The Gauss-Newton Method - Nonlinear Output Relationship

3 THE GAUSS-NEWTON METHOD - NONLINEAR OUTPUT RELATIONSHIP 

When the output vector (measured variables) are related to the state variables (and possibly to the parameters) through a nonlinear relationship of the form y(t) = h(x(t),k), we need to make some additional minor modifications. The sensitivity of the output vector to the parameters can be obtained by performing the implicit differentiation to yield  

If the nonlinear output relationship is independent of the parameters, i.e.. it is of the form 

In other words, the observation matrix C from the case of a linear output relationship is substituted with the Jacobean matrix (dhT/dx)T in setting up matrix A and vector b. 

---

Implementation Guidelines for ODE Models The Gauss-Newton Method — Nonlinear Output Relationship The Gauss-Newton Method - Systems with Unknown Initial Conditions Examples... 

---