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.Comment: Accepted by AIAA Journal of Guidance, Control and Dynamics, Dec 201
