Probability and Stochastic Processes in Dynamical Systems
MAE C175A

Fall 2014
MAE 271A Project
Calibration of an Accelerometer Using GPS
Measurements
Due December 10, 2014
Consider that a vehicle accelerates in one dimension in an inertial frame.
Assume that the acceleration is a harmonic of the form
a(t) = 10sin(2t) meters/sec2
wh
Probability and Stochastic Processes in Dynamical Systems
MAE C175A

Fall 2014
Least Squares, the Orthogonal Projection Lemma, and DiscreteTime Kalman Filtering
1 / 56
Least Squares, the Orthogonal Projection Lemma, and
DiscreteTime Kalman Filtering
Least Squares, the Orthogonal Projection Lemma, and DiscreteTime Kalman Filtering
Probability and Stochastic Processes in Dynamical Systems
MAE C175A

Fall 2014
Random Variables and Stochastic Processes
Random Variables and Stochastic Processes
1 / 96
Random Variables and Stochastic Processes
Table of content
1 Random Variables
2 Probability Distribution Function
3 Probability Density Function
4 Probabilistic Con
Probability and Stochastic Processes in Dynamical Systems
MAE C175A

Fall 2014
Probability Theory
1 / 34
Probability Theory
1 Probability Theory Is Based on a Set of Outcomes: Sample
Space
2 Set Theory
3 Probability Space and the Probability Measure
4 Algebras of Sets and Probability Space
5 Key Concepts in Probability Theory
Probab