Answered step by step
Verified Expert Solution
Question
1 Approved Answer
ou are asked to fit a circle with unknown radius but known center ( , ) to points (, ), [1, ]. Points on a
ou are asked to fit a circle with unknown radius but known center ( , ) to points (, ), [1, ]. Points on a circle satisfy: ( )2 ( )2 = . (a) Specify the over-constrained system of linear equations in matrix/vector form. If this is not possible, briefly explain why. (b) Complete the following if it is possible to solve the system: i. How many points are needed for the system to be over-constrained? Why? ii. Give the quadratic-error function for this least-squares estimator in matrix/vec- tor form. You need to specify the dimension of your matrices and vectors and their elements. iii. Differentiate this error function (in matrix/vector form) and set it equal to zero to obtain the normal equations. iv. Solve for . Show that the least-squares solution for the radius is simply the average distance of each point to the center
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started