A New Unbiased FIR Filter with Improved Robustness Based on Frobenius Norm with Exponential Weight

This brief proposes a new unbiased finite impulse response (FIR) filter with improved robustness for state-space models in continuous time. The FIR filter proposed in this brief is called the unbiased FIR filter based on the Frobenius norm and exponential weight (UFFFNE). A new integral cost function based on the Frobenius norm for the filter gain function with exponential weight is introduced to improve its robustness. It is shown that the UFFFNE design problem can be cast into the constrained minimum-energy optimal control problem. A new analytic expression for the gain function of the UFFFNE is also proposed. The higher robustness of the proposed UFFFNE is demonstrated through a comparison with the existing minimum variance unbiased FIR filter and the conventional Kalman-Bucy filter based on a numerical example.