16.322 | Fall 2004 | Graduate
Stochastic Estimation and Control

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.

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

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