A Two-Stage Batch Algorithm for Nonlinear Static Parameter Estimation

A two-stage batch estimation algorithm for solving a class of nonlinear, static parameter estimation problems that appear in aerospace engineering applications is proposed. It is shown how these problems can be recast into a form suitable for the proposed two-stage estimation process. In the first stage, linear least squares is used to obtain a subset of the unknown parameters (set 1), while a residual sampling procedure is used for selecting initial values for the rest of the parameters (set 2). In the second stage, depending on the uniqueness of the local minimum, either only the parameters in the second set need to be re-estimated, or all the parameters will have to be re-estimated simultaneously, by a nonlinear constrained optimization. The estimates from the first stage are used as initial conditions for the second stage optimizer. It is shown that this approach alleviates the sensitivity to initial conditions and minimizes the likelihood of converging to an incorrect local minimum of the nonlinear cost function. An error bound analysis is presented to show that the first stage can be solved in such a way that the total cost function will be driven to the optimal cost, and the difference has an upper bound. Two tutorial examples are used to show how to implement this estimator and compare its performance to other similar nonlinear estimators. Finally, the estimator is used on a 5-hole Pitot tube calibration problem using flight test data collected from a small Unmanned Aerial Vehicle (UAV) which cannot be easily solved with single-stage methods.