A Research On Design And Application Of Kalman Filter

The theory of Kalman filtering was proposed by R.E.Kalman in the1960s, whichbroke through the limitations of the classical Wiener filtering theory. Kalman filteringis the optimization of regression algorithm of data processing. The standard toestimate is that the mean square error (MSE) is minimum. Then a recursiveestimation in Kalman method is successfully achieved. Kalman filtering algorithmuses state space method in time domain to design filter, which can solve the problemof multi-dimensional system and non-stationary random process.The optimalestimation of Linear dynamic system under the random disturbance can be achieved.Kalman filter has a wide application in engineering because of its own advantages,such as recursive estimate, simple calculation, adaptability, forward-looking characteretc..At present, the Kalman filtering has been widely applied in navigation andguidance, communication engineering, fault diagnosis, speech processing, industrialprocess control and many other fields. However, when the application of Kalmanfiltering algorithm is proceeded, for example, the speech enhancement, the estimatedsignals usually have the filtering divergence problem and can not meet the real-timerequirements.In order to figure out these problems, the causes and the correspondingsuppression methods of Kalman filtering divergence are synthetically analyzed. Thenthe new ways and methods are discussed. The FPGA implementation of the algorithmis deeply analyzed.Some researchs are made when Kalman filtering is applied intospeech enhancement. The main contents are following:(1)The methods of suppressing Kalman filtering divergence are summarized andanalyzed. The comparative advantages of these methods are concluded. Theconclusion shows that weighting Kalman filtering algorithm can reach a balancebetween calculation accuracy and computing speed. So a new variable weightingKalman filtering method is proposed, which provides different weighted coefficientsto the observation with the different moments. The feasibility of new method isproved successfully through simulation examples.(2) The problem which Kalman filtering can meet the real-time requirements or not in application is discussed. The traditional implementation methods and the FPGAhardware implementation are compared. Kalman filter model is established by usingFPGA aided design tool DSP Builder. And then by the model simulation, the functionsimulation and timing simulation, it is proved that the FPGA implementation ofKalman filter is successful.(3)It is discussed how Kalman filter takes the most effective filtering anddenoising effect in the application of speech enhancement. A speech enhancementsystem is established. The subsystems which are the framing of speech signal, theextract of phonetic parameter and the Kalman filter are respectively researched.Finally the availability of Kalman filtering method is confirmed through thesimulation analysis.