Efficient Parameters Estimation Method for the Separable Nonlinear Least Squares Problem

Algorithm 1

Parameter estimation algorithm for the separable nonlinear least squares problem.

	Step 1: given initial values , set , , . is a very small positive number.
	Step 2: calculate the matrix of the nonlinear function and Jacobian matrix of the objective function after VP, using (17).
	Step 3: calculate the iteration step length and iteration direction using (15) and (16), and then update the nonlinear parameters using (14).
	Step 4: if , terminate the algorithm; otherwise, , go to Step 3.
	Step 5: calculate linear parameters when is a nonsingular matrix. The least squares method is used to calculate this directly; when is singular or the condition number of exceeds 100, the solution is obtained using (23).