1 Basic Probability. - 1. 1. Definitions. - 1. 2. Probability Distributions and Densities. - 1. 3. Expected Value Covariance. - 1. 4. Independence. - 1. 5. The RadonNikodym 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 EstimationHow the Theory Fits. - 2. 1. Theory Versus PracticeSome 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. Language: English