Random Signals

Intuitive Notion of Probability

Axiomatic Probability

Joint and Conditional Probability

Random Variables

Probability Distribution and Density Functions
3Expectation, Averages and Characteristic Function

Normal or Gaussian Random Variables

Impulsive Probability Density Functions

Multiple Random Variables
4Correlation, Covariance, and Orthogonality

Sum of Independent Random Variables and Tendency Toward Normal Distribution

Transformation of Random Variables
5Some Common Distributions
6More Common Distributions

Multivariate Normal Density Function

Linear Transformation and General Properties of Normal Random Variables
7Linearized Error Propagation
8More Linearized Error Propagation
9Concept of a Random Process

Probabilistic Description of a Random Process

Gaussian Random Process

Stationarity, Ergodicity, and Classification of Processes
10Autocorrelation Function

Crosscorrelation Function
11Power Spectral Density Function

Cross Spectral Density Function

White Noise
 Quiz 1 (Covers Sections 1-11)
12Gauss-Markov Process

Random Telegraph Wave

Wiener or Brownian-Motion Process
13Determination of Autocorrelation and Spectral Density Functions from Experimental Data
14Introduction: The Analysis Problem

Stationary (Steady-State) Analysis

Integral Tables for Computing Mean-Square Value
15Pure White Noise and Bandlimited Systems

Noise Equivalent Bandwidth

Shaping Filter
16Nonstationary (Transient) Analysis - Initial Condition Response

Nonstationary (Transient) Analysis - Forced Response
17The Wiener Filter Problem

Optimization with Respect to a Parameter
18The Stationary Optimization Problem - Weighting Function Approach

19Complementary Filter


A Simple Recursive Example
 Quiz 2 (Covers Sections 12-20)
21Markov Processes
22State Space Description

Vector Description of a Continuous-Time Random Process

Discrete-Time Model 
23Monte Carlo Simulation of Discrete-Time Systems

The Discrete Kalman Filter

Scalar Kalman Filter Examples
24Transition from the Discrete to Continuous Filter Equations

Solution of the Matrix Riccati Equation
25Divergence Problems
26Complementary Filter Methodology

INS Error Models

Damping the Schuler Oscillation with External Velocity Reference Information
 Final Exam