Page 9 - Classification Parameter Estimation & State Estimation An Engg Approach Using MATLAB

viii CONTENTS

7.2.3 Mixture of Gaussians 234
7.2.4 Mixture of probabilistic PCA 240
7.2.5 Self-organizing maps 241
7.2.6 Generative topographic mapping 246
7.3 References 250
7.4 Exercises 250

8 State Estimation in Practice 253
8.1 System identification 256
8.1.1 Structuring 256
8.1.2 Experiment design 258
8.1.3 Parameter estimation 259
8.1.4 Evaluation and model selection 263
8.1.5 Identification of linear systems with
a random input 264
8.2 Observability, controllability and stability 266
8.2.1 Observability 266
8.2.2 Controllability 269
8.2.3 Dynamic stability and steady state solutions 270
8.3 Computational issues 276
8.3.1 The linear-Gaussian MMSE form 280
8.3.2 Sequential processing of the measurements 282
8.3.3 The information filter 283
8.3.4 Square root filtering 287
8.3.5 Comparison 291
8.4 Consistency checks 292
8.4.1 Orthogonality properties 293
8.4.2 Normalized errors 294
8.4.3 Consistency checks 296
8.4.4 Fudging 299
8.5 Extensions of the Kalman filter 300
8.5.1 Autocorrelated noise 300
8.5.2 Cross-correlated noise 303
8.5.3 Smoothing 303
8.6 References 306
8.7 Exercises 307

9 Worked Out Examples 309
9.1 Boston Housing classification problem 309
9.1.1 Data set description 309
9.1.2 Simple classification methods 311