MODEL-BASED SIGNAL PROCESSING
CONTENTS 1 INTRODUCTION BACKGROUND / SIGNAL ESTIMATION / MODEL-BASED PROCESSING EXAMPLE / MODEL-BASED SIGNAL PROCESSING CONCEPTS / NOTATION AND TERMINOLOGY / SUMMARY / MATLAB?NOTES / REFERENCES / PROBLEMS / 2 DISCRETE RANDOM SIGNALS AND SYSTEMS INTRODUCTION / DETERMINISTIC SIGNALS AND SYSTEMS / SPECTRAL REPRESENTATION OF DISCRETE SIGNALS / DISCRETE SYSTEMS / FREQUENCY RESPONSE OF DISCRETE SYSTEMS / DISCRETE RANDOM SIGNALS / MOTIVATION / RANDOM SIGNALS / SPECTRAL REPRESENTATION OF RANDOM SIGNALS / DISCRETE SYSTEMS WITH RANDOM INPUTS / ARMAX (AR, ARX, MA, ARMA) MODELS / LATTICE MODELS / EXPONENTIAL (HARMONIC) MODELS / 2 10 SPATIOTEMPORAL WAVE MODELS / 2 10 1 PLANE WAVES / 2 10 2 SPHERICAL WAVES / 2 10 3 SPATIOTEMPORAL WAVE MODEL / 2 11 STATE-SPACE MODELS / 2 11 1 CONTINUOUS STATE-SPACE MODELS / 2 11 2 DISCRETE STATE-SPACE MODELS / 2 11 3 DISCRETE SYSTEMS THEORY / 2 11 4 GAUSS-MARKOV (STATE-SPACE) MODELS / 2 11 5 INNOVATIONS (STATE-SPACE) MODELS / 2 12 STATE-SPACE, ARMAX (AR, MA, ARMA, LATTICE) EQUIVALENCE MODELS / 2 13 STATE-SPACE AND WAVE MODEL EQUIVALENCE / 2 14 SUMMARY / MATLAB NOTES / 3 ESTIMATION THEORY ESTIMATOR PROPERTIES / ESTIMATOR PERFORMANCE / MINIMUM VARIANCE (MV ) ESTIMATION / MAXIMUM A POSTERIORI (MAP) ESTIMATION / MAXIMUM LIKELIHOOD (ML) ESTIMATION / LEAST-SQUARES (LS) ESTIMATION / BATCH LEAST SQUARES / LS: A GEOMETRIC PERSPECTIVE / RECURSIVE LEAST SQUARES / OPTIMAL SIGNAL ESTIMATION / 4 AR, MA, ARMAX, LATTICE, EXPONENTIAL, WAVE MODEL-BASED PROCESSORS AR (ALL-POLE) MBP / LEVINSON-DURBIN RECURSION / TOEPLITZ MATRICES FOR AR MODEL-BASED PROCESSORS / MODEL-BASED AR SPECTRAL ESTIMATION / MA (ALL-ZERO) MBP / LEVINSON-WIGGINS-ROBINSON (LWR) RECURSION / OPTIMAL DECONVOLUTION / OPTIMAL TIME DELAY ESTIMATION / LATTICE MBP / ARMAX (POLE-ZERO) MBP / ORDER ESTIMATION FOR MBP / CASE STUDY: ELECTROMAGNETIC SIGNAL PROCESSING / EXPONENTIAL (HARMONIC) MBP / EXPONENTIAL MBP / SVD EXPONENTIAL MBP / HARMONIC MBP / WAVE MBP / 4 10 SUMMARY / 5 LINEAR STATE-SPACE MODEL-BASED PROCESSORS STATE-SPACE MBP (KALMAN FILTER) / INNOVATIONS APPROACH TO THE MBP / INNOVATIONS SEQUENCE OF THE MBP / BAYESIAN APPROACH TO THE MBP / TUNED MBP / TUNING AND MODEL MISMATCH IN THE MBP / TUNING WITH STATE-SPACE MBP PARAMETERS / MODEL MISMATCH PERFORMANCE IN THE STATE-SPACE MBP / MBP DESIGN METHODOLOGY / MBP EXTENSIONS / MODEL-BASED PROCESSOR: PREDICTION-FORM / MODEL-BASED PROCESSOR: COLORED NOISE / MODEL-BASED PROCESSOR: BIAS CORRECTION / MBP IDENTI?ER / 5 10 MBP DECONVOLVER / 5 11 STEADY-STATE MBP DESIGN / 5 11 1 STEADY-STATE