LEC #  TOPICS  LECTURE NOTES 

1 
Introduction
Random Signals Intuitive Notion of Probability Axiomatic Probability Joint and Conditional Probability 
(PDF) 
2 
Independence
Random Variables Probability Distribution and Density Functions 
(PDF) 
3 
Expectation, Averages and Characteristic Function
Normal or Gaussian Random Variables Impulsive Probability Density Functions Multiple Random Variables 
(PDF) 
4 
Correlation, Covariance, and Orthogonality
Sum of Independent Random Variables and Tendency Toward Normal Distribution Transformation of Random Variables 
(PDF) 
5  Some Common Distributions  (PDF) 
6 
More Common Distributions
Multivariate Normal Density Function Linear Transformation and General Properties of Normal Random Variables 
(PDF) 
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 
(PDF) 
10 
Autocorrelation Function
Crosscorrelation Function 
(PDF) 
11 
Power Spectral Density Function
Cross Spectral Density Function White Noise 
(PDF) 
Quiz 1 (Covers Sections 111)  
12 
GaussMarkov Process
Random Telegraph Wave Wiener or BrownianMotion Process 
(PDF) 
13  Determination of Autocorrelation and Spectral Density Functions from Experimental Data  (PDF) 
14 
Introduction: The Analysis Problem
Stationary (SteadyState) Analysis Integral Tables for Computing MeanSquare Value 
(PDF) 
15 
Pure White Noise and Bandlimited Systems
Noise Equivalent Bandwidth Shaping Filter 
(PDF) 
16 
Nonstationary (Transient) Analysis  Initial Condition Response
Nonstationary (Transient) Analysis  Forced Response 
(PDF) 
17 
The Wiener Filter Problem
Optimization with Respect to a Parameter 
(PDF) 
18 
The Stationary Optimization Problem  Weighting Function Approach
Orthogonality 
(PDF) 
19 
Complementary Filter
Perspective 
(PDF) 
20 
Estimation
A Simple Recursive Example 
(PDF) 
Quiz 2 (Covers Sections 1220)  
21  Markov Processes  (PDF) 
22 
State Space Description
Vector Description of a ContinuousTime Random Process DiscreteTime Model 
(PDF) 
23 
Monte Carlo Simulation of DiscreteTime Systems
The Discrete Kalman Filter Scalar Kalman Filter Examples 
(PDF) 
24 
Transition from the Discrete to Continuous Filter Equations
Solution of the Matrix Riccati Equation 
(PDF) 
25  Divergence Problems  (PDF) 
26 
Complementary Filter Methodology
INS Error Models Damping the Schuler Oscillation with External Velocity Reference Information 

Final Exam 
Lecture Notes
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Fall
2004
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