| 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 |