For certain system models, the structure of the Kalman filter is equivalent to a second-order vari- able gain digital phase-locked loop （DPLL）. To apply the knowledge of DPLLs to the design of Kalman filters this pa...For certain system models, the structure of the Kalman filter is equivalent to a second-order vari- able gain digital phase-locked loop （DPLL）. To apply the knowledge of DPLLs to the design of Kalman filters this paper studies the steady-state performance of Kalman filters for these system models. The results show that the steady-state Kalman gain has the same form as the DPLL gain. An approximate simple form for the steady-state Kalman gain is used to derive an expression for the equivalent loop bandwidth of the Kalman filter as a function of the process and observation noise variances. These results can be used to analyze the steady-state performance of a Kalman filter with DPLL theory or to design a Kalman filter model with the same steady-state performance as a given DPLL.展开更多
文摘For certain system models, the structure of the Kalman filter is equivalent to a second-order vari- able gain digital phase-locked loop （DPLL）. To apply the knowledge of DPLLs to the design of Kalman filters this paper studies the steady-state performance of Kalman filters for these system models. The results show that the steady-state Kalman gain has the same form as the DPLL gain. An approximate simple form for the steady-state Kalman gain is used to derive an expression for the equivalent loop bandwidth of the Kalman filter as a function of the process and observation noise variances. These results can be used to analyze the steady-state performance of a Kalman filter with DPLL theory or to design a Kalman filter model with the same steady-state performance as a given DPLL.
