| Abstract: |
| This paper considers robust state estimation for continuous time-varying systems involving arbitrary unknown inputs and random noises. After a time-varying transformation decoupling the system from the unknown inputs, the Kalman filter is applied to the transformed system before recovering the state of the original system. With the decoupling transformation in a simple closed-form, the computational cost of the whole algorithm is close to that of the classical Kalman filter. Under assumptions involving a Gramian matrix similar to the classical observability Gramian, it is shown that the proposed algorithm is an asymptotically unbiased state estimator, i.e., the mathematical expectation of the state estimation error converges exponentially to zero, and the covariance of the state estimation error is bounded. Simulation examples illustrate the effectiveness of the proposed algorithm. |
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