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Stochastic Estimation and Control >> Content Detail



Lecture Notes



Lecture Notes

LEC #TOPICSLECTURE NOTES
1Introduction

Random Signals

Intuitive Notion of Probability

Axiomatic Probability

Joint and Conditional Probability
(PDF)
2Independence

Random Variables

Probability Distribution and Density Functions
(PDF)
3Expectation, Averages and Characteristic Function

Normal or Gaussian Random Variables

Impulsive Probability Density Functions

Multiple Random Variables
(PDF)
4Correlation, Covariance, and Orthogonality

Sum of Independent Random Variables and Tendency Toward Normal Distribution

Transformation of Random Variables
(PDF)
5Some Common Distributions(PDF)
6More Common Distributions

Multivariate Normal Density Function

Linear Transformation and General Properties of Normal Random Variables
(PDF)
7Linearized Error Propagation(PDF)
8More Linearized Error Propagation(PDF)
9Concept of a Random Process

Probabilistic Description of a Random Process

Gaussian Random Process

Stationarity, Ergodicity, and Classification of Processes
(PDF)
10Autocorrelation Function

Crosscorrelation Function
(PDF)
11Power Spectral Density Function

Cross Spectral Density Function

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

Random Telegraph Wave

Wiener or Brownian-Motion Process
(PDF)
13Determination of Autocorrelation and Spectral Density Functions from Experimental Data(PDF)
14Introduction: The Analysis Problem

Stationary (Steady-State) Analysis

Integral Tables for Computing Mean-Square Value
(PDF)
15Pure White Noise and Bandlimited Systems

Noise Equivalent Bandwidth

Shaping Filter
(PDF)
16Nonstationary (Transient) Analysis - Initial Condition Response

Nonstationary (Transient) Analysis - Forced Response
(PDF)
17The Wiener Filter Problem

Optimization with Respect to a Parameter
(PDF)
18The Stationary Optimization Problem - Weighting Function Approach

Orthogonality
(PDF)
19Complementary Filter

Perspective
(PDF)
20Estimation

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

Vector Description of a Continuous-Time Random Process

Discrete-Time Model 
(PDF)
23Monte Carlo Simulation of Discrete-Time Systems

The Discrete Kalman Filter

Scalar Kalman Filter Examples
(PDF)
24Transition from the Discrete to Continuous Filter Equations

Solution of the Matrix Riccati Equation
(PDF)
25Divergence Problems(PDF)
26Complementary Filter Methodology

INS Error Models

Damping the Schuler Oscillation with External Velocity Reference Information
Final Exam

 








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