Stochastic Estimation and Control

Lecture Notes

LEC #	TOPICS	LECTURE NOTES
1	Introduction Random Signals Intuitive Notion of Probability Axiomatic Probability Joint and Conditional Probability	(PDF)
2	Independence Random Variables Probability Distribution and Density Functions	(PDF)
3	Expectation, Averages and Characteristic Function Normal or Gaussian Random Variables Impulsive Probability Density Functions Multiple Random Variables	(PDF)
4	Correlation, Covariance, and Orthogonality Sum of Independent Random Variables and Tendency Toward Normal Distribution Transformation of Random Variables	(PDF)
5	Some Common Distributions	(PDF)
6	More Common Distributions Multivariate Normal Density Function Linear Transformation and General Properties of Normal Random Variables	(PDF)
7	Linearized Error Propagation	(PDF)
8	More Linearized Error Propagation	(PDF)
9	Concept of a Random Process Probabilistic Description of a Random Process Gaussian Random Process Stationarity, Ergodicity, and Classification of Processes	(PDF)
10	Autocorrelation Function Crosscorrelation Function	(PDF)
11	Power Spectral Density Function Cross Spectral Density Function White Noise	(PDF)
	Quiz 1 (Covers Sections 1-11)
12	Gauss-Markov Process Random Telegraph Wave Wiener or Brownian-Motion Process	(PDF)
13	Determination of Autocorrelation and Spectral Density Functions from Experimental Data	(PDF)
14	Introduction: The Analysis Problem Stationary (Steady-State) Analysis Integral Tables for Computing Mean-Square Value	(PDF)
15	Pure White Noise and Bandlimited Systems Noise Equivalent Bandwidth Shaping Filter	(PDF)
16	Nonstationary (Transient) Analysis - Initial Condition Response Nonstationary (Transient) Analysis - Forced Response	(PDF)
17	The Wiener Filter Problem Optimization with Respect to a Parameter	(PDF)
18	The Stationary Optimization Problem - Weighting Function Approach Orthogonality	(PDF)
19	Complementary Filter Perspective	(PDF)
20	Estimation A Simple Recursive Example	(PDF)
	Quiz 2 (Covers Sections 12-20)
21	Markov Processes	(PDF)
22	State Space Description Vector Description of a Continuous-Time Random Process Discrete-Time Model	(PDF)
23	Monte Carlo Simulation of Discrete-Time Systems The Discrete Kalman Filter Scalar Kalman Filter Examples	(PDF)
24	Transition from the Discrete to Continuous Filter Equations Solution of the Matrix Riccati Equation	(PDF)
25	Divergence Problems	(PDF)
26	Complementary Filter Methodology INS Error Models Damping the Schuler Oscillation with External Velocity Reference Information
	Final Exam