Continuous-time norm-constrained Kalman filtering |
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Authors: | James Richard Forbes Anton HJ de Ruiter David Evan Zlotnik |
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Affiliation: | 1. Department of Aerospace Engineering, University of Michigan, FXB Building, 1320 Beal Avenue, Ann Arbor, MI, 48109, USA;2. Department of Aerospace Engineering, Ryerson University, 350 Victoria Street, Toronto, ON, Canada, M5B 2K3 |
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Abstract: | This paper considers continuous-time state estimation when part of the state estimate or the entire state estimate is norm-constrained. In the former case continuous-time state estimation is considered by posing a constrained optimization problem. The optimization problem can be broken up into two separate optimization problems, one which solves for the optimal observer gain associated with the unconstrained state estimates, while the other solves for the optimal observer gain associated with the constrained state estimates. The optimal constrained state estimate is found by projecting the time derivative of an unconstrained estimate onto the tangent space associated with the norm constraint. The special case where the entire state estimate is norm-constrained is briefly discussed. The utility of the filtering results developed are highlighted through a spacecraft attitude estimation example. Numerical simulation results are included. |
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Keywords: | State estimation Constraints Kalman filters Extended Kalman filters |
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