Preface |
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xiii | |
Acknowledgements |
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xxi | |
Glossary |
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xxiii | |
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1 | (28) |
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1 | (1) |
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2 | (6) |
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1.3 Model-Based Processing |
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8 | (8) |
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1.4 Model-Based Identification |
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16 | (4) |
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1.5 Subspace Identification |
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20 | (2) |
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1.6 Notation and Terminology |
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22 | (2) |
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24 | (1) |
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25 | (1) |
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25 | (1) |
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26 | (3) |
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2 Random Signals and Systems |
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29 | (40) |
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29 | (3) |
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2.2 Discrete Random Signals |
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32 | (4) |
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2.3 Spectral Representation of Random Signals |
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36 | (4) |
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2.4 Discrete Systems with Random Inputs |
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40 | (4) |
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41 | (1) |
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42 | (2) |
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44 | (15) |
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2.5.1 Classical (Nonparametric) Spectral Estimation |
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44 | (1) |
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2.5.1.1 Correlation Method (Blackman--Tukey) |
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45 | (1) |
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2.5.1.2 Average Periodogram Method (Welch) |
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46 | (1) |
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2.5.2 Modern (Parametric) Spectral Estimation |
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47 | (1) |
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2.5.2.1 Autoregressive (All-Pole) Spectral Estimation |
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48 | (3) |
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2.5.2.2 Autoregressive Moving Average Spectral Estimation |
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51 | (1) |
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2.5.2.3 Minimum Variance Distortionless Response (MVDR) Spectral Estimation |
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52 | (3) |
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2.5.2.4 Multiple Signal Classification (MUSIC) Spectral Estimation |
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55 | (4) |
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2.6 Case Study: Spectral Estimation of Bandpass Sinusoids |
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59 | (2) |
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61 | (1) |
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61 | (1) |
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62 | (2) |
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64 | (5) |
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3 State-Space Models for Identification |
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69 | (38) |
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69 | (1) |
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3.2 Continuous-Time State-Space Models |
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69 | (4) |
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3.3 Sampled-Data State-Space Models |
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73 | (1) |
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3.4 Discrete-Time State-Space Models |
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74 | (9) |
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3.4.1 Linear Discrete Time-Invariant Systems |
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77 | (1) |
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3.4.2 Discrete Systems Theory |
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78 | (4) |
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3.4.3 Equivalent Linear Systems |
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82 | (1) |
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3.4.4 Stable Linear Systems |
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83 | (1) |
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3.5 Gauss--Markov State-Space Models |
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83 | (6) |
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3.5.1 Discrete-Time Gauss--Markov Models |
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83 | (6) |
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89 | (1) |
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3.7 State-Space Model Structures |
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90 | (7) |
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91 | (1) |
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3.7.2 State-Space and Time-Series Equivalence Models |
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91 | (6) |
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3.8 Nonlinear (Approximate) Gauss--Markov State-Space Models |
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97 | (4) |
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101 | (1) |
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102 | (1) |
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102 | (1) |
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103 | (4) |
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107 | (78) |
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107 | (1) |
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4.2 Linear Model-Based Processor: Kalman Filter |
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108 | (21) |
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4.2.1 Innovations Approach |
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110 | (4) |
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114 | (2) |
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4.2.3 Innovations Sequence |
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116 | (1) |
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4.2.4 Practical Linear Kalman Filter Design: Performance Analysis |
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117 | (8) |
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4.2.5 Steady-State Kalman Filter |
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125 | (3) |
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4.2.6 Kalman Filter/Wiener Filter Equivalence |
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128 | (1) |
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4.3 Nonlinear State-Space Model-Based Processors |
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129 | (37) |
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4.3.1 Nonlinear Model-Based Processor: Linearized Kalman Filter |
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130 | (3) |
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4.3.2 Nonlinear Model-Based Processor: Extended Kalman Filter |
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133 | (5) |
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4.3.3 Nonlinear Model-Based Processor: Iterated-Extended Kalman Filter |
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138 | (3) |
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4.3.4 Nonlinear Model-Based Processor: Unscented Kalman Filter |
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141 | (7) |
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4.3.5 Practical Nonlinear Model-Based Processor Design: Performance Analysis |
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148 | (3) |
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4.3.6 Nonlinear Model-Based Processor: Particle Filter |
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151 | (9) |
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4.3.7 Practical Bayesian Model-Based Design: Performance Analysis |
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160 | (6) |
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4.4 Case Study: 2D-Tracking Problem |
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166 | (7) |
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173 | (1) |
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173 | (1) |
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174 | (3) |
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177 | (8) |
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5 Parametrically Adaptive Processors |
