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Amazon logo Brown, Robert Grover, and Patrick Y. C. Hwang. Introduction to Random Signals and Applied Kalman Filtering. New York: John Wiley & Sons, March 1992. ISBN: 0471525685.

LEC #TOPICSREADINGS
1Introduction

Random Signals

Intuitive Notion of Probability

Axiomatic Probability

Joint and Conditional Probability
Sections 1.1-1.4
2Independence

Random Variables

Probability Distribution and Density Functions
Sections 1.5-1.7
3Expectation, Averages and Characteristic Function

Normal or Gaussian Random Variables

Impulsive Probability Density Functions

Multiple Random Variables
Sections 1.8-1.11
4Correlation, Covariance, and Orthogonality

Sum of Independent Random Variables and Tendency Toward Normal Distribution

Transformation of Random Variables
Sections 1.12-1.14
5Some Common Distributions
6More Common Distributions

Multivariate Normal Density Function

Linear Transformation and General Properties of Normal Random Variables
Sections 1.15, 1.16
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
Sections 2.1-2.4
10Autocorrelation Function

Crosscorrelation Function
Sections 2.5, 2.6
11Power Spectral Density Function

Cross Spectral Density Function

White Noise
Sections 2.7-2.9
Quiz 1 (Covers Sections 1-11)
12Gauss-Markov Process

Random Telegraph Wave

Wiener or Brownian-Motion Process
Sections 2.10, 2.11, 2.13
13Determination of Autocorrelation and Spectral Density Functions from Experimental DataSection 2.15
14Introduction: The Analysis Problem

Stationary (Steady-State) Analysis

Integral Tables for Computing Mean-Square Value
Sections 3.1-3.3
15Pure White Noise and Bandlimited Systems

Noise Equivalent Bandwidth

Shaping Filter
Sections 3.4-3.6
16Nonstationary (Transient) Analysis - Initial Condition Response

Nonstationary (Transient) Analysis - Forced Response
Sections 3.7, 3.8
17The Wiener Filter Problem

Optimization with Respect to a Parameter
Sections 4.1, 4.2
18The Stationary Optimization Problem - Weighting Function Approach

Orthogonality
Sections 4.3, 4.5
19Complementary Filter

Perspective
Sections 4.6, 4.8
20Estimation

A Simple Recursive Example
Section 5.1
Quiz 2 (Covers Sections 12-20)
21Markov Processes
22State Space Description

Vector Description of a Continuous-Time Random Process

Discrete-Time Model 
Sections 5.2, 5.3
23Monte Carlo Simulation of Discrete-Time Systems

The Discrete Kalman Filter

Scalar Kalman Filter Examples
Sections 5.4-5.6
24Transition from the Discrete to Continuous Filter Equations

Solution of the Matrix Riccati Equation
Sections 7.1, 7.2
25Divergence ProblemsSection 6.6
26Complementary Filter Methodology

INS Error Models

Damping the Schuler Oscillation with External Velocity Reference Information
Sections 10.1-10.3
Final Exam

 








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