Extending the Practical Applicability of the Kalman Filter
Abstract
A Schmidt filter is a modification of the Kalman filter that allows to append system parameters
as states and considers their uncertainty effect in the filtering process without attempting to estimate such parameters. The states that are only considered but not estimated, are generally known as consider or considered states. The main contributions of this research are the formulations of a Schmidt-Kalman filter that incorporates the numerical robustness of the well-known square root and factorized filtering forms plus the capacity of actively attempting to update the considered states.
The filters formulations proposed in this research are a fundamental extension of the Kalman
filter. Therefore, the formulations of this work also apply within the Extended Kalman filter framework. More importantly, they are shown to handle nonlinearities, larger initial uncertainties, and poorly conditioned systems better than a typical Extended or Schmidt Kalman filter. Because the new filters directly based on the Schmidt filter, they offer a novel and straight-forward filtering framework, allowing the use of a more simple filter where a more advanced or elaborated technique could have been needed.
The proposed contributions of this research are organized as follows. First, the Partial-update
Kalman filter, a generalized Schmidt filter that allows updating the user-selected consider states
partially, is introduced. The indirect or multiplicative error version of this new filter is also derived. An error stability analysis (for linear systems) of the partial-update filter and a discussion on its numerical stability and the potential numerical robustness improvements is presented. Second, a square root formulation to improve the numerical stability of the partial-update Schmidt filter is developed. The derivation of sequential and vector measurement processing schemes for the square root formulation are both presented along with a brief computational complexity and Montecarlo analysis. Third, to gain computational efficiency but still retaining a numerically robust formulation, as an alternative, a U-D factorized version of the partial-update filter is also developed. Fourth, to improve estimation consistency and accuracy of the partial-update filter, baseline methods are proposed to attempt the estimation of the considered states. Finally, formulations proposed in this research are validated through hardware implementations to solve aerospace engineering-related problems.
Subject
Partial-updateSchmidt filter
Schmidt
consider filter
Kalman filter
high uncertainty
robust Kalman filter
factorized filter
high precision
hardware
camera calibration
estimation
optimal state estimation
multiplicative extended Kalman filter
nonlinear
extended Kalman filter
robust extended Kalman filter
Citation
Ramos Zuniga, Jose Humberto (2020). Extending the Practical Applicability of the Kalman Filter. Doctoral dissertation, Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /192487.
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