## 1 Introduction  
It is well known that teleoperation systems have gained widespread applications in many fields, such as medicine, space exploration, etc. ; see [1; 2; 3] for examples. For such applications, it is generally required that the telerobot or its end-effector moves along the same trajectory as the operator hand to accomplish some specific tasks [4; 5; 6]. According to each human's mechanism, slight tremors always exist in every human hand and are not pathological but natural [7; 8]. During teleoperation, these physiological tremors can cause movement deflections of the telerobot from the objective. The physiological tremors have characteristics, i.e., a small amplitude range between 50 \(\upmu\)m and 100 \(\upmu\)m and a domain frequency range between 8 Hz and 12 Hz [9; 10]. Hence, in some occasions requiring an accuracy of about 10 \(\upmu\)m, such as microsurgery [11; 12], the physiological tremor attenuation is a significant yet challenging problem. To overcome the problem, numerous studies have been performed, with particular emphasis on cancelling out the physiological tremors, see [13; 14], just to list a few. Generally, linear low-pass filters (LPFs) are employed for canceling tremors, but digital filters have a disadvantage that introduces amplitude and phase distortions [15]. Related studies have been proposed to overcome the limits of digital filters [16; 17; 18]. An adaptive band-limitedmultiple Fourier linear combiner with Kalman filter (BMFLC-KF) has been proposed to provide accurate time-frequency decomposition components in the band-limited signal for filtering and compensation [19]. Moreover, an autoregressive model with Kalman filter (AR-KF) has been proposed to estimate a real-time tremor based on the previous outputs [20]. These methods can reduce most phase distortion but still have a problem with a phase delay of 5 to 10 ms. Later, the multistep prediction-based algorithms were proposed to address the existence of phase delay in sensors and filter for accurate canceling of real-time tremors [21]. Because of the fusion of various algorithms, the computation costs are increased, which can be alleviated by the reduced-order Kalman-based enhanced band-limited multiple Fourier linear combiner (RKE-BMFLC) [22]. Although the algorithms mentioned above have a good performance in predicting tremors, they have some restrictions that need to be removed: the AR-KF method is a linear prediction model, which characterizes tremor signals as linear Gaussian distribution. It needs to consider the characteristic of tremors; when applying the BMFLC-KF method, a careful choice of proper parameters is required, since even a small frequency gap can make the method ineffective [19]. To overcome the problems, some small-scale sample machine learning algorithms are raised to compensate tremors; see typically the support vector machine (SVM)-based approaches [23; 24], which exhibit a good generalization capability and are computationally attractive. Note that SVM may not be assigned exactly in the learning process and is not sensitive to small amplitude signals, and this could cause substantial losses in accuracy [25]. Such an issue can be well addressed by the deep-learning methodology. Moreover, the deep learning network has a high accuracy in predicting small signals due to its strong network depth [26]. In addition, to improve the accuracy of tremor prediction, a multi-step long-short-term memory (MS-LSTM) method has been used in [27]. While the deep learning network is a powerful tool, due to the need for many hyperparameters, and the use of complicated structures, a time-consuming training process is generally required. In addition, the deep structures are the black box that is difficult to analyze. Recently, a novel network structure broad learning system (BLS) has been proposed in [28]. Unlike the deep network, BLS has a simple structure and trains without hyper-parameters. It updates the weights of network by the pseudo-inverse calculation.