# Readings

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 # TOPICS READINGS
1 Introduction

Random Signals

Intuitive Notion of Probability

Axiomatic Probability

Joint and Conditional Probability
Sections 1.1-1.4
2 Independence

Random Variables

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

Normal or Gaussian Random Variables

Impulsive Probability Density Functions

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

Sum of Independent Random Variables and Tendency Toward Normal Distribution

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

Multivariate Normal Density Function

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

Crosscorrelation Function
Sections 2.5, 2.6
11 Power Spectral Density Function

Cross Spectral Density Function

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

Random Telegraph Wave

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

Stationary (Steady-State) Analysis

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

Noise Equivalent Bandwidth

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

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

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

Orthogonality
Sections 4.3, 4.5
19 Complementary Filter

Perspective
Sections 4.6, 4.8
20 Estimation

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

Vector Description of a Continuous-Time Random Process

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

The Discrete Kalman Filter

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

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

INS Error Models

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