Smoothed Multiple Model Adaptive Estimation

This paper discusses the subject of unmeasurable parameter (or state) estimation. It presents a viable option for carrying out this task, as well as augmentations for mending its flaws. The selected basic method is Multiple Model Adaptive Estimation, using multiple Kalman Filters (KFs) in parallel to determine the current value of the parameter (or state) using other sensor measurements. However, this method is proven to give a staircase function as estimate in case of continuous variation of the unknown parameter. In some cases this leads to unacceptable estimation errors. One possible solution is to increase the number of KFs but this can also highly increase the computational load. Searching for alternative solutions resulted in the idea of using parabolic curve fitting on the discrete parameter values, so that the minimal value of the parabola could interpolate between the fixed values and so better locate the true parameter. Tests in an example showed that this method gives satisfactory results inside the covered parameter range but on the boundaries it can be inaccurate. With supplementation of the original parameter range (extension of the boundaries) and extrapolation of the parabolic curve one can finally achieve a highly accurate parameter estimate. This is demonstrated by an application example which offers calibrated airspeed estimation on a high-fidelity Airbus civil aircraft model.