Lecture Notes

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 (PDF)
6 More Common Distributions

Multivariate Normal Density Function

Linear Transformation and General Properties of Normal Random Variables
7 Linearized Error Propagation (PDF)
8 More Linearized Error Propagation (PDF)
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 (PDF)
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

19 Complementary Filter

20 Estimation

A Simple Recursive Example
  Quiz 2 (Covers Sections 12-20)  
21 Markov Processes (PDF)
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 (PDF)
26 Complementary Filter Methodology

INS Error Models

Damping the Schuler Oscillation with External Velocity Reference Information
  Final Exam