Abstract: In this paper, a new nonlinear adaptive filter is presented. This filter consists of three main parts. In the first part, the input space is mapped into the high dimensional space, HDS, using the RBF kernel. The second part employs the Kalman filter as a smoother in HDS. The RLS adaptation algorithm is used for weight updating in the third part. The innovation of this work lies in using Kalman filter as the smoother in HDS. It is shown that HDS has a smaller mean square error, MSE, and in noisy environment has a smaller signal variance relative to the input space, therefore Kalman smoother was applied to HDS instead of the input space. Experimental results show better performance of the new structure compared to the conventional RLS in tracking a nonlinear noisy chirp sinusoid and for vehicle tracking in the analysis of traffic scene.

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