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 | READINGS |
---|---|---|

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

2 |
Independence
Random Variables Probability Distribution and Density Functions |
Sections 1.5-1.7 |

3 |
Expectation, Averages and Characteristic Function
Normal or Gaussian Random Variables Impulsive Probability Density Functions Multiple Random Variables |
Sections 1.8-1.11 |

4 |
Correlation, Covariance, and Orthogonality
Sum of Independent Random Variables and Tendency Toward Normal Distribution Transformation of Random Variables |
Sections 1.12-1.14 |

5 | Some Common Distributions | |

6 |
More Common Distributions
Multivariate Normal Density Function Linear Transformation and General Properties of Normal Random Variables |
Sections 1.15, 1.16 |

7 | Linearized Error Propagation | |

8 | More Linearized Error Propagation | |

9 |
Concept of a Random Process
Probabilistic Description of a Random Process Gaussian Random Process Stationarity, Ergodicity, and Classification of Processes |
Sections 2.1-2.4 |

10 |
Autocorrelation Function
Crosscorrelation Function |
Sections 2.5, 2.6 |

11 |
Power Spectral Density Function
Cross Spectral Density Function White Noise |
Sections 2.7-2.9 |

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

12 |
Gauss-Markov Process
Random Telegraph Wave Wiener or Brownian-Motion Process |
Sections 2.10, 2.11, 2.13 |

13 | Determination of Autocorrelation and Spectral Density Functions from Experimental Data | Section 2.15 |

14 |
Introduction: The Analysis Problem
Stationary (Steady-State) Analysis Integral Tables for Computing Mean-Square Value |
Sections 3.1-3.3 |

15 |
Pure White Noise and Bandlimited Systems
Noise Equivalent Bandwidth Shaping Filter |
Sections 3.4-3.6 |

16 |
Nonstationary (Transient) Analysis - Initial Condition Response
Nonstationary (Transient) Analysis - Forced Response |
Sections 3.7, 3.8 |

17 |
The Wiener Filter Problem
Optimization with Respect to a Parameter |
Sections 4.1, 4.2 |

18 |
The Stationary Optimization Problem - Weighting Function Approach
Orthogonality |
Sections 4.3, 4.5 |

19 |
Complementary Filter
Perspective |
Sections 4.6, 4.8 |

20 |
Estimation
A Simple Recursive Example |
Section 5.1 |

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

21 | Markov Processes | |

22 |
State Space Description
Vector Description of a Continuous-Time Random Process Discrete-Time Model |
Sections 5.2, 5.3 |

23 |
Monte Carlo Simulation of Discrete-Time Systems
The Discrete Kalman Filter Scalar Kalman Filter Examples |
Sections 5.4-5.6 |

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

25 | Divergence Problems | Section 6.6 |

26 |
Complementary Filter Methodology
INS Error Models Damping the Schuler Oscillation with External Velocity Reference Information |
Sections 10.1-10.3 |

Final Exam |