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185 | (46) |
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185 | (1) |
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5.2 Parametrically Adaptive Processors: Bayesian Approach |
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186 | (1) |
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5.3 Parametrically Adaptive Processors: Nonlinear Kalman Filters |
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187 | (14) |
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188 | (2) |
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5.3.2 Classical Joint State/Parametric Processors: Augmented Extended Kalman Filter |
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190 | (8) |
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5.3.3 Modern Joint State/Parametric Processor: Augmented Unscented Kalman Filter |
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198 | (3) |
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5.4 Parametrically Adaptive Processors: Particle Filter |
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201 | (7) |
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5.4.1 Joint State/Parameter Estimation: Particle Filter |
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201 | (7) |
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5.5 Parametrically Adaptive Processors: Linear Kalman Filter |
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208 | (6) |
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5.6 Case Study: Random Target Tracking |
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214 | (8) |
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222 | (1) |
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223 | (1) |
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223 | (3) |
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226 | (5) |
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6 Deterministic Subspace Identification |
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231 | (78) |
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231 | (1) |
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6.2 Deterministic Realization Problem |
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232 | (9) |
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233 | (5) |
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6.2.2 Balanced Realizations |
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238 | (1) |
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6.2.3 Systems Theory Summary |
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239 | (2) |
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6.3 Classical Realization |
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241 | (23) |
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6.3.1 Ho--Kalman Realization Algorithm |
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241 | (2) |
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6.3.2 SVD Realization Algorithm |
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243 | (3) |
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6.3.2.1 Realization: Linear Time-Invariant Mechanical Systems |
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246 | (5) |
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6.3.3 Canonical Realization |
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251 | (1) |
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6.3.3.1 Invariant System Descriptions |
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251 | (6) |
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6.3.3.2 Canonical Realization Algorithm |
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257 | (7) |
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6.4 Deterministic Subspace Realization: Orthogonal Projections |
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264 | (10) |
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6.4.1 Subspace Realization: Orthogonal Projections |
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266 | (5) |
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6.4.2 Multivariable Output Error State-Space (MOESP) Algorithm |
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271 | (3) |
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6.5 Deterministic Subspace Realization: Oblique Projections |
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274 | (11) |
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6.5.1 Subspace Realization: Oblique Projections |
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278 | (2) |
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6.5.2 Numerical Algorithms for Subspace State-Space System Identification (N4SID) Algorithm |
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280 | (5) |
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6.6 Model Order Estimation and Validation |
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285 | (10) |
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6.6.1 Order Estimation: SVD Approach |
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286 | (3) |
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289 | (6) |
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6.7 Case Study: Structural Vibration Response |
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295 | (4) |
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299 | (1) |
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300 | (1) |
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300 | (3) |
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303 | (6) |
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7 Stochastic Subspace Identification |
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309 | (82) |
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309 | (3) |
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7.2 Stochastic Realization Problem |
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312 | (5) |
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7.2.1 Correlated Gauss--Markov Model |
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312 | (1) |
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7.2.2 Gauss--Markov Power Spectrum |
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313 | (1) |
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7.2.3 Gauss--Markov Measurement Covariance |
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314 | (1) |
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7.2.4 Stochastic Realization Theory |
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315 | (2) |
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7.3 Classical Stochastic Realization via the Riccati Equation |
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317 | (4) |
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7.4 Classical Stochastic Realization via Kalman Filter |
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321 | (9) |
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321 | (1) |
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7.4.2 Innovations Power Spectrum |
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322 | (1) |
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7.4.3 Innovations Measurement Covariance |
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323 | (2) |
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7.4.4 Stochastic Realization: Innovations Model |
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325 | (5) |
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7.5 Stochastic Subspace Realization: Orthogonal Projections |
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330 | (12) |
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7.5.1 Multivariable Output Error State-Space (MOESP) Algorithm |
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334 | (8) |
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7.6 Stochastic Subspace Realization: Oblique Projections |
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342 | (11) |
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7.6.1 Numerical Algorithms for Subspace State-Space System Identification (N4SID) Algorithm |
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346 | (5) |
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7.6.2 Relationship: Oblique (N4SID) and Orthogonal (MOESP) Algorithms |
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351 | (2) |
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7.7 Model Order Estimation and Validation |
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353 | (16) |
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7.7.1 Order Estimation: Stochastic Realization Problem |
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354 | (2) |
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7.7.1.1 Order Estimation: Statistical Methods |
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356 | (6) |
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362 | (1) |
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363 | (6) |
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7.8 Case Study: Vibration Response of a Cylinder: Identification and Tracking |
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369 | (9) |
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378 | (13) |
Matlab Notes |
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378 | (1) |
References |
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379 | (3) |
