MIT6_241JS11_lec02

# MIT6_241JS11_lec02 - 6.241 Dynamic Systems and Control...

This preview shows pages 1–5. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 6.241 Dynamic Systems and Control Lecture 2: Least Square Estimation Readings: DDV, Chapter 2 Emilio Frazzoli Aeronautics and Astronautics Massachusetts Institute of Technology February 7, 2011 E. Frazzoli (MIT) Lecture 2: Least Squares Estimation Feb 7, 2011 1 / 9 Outline 1 Least Squares Estimation E. Frazzoli (MIT) Lecture 2: Least Squares Estimation Feb 7, 2011 2 / 9 Least Squares Estimation Consider an system of m equations in n unknown, with m > n , of the form y = Ax . Assume that the system is inconsistent : there are more equations than unknowns, and these equations are non linear combinations of one another. In these conditions, there is no x such that y − Ax = 0. However, one can write e = y − Ax , and find x that minimizes e . In particular, the problem min e 2 = min y − Ax 2 x x is a least squares problem. The optimal x is the least squares estimate . E. Frazzoli (MIT) Lecture 2: Least Squares Estimation Feb 7, 2011 3 / 9 Computing the Least-Square Estimate The set M := { z ∈ R m : z = Ax , x ∈ R n } is a subspace of R m , called the range of A , R ( A ), i.e., the set of all vectors that can be obtained by linear combinations...
View Full Document

## This note was uploaded on 01/12/2012 for the course ECE 6.241j taught by Professor Prof.emiliofrazzoli during the Spring '11 term at MIT.

### Page1 / 10

MIT6_241JS11_lec02 - 6.241 Dynamic Systems and Control...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online