| 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 |