Problems |
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382 | (113) |
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8 Subspace Processors for Physics-Based Application |
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391 | (76) |
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8.1 Subspace Identification of a Structural Device |
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391 | (14) |
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8.1.1 State-Space Vibrational Systems |
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392 | (2) |
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8.1.1.1 State-Space Realization |
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394 | (2) |
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8.1.2 Deterministic State-Space Realizations |
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396 | (1) |
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8.1.2.1 Subspace Approach |
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396 | (2) |
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8.1.3 Vibrational System Processing |
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398 | (2) |
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8.1.4 Application: Vibrating Structural Device |
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400 | (4) |
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404 | (1) |
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8.2 MBID for Scintillator System Characterization |
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405 | (13) |
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8.2.1 Scintillation Pulse Shape Model |
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407 | (2) |
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8.2.2 Scintillator State-Space Model |
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409 | (1) |
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8.2.3 Scintillator Sampled-Data State-Space Model |
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410 | (1) |
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8.2.4 Gauss--Markov State-Space Model |
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411 | (1) |
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8.2.5 Identification of the Scintillator Pulse Shape Model |
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412 | (2) |
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8.2.6 Kalman Filter Design: Scintillation/Photomultiplier System |
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414 | (2) |
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8.2.6.1 Kalman Filter Design: Scintillation/Photomultiplier Data |
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416 | (1) |
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417 | (1) |
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8.3 Parametrically Adaptive Detection of Fission Processes |
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418 | (17) |
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8.3.1 Fission-Based Processing Model |
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419 | (1) |
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8.3.2 Interarrival Distribution |
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420 | (2) |
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8.3.3 Sequential Detection |
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422 | (1) |
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8.3.4 Sequential Processor |
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422 | (2) |
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8.3.5 Sequential Detection for Fission Processes |
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424 | (2) |
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8.3.6 Bayesian Parameter Estimation |
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426 | (1) |
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8.3.7 Sequential Bayesian Processor |
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427 | (2) |
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8.3.8 Particle Filter for Fission Processes |
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429 | (1) |
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8.3.9 SNM Detection and Estimation: Synthesized Data |
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430 | (3) |
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433 | (2) |
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8.4 Parametrically Adaptive Processing for Shallow Ocean Application |
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435 | (17) |
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8.4.1 State-Space Propagator |
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436 | (1) |
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436 | (2) |
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8.4.2.1 Augmented State-Space Models |
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438 | (3) |
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441 | (3) |
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8.4.4 Model-Based Ocean Acoustic Processing |
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444 | (1) |
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8.4.4.1 Adaptive PF Design: Modal Coefficients |
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445 | (2) |
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8.4.4.2 Adaptive PF Design: Wavenumbers |
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447 | (3) |
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450 | (2) |
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8.5 MBID for Chirp Signal Extraction |
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452 | (10) |
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453 | (1) |
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453 | (2) |
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8.5.1.2 Frequency-Shift Key (FSK) Signal |
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455 | (2) |
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8.5.2 Model-Based Identification: Linear Chirp Signals |
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457 | (1) |
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8.5.2.1 Gauss--Markov State-Space Model: Linear Chirp |
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457 | (2) |
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8.5.3 Model-Based Identification: FSK Signals |
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459 | (1) |
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8.5.3.1 Gauss--Markov State-Space Model: FSK Signals |
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460 | (2) |
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462 | (1) |
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462 | (5) |
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Appendix A Probability and Statistics Overview |
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467 | (10) |
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467 | (6) |
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A.2 Gaussian Random Vectors |
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473 | (1) |
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A.3 Uncorrelated Transformation: Gaussian Random Vectors |
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473 | (1) |
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A.4 Toeplitz Correlation Matrices |
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474 | (1) |
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474 | (2) |
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476 | (1) |
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Appendix B Projection Theory |
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477 | (8) |
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B.1 Projections: Deterministic Spaces |
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477 | (1) |
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B.2 Projections: Random Spaces |
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478 | (1) |
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B.3 Projection: Operators |
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479 | (4) |
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B.3.1 Orthogonal (Perpendicular) Projections |
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479 | (2) |
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B.3.2 Oblique (Parallel) Projections |
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481 | (2) |
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483 | (2) |
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Appendix C Matrix Decompositions |
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485 | (4) |
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C.1 Singular-Value Decomposition |
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485 | (2) |
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487 | (1) |
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487 | (1) |
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488 | (1) |
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Appendix D Output-Only Subspace Identification |
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489 | (6) |
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492 | (3) |
Index |
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495 | |