程序代写代做代考 exercise3

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