MBP / 5 11 2 STEADY-STATE MBP AND THE WIENER FILTER / 5 12 CASE STUDY: MBP DESIGN FOR A STORAGE TANK / 5 13 SUMMARY / 6 NONLINEAR STATE-SPACE MODEL-BASED PROCESSORS LINEARIZED MBP (KALMAN FILTER) / EXTENDED MBP (EXTENDED KALMAN FILTER) / ITERATED-EXTENDED MBP (ITERATED-EXTENDED KALMAN FILTER) / UNSCENTED MBP (KALMAN FILTER) / UNSCENTED TRANSFORMATIONS / UNSCENTED PROCESSOR / CASE STUDY: 2D-TRACKING PROBLEM / 7 ADAPTIVE AR, MA, ARMAX, EXPONENTIAL MODEL-BASED PRO- CESSORS ADAPTION ALGORITHMS / ALL-ZERO ADAPTIVE MBP / STOCHASTIC GRADIENT ADAPTIVE PROCESSOR / INSTANTANEOUS GRADIENT LMS ADAPTIVE PROCESSOR / NORMALIZED LMS ADAPTIVE PROCESSOR / RECURSIVE LEAST-SQUARES (RLS) ADAPTIVE PROCESSOR / POLE-ZERO ADAPTIVE MBP / IIR ADAPTIVE MBP / ALL-POLE ADAPTIVE PREDICTOR / LATTICE ADAPTIVE MBP / ALL-POLE ADAPTIVE LATTICE MBP / JOINT ADAPTIVE LATTICE PROCESSOR / ADAPTIVE MBP APPLICATIONS / ADAPTIVE NOISE CANCELER MBP / ADAPTIVE D-STEP PREDICTOR MBP / ADAPTIVE HARMONIC MBP / ADAPTIVE TIME-FREQUENCY MBP / CASE STUDY: PLASMA PULSE ESTIMATION USING MBP / 8 ADAPTIVE STATE-SPACE MODEL-BASED PROCESSORS STATE-SPACE ADAPTION ALGORITHMS / ADAPTIVE LINEAR STATE-SPACE MBP / ADAPTIVE INNOVATIONS STATE-SPACE MBP / INNOVATIONS MODEL / RPE APPROACH USING THE INNOVATIONS MODEL / ADAPTIVE COVARIANCE STATE-SPACE MBP / ADAPTIVE NONLINEAR STATE-SPACE MBP / CASE STUDY: AMBP FOR OCEAN ACOUSTIC SOUND SPEED INVERSION / STATE-SPACE FORWARD PROPAGATOR / SOUND-SPEED ESTIMATION: AMBP DEVELOPMENT / EXPERIMENTAL DATA RESULTS / 9 APPLIED PHYSICS-BASED PROCESSORS MBP FOR REENTRY VEHICLE TRACKING / RV SIMPLI?ED DYNAMICS / SIGNAL PROCESSING MODEL / PROCESSING OF RV SIGNATURES / FLIGHT DATA PROCESSING / MBP FOR LASER ULTRASONIC INSPECTIONS / LASER ULTRASONIC PROPAGATION MODELING / MODEL-BASED LASER ULTRASONIC PROCESSING / LASER ULTRASONICS EXPERIMENT / MBP FOR STRUCTURAL FAILURE DETECTION / STRUCTURAL DYNAMICS MODEL / MODEL-BASED CONDITION MONITOR / MODEL-BASED MONITOR DESIGN / MBP VIBRATIONS APPLICATION / MBP FOR PASSIVE SONAR DIRECTION-OF-ARRIVAL AND RANGE ESTIMATION / MODEL-BASED ADAPTIVE ARRAY PROCESSING FOR PASSIVE SONAR APPLICATIONS / MODEL-BASED ADAPTIVE PROCESSING APPLICATION TO SYNTHESIZED SONAR DATA / MODEL-BASED RANGING / MBP FOR PASSIVE LOCALIZATION IN A SHALLOW OCEAN / OCEAN ACOUSTIC FORWARD PROPAGATOR / AMBP FOR LOCALIZATION / AMBP APPLICATION TO EXPERIMENTAL DATA / MBP FOR DISPERSIVE WAVES / DISPERSIVE STATE-SPACE PROPAGATOR / DISPERSIVE MODEL-BASED PROCESSOR / INTERNAL WAVE PROCESSOR / MBP FOR GROUNDWATER FLOW / GROUNDWATER FLOW MODEL / AMBP DESIGN /