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

1 |
Introduction
Random Signals Intuitive Notion of Probability Axiomatic Probability Joint and Conditional Probability |

2 |
Independence
Random Variables Probability Distribution and Density Functions |

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

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

5 | Some Common Distributions |

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

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 |

10 |
Autocorrelation Function
Crosscorrelation Function |

11 |
Power Spectral Density Function
Cross Spectral Density Function White Noise |

Quiz 1 (Covers Sections 1-11) | |

12 |
Gauss-Markov Process
Random Telegraph Wave Wiener or Brownian-Motion Process |

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

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

15 |
Pure White Noise and Bandlimited Systems
Noise Equivalent Bandwidth Shaping Filter |

16 |
Nonstationary (Transient) Analysis - Initial Condition Response
Nonstationary (Transient) Analysis - Forced Response |

17 |
The Wiener Filter Problem
Optimization with Respect to a Parameter |

18 |
The Stationary Optimization Problem - Weighting Function Approach
Orthogonality |

19 |
Complementary Filter
Perspective |

20 |
Estimation
A Simple Recursive Example |

Quiz 2 (Covers Sections 12-20) | |

21 | Markov Processes |

22 |
State Space Description
Vector Description of a Continuous-Time Random Process Discrete-Time Model |

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

24 |
Transition from the Discrete to Continuous Filter Equations
Solution of the Matrix Riccati Equation |

25 | Divergence Problems |

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

Final Exam |

## Calendar

## Course Info

##### Instructor

##### Departments

##### As Taught In

Fall
2004

##### Level

##### Topics

##### Learning Resource Types

*notes*Lecture Notes

*assignment*Problem Sets