exercise3
Exercise 3
(a)
Let be the measurement at time .
Let be the number of measurements. In this case, .
The residual at time is
The objective function is
Our goal is to minimize , it is a least-squares problem.
The Jacobian matrix is
(b)
Gauss-Newton
Parameters
Name Value
x0 [1,1,1]’
descent ‘gauss’
alpha0 0.05
tol 0.00001
maxIter 10000
3.3976 147.2555 1.9922 88.0913
Result
Plot
Levenberg-Marquardt
Parameters
Name Value
x0 [1,1,1]’
Delta 1
eta 0.001
tol 0.00001
maxIter 10000
3.3984 147.2763 1.9922 88.0908
Result
Plot
Discussion
We can see that the parameters estimated by Gauss-Newton and Levenberg-Marquardt are
very similar. The objective value achieved by Levenberg-Marquardt is a little lower than Gauss-
Newton (88.0908 compared with 88.0913).
From the fit plots, we also can see their estimation have no obvious difference, both are good
fit the noisy measurements. The estimated paraeters are close to the actual value.
Exercise 3
(a)
(b)
Gauss-Newton
Parameters
Result
Plot
Levenberg-Marquardt
Parameters
Result
Plot
Discussion