5.5 FDI with Robustness to Failure Mode, Noise and Plant Uncertainties.- 5.6 Summary.- 6 Two Applications.- 6.1 Introduction.- 6.2 Application to an Underwater Vehicle.- 6.3 Application to Reentry Vehicle attitude Control Systems.- 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.