16.322 | Fall 2004 | Graduate
Stochastic Estimation and Control

## Calendar

LEC # TOPICS
1 Introduction

Random Signals

Intuitive Notion of Probability

Axiomatic Probability

Joint and Conditional Probability

2 Independence

Random Variables

Probability Distribution and Density Functions

3 Expectation, Averages and Characteristic Function

Normal or Gaussian Random Variables

Impulsive Probability Density Functions

Multiple Random Variables

4 Correlation, Covariance, and Orthogonality

Sum of Independent Random Variables and Tendency Toward Normal Distribution

Transformation of Random Variables

5 Some Common Distributions
6 More Common Distributions

Multivariate Normal Density Function

Linear Transformation and General Properties of Normal Random Variables

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

10 Autocorrelation Function

Crosscorrelation Function

11 Power Spectral Density Function

Cross Spectral Density Function

White Noise

Quiz 1 (Covers Sections 1-11)
12 Gauss-Markov Process

Random Telegraph Wave

Wiener or Brownian-Motion Process

13 Determination of Autocorrelation and Spectral Density Functions from Experimental Data
14 Introduction: The Analysis Problem

Integral Tables for Computing Mean-Square Value

15 Pure White Noise and Bandlimited Systems

Noise Equivalent Bandwidth

Shaping Filter

16 Nonstationary (Transient) Analysis - Initial Condition Response

Nonstationary (Transient) Analysis - Forced Response

17 The Wiener Filter Problem

Optimization with Respect to a Parameter

18 The Stationary Optimization Problem - Weighting Function Approach

Orthogonality

19 Complementary Filter

Perspective

20 Estimation

A Simple Recursive Example

Quiz 2 (Covers Sections 12-20)
21 Markov Processes
22 State Space Description

Vector Description of a Continuous-Time Random Process

Discrete-Time Model

23 Monte Carlo Simulation of Discrete-Time Systems

The Discrete Kalman Filter

Scalar Kalman Filter Examples

24 Transition from the Discrete to Continuous Filter Equations

Solution of the Matrix Riccati Equation

25 Divergence Problems
26 Complementary Filter Methodology

INS Error Models

Damping the Schuler Oscillation with External Velocity Reference Information

Final Exam