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 |