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 Stationary (Steady-State) Analysis 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