Author | Catlin, Donald E. author |
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Title | Estimation, Control, and the Discrete Kalman Filter [electronic resource] / by Donald E. Catlin |
Imprint | New York, NY : Springer New York, 1989 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4528-5 |
Descript | XIV, 276 p. online resource |
1 Basic Probability -- 1.1. Definitions -- 1.2. Probability Distributions and Densities -- 1.3. Expected Value, Covariance -- 1.4. Independence -- 1.5. The RadonโNikodym Theorem -- 1.6. Continuously Distributed Random Vectors -- 1.7. The Matrix Inversion Lemma -- 1.8. The Multivariate Normal Distribution -- 1.9. Conditional Expectation -- 1.10. Exercises -- 2 Minimum Variance EstimationโHow the Theory Fits -- 2.1. Theory Versus PracticeโSome General Observations -- 2.2. The Genesis of Minimum Variance Estimation -- 2.3. The Minimum Variance Estimation Problem -- 2.4. Calculating the Minimum Variance Estimator -- 2.5. Exercises -- 3 The Maximum Entropy Principle -- 3.1. Introduction -- 3.2. The Notion of Entropy -- 3.3. The Maximum Entropy Principle -- 3.4. The Prior Covariance Problem -- 3.5. Minimum Variance Estimation with Prior Covariance -- 3.6. Some Criticisms and Conclusions -- 3.7. Exercises -- 4 Adjoints, Projections, Pseudoinverses -- 4.1. Adjoints -- 4.2. Projections -- 4.3. Pseudoinverses -- 4.4. Calculating the Pseudoinverse in Finite Dimensions -- 4.5. The Grammian -- 4.6. Exercises -- 5 Linear Minimum Variance Estimation -- 5.1. Reformulation -- 5.2. Linear Minimum Variance Estimation -- 5.3. Unbiased Estimators, Affine Estimators -- 5.4. Exercises -- 6 Recursive Linear Estimation (Bayesian Estimation) -- 6.1. Introduction -- 6.2. The Recursive Linear Estimator -- 6.3. Exercises -- 7 The Discrete Kalman Filter -- 7.1. Discrete Linear Dynamical Systems -- 7.2. The Kalman Filter -- 7.3. Initialization, Fisher Estimation -- 7.4. Fisher Estimation with Singular Measurement Noise -- 7.5. Exercises -- 8 The Linear Quadratic Tracking Problem -- 8.1. Control of Deterministic Systems -- 8.2. Stochastic Control with Perfect Observations -- 8.3. Stochastic Control with Imperfect Measurement -- 8.4. Exercises -- 9 Fixed Interval Smoothing -- 9.1. Introduction -- 9.2. The Rauch, Tung, Streibel Smoother -- 9.3. The Two-Filter Form of the Smoother -- 9.4. Exercises -- Appendix A Construction Measures -- Appendix B Two Examples from Measure Theory -- Appendix C Measurable Functions -- Appendix D Integration -- Appendix E Introduction to Hilbert Space -- Appendix F The Uniform Boundedness Principle and Invertibility of Operators