Measurement covariance-constrained estimation for poorly modeled dynamic systems
An optimal estimation strategy is developed for post-experiment estimation of discretely measured dynamic systems which accounts for system model errors in a much more rigorous manner than Kalman filter-smoother type methods. The Kalman filter-smoother type methods, which currently dominate post-experiment estimation practice, treat model errors via “process noise", which essentially shifts emphasis away from the model and onto the measurements. The usefulness of this approach is subject to the measurement frequency and accuracy.
The current method treats model errors by use of an estimation strategy based on concepts from optimal control theory. Unknown model error terms are explicitly included in the formulation of the problem and estimated as a part of the solution. In this manner, the estimate is improved; the model is improved; and an estimate of the model error is obtained. Implementation of the current method is straightforward, and the resulting state trajectories do not contain jump discontinuities as do the Kalman filter-smoother type estimates.
Results from a number of simple examples, plus some examples from spacecraft attitude estimation, are included. The current method is shown to obtain significantly more accurate estimates than the Kalman filter-smoother type methods in many of the examples. The difference in accuracy is accentuated when the assumed model is relatively poor and when the measurements are relatively sparse in time and/or of low accuracy. Even for some well-modeled, densely measured applications, the current method is shown to be competitive with the Kalman filter-smoother type methods.