Brown, Robert Grover, and Patrick Y. C. Hwang. *Introduction to Random Signals and Applied Kalman Filtering.* New York: John Wiley & Sons, March 1992. ISBN: 0471525685.

LEC # | TOPICS | ASSIGNMENTS |
---|---|---|

1 |
Introduction
Random Signals Intuitive Notion of Probability Axiomatic Probability Joint and Conditional Probability |
Problems 1.1-1.4, 1.8 |

2 |
Independence
Random Variables Probability Distribution and Density Functions |
Problems 1.9, 1.10, 1.12-1.14 |

3 |
Expectation, Averages and Characteristic Function
Normal or Gaussian Random Variables Impulsive Probability Density Functions Multiple Random Variables |
Problems 1.18-1.20, 1.30, 1.38 |

4 |
Correlation, Covariance, and Orthogonality
Sum of Independent Random Variables and Tendency Toward Normal Distribution Transformation of Random Variables |
Problems 1.21-1.24, 1.26 |

5 | Some Common Distributions | Problems 1.15, 1.16, 1.27-1.29 |

6 |
More Common Distributions
Multivariate Normal Density Function Linear Transformation and General Properties of Normal Random Variables |
Problems 1.33-1.37 |

7 | Linearized Error Propagation | Problems A.1, A.6 |

8 | More Linearized Error Propagation | Problems A.8, A.13 |

9 |
Concept of a Random Process
Probabilistic Description of a Random Process Gaussian Random Process Stationarity, Ergodicity, and Classification of Processes |
Problems 2.9-2.11, A.5 |

10 |
Autocorrelation Function
Crosscorrelation Function |
Problems 2.2, 2.12, 2.17, 2.19, 2.20 |

11 |
Power Spectral Density Function
Cross Spectral Density Function White Noise |
Problems 2.1, 2.8, 2.14, 2.18, 2.22 |

Quiz 1 (Covers Sections 1-11) | ||

12 |
Gauss-Markov Process
Random Telegraph Wave Wiener or Brownian-Motion Process |
Problems 2.16, 2.21, 2.23-2.25 |

13 | Determination of Autocorrelation and Spectral Density Functions from Experimental Data | Problem 2.27 |

14 |
Introduction: The Analysis Problem
Stationary (Steady-State) Analysis Integral Tables for Computing Mean-Square Value |
Problems 3.4, 3.5, 3.7 |

15 |
Pure White Noise and Bandlimited Systems
Noise Equivalent Bandwidth Shaping Filter |
Problems 3.8, 3.9, 3.17 |

16 |
Nonstationary (Transient) Analysis - Initial Condition Response
Nonstationary (Transient) Analysis - Forced Response |
Problems 3.18, 3.21, 3.24 |

17 |
The Wiener Filter Problem
Optimization with Respect to a Parameter |
Problems 4.4, 4.5 |

18 |
The Stationary Optimization Problem - Weighting Function Approach
Orthogonality |
Problems 4.7, 4.8 |

19 |
Complementary Filter
Perspective |
Problems 4.13, 4.14 |

20 |
Estimation
A Simple Recursive Example |
Problems A.7, A.9 |

Quiz 2 (Covers Sections 12-20) | ||

21 | Markov Processes | Problems A.14, A.15 |

22 |
State Space Description
Vector Description of a Continuous-Time Random Process Discrete-Time Model |
Problems A.10, A.11, A.16 |

23 |
Monte Carlo Simulation of Discrete-Time Systems
The Discrete Kalman Filter Scalar Kalman Filter Examples |
Problems 5.1, 5.2 |

24 |
Transition from the Discrete to Continuous Filter Equations
Solution of the Matrix Riccati Equation |
Problems 7.1, 7.2 |

25 | Divergence Problems | Problems 6.8, 6.9 |

26 |
Complementary Filter Methodology
INS Error Models Damping the Schuler Oscillation with External Velocity Reference Information |
Problem 10.3 |

Final Exam |