Wavelet Broad Learning Filter: A Novel Adaptive Filter for estimating the Physiological Tremor in Teleoperation In this paper, a wavelet broad learning filter is proposed to estimate the tremor. At first, the structure of original broad learning system (BLS) is redesigned. To extract the features of tremor, the novel WBLAF maps each dimensional data as the feature nodes respectively by the wavelet function. Secondly, a novel selfpaced wavelet autoencoder (SPWAE) is proposed to train the weights of feature mapping. In addition, the ridge regression learning algorithm and the incremental learning of the proposed filter are applied to learning online. Finally, semiphysical simulation experiment is accomplished. As shown in the results, the new proposed WBLAF can effectively estimate and filter out the physiological tremor in teleoperation.

Sparse Wavelet Networks A wavelet network (WN) is a feedforward neural network that uses wavelets as activation functions for the neurons in its hidden layer. By predetermining the wavelet positions and dilations, the WN can turn into a linear regression model. The common approach for the construction of these WN families is to use leastsquares type algorithms. In this letter, we propose a novel approach by formulating a WN as a sparse linear regression problem, which we call a sparse wavelet network (SWN). In this WN, the problem of calculating the unknown inner parameters of the network becomes that of finding the sparse solution of an underdetermined system of linear equations. Our sparse solution algorithm is a nonconvex sparse relaxation approach inspired by smoothed L0 (SL0), a distinguished sparse recovery algorithm. The proposed SWN can be applied as a tool for the prediction and identification of dynamical systems.