16.322 | Fall 2004 | Graduate

# Stochastic Estimation and Control

## Assignments

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 ASSIGNMENTS
1 Introduction

Random Signals

Intuitive Notion of Probability

Axiomatic Probability

Joint and Conditional Probability

Problems 1.1-1.4, 1.8
2 Independence

Random Variables

Probability Distribution and Density Functions

Problems 1.9, 1.10, 1.12-1.14
3 Expectation, Averages and Characteristic Function

Normal or Gaussian Random Variables

Impulsive Probability Density Functions

Multiple Random Variables

Problems 1.18-1.20, 1.30, 1.38
4 Correlation, Covariance, and Orthogonality

Sum of Independent Random Variables and Tendency Toward Normal Distribution

Transformation of Random Variables

Problems 1.21-1.24, 1.26
5 Some Common Distributions Problems 1.15, 1.16, 1.27-1.29
6 More Common Distributions

Multivariate Normal Density Function

Linear Transformation and General Properties of Normal Random Variables

Problems 1.33-1.37
7 Linearized Error Propagation Problems A.1, A.6
8 More Linearized Error Propagation Problems A.8, A.13
9 Concept of a Random Process

Probabilistic Description of a Random Process

Gaussian Random Process

Stationarity, Ergodicity, and Classification of Processes

Problems 2.9-2.11, A.5
10 Autocorrelation Function

Crosscorrelation Function

Problems 2.2, 2.12, 2.17, 2.19, 2.20
11 Power Spectral Density Function

Cross Spectral Density Function

White Noise

Problems 2.1, 2.8, 2.14, 2.18, 2.22

Quiz 1 (Covers Sections 1-11)

12 Gauss-Markov Process

Random Telegraph Wave

Wiener or Brownian-Motion Process

Problems 2.16, 2.21, 2.23-2.25
13 Determination of Autocorrelation and Spectral Density Functions from Experimental Data Problem 2.27
14 Introduction: The Analysis Problem

Integral Tables for Computing Mean-Square Value

Problems 3.4, 3.5, 3.7
15 Pure White Noise and Bandlimited Systems

Noise Equivalent Bandwidth

Shaping Filter

Problems 3.8, 3.9, 3.17
16 Nonstationary (Transient) Analysis - Initial Condition Response

Nonstationary (Transient) Analysis - Forced Response

Problems 3.18, 3.21, 3.24
17 The Wiener Filter Problem

Optimization with Respect to a Parameter

Problems 4.4, 4.5
18 The Stationary Optimization Problem - Weighting Function Approach

Orthogonality

Problems 4.7, 4.8
19 Complementary Filter

Perspective

Problems 4.13, 4.14
20 Estimation

A Simple Recursive Example

Problems A.7, A.9

Quiz 2 (Covers Sections 12-20)

21 Markov Processes Problems A.14, A.15
22 State Space Description

Vector Description of a Continuous-Time Random Process

Discrete-Time Model

Problems A.10, A.11, A.16
23 Monte Carlo Simulation of Discrete-Time Systems

The Discrete Kalman Filter

Scalar Kalman Filter Examples

Problems 5.1, 5.2
24 Transition from the Discrete to Continuous Filter Equations

Solution of the Matrix Riccati Equation

Problems 7.1, 7.2
25 Divergence Problems Problems 6.8, 6.9
26 Complementary Filter Methodology

INS Error Models

Damping the Schuler Oscillation with External Velocity Reference Information

Problem 10.3

Final Exam

Fall 2004
Lecture Notes
Problem Sets