In stock market， investors can predict the future stock return by capturing the potential trading patterns in historical data. The key issue for predicting stock return is how to find out the trading patterns accurately. However， it is generally difficult to capture them due to the influence of uncertain factors such as corporate performance， financial policies， and national economic growth. To solve this problem， a Multi-Scale Kernel Adaptive Filtering （MSKAF） method was proposed to capture the multi-scale trading patterns from past market data. In this method， in order to describe the multi-scale features of stocks， Stationary Wavelet Transform （SWT） was employed to obtain data components with different scales. The different trading patterns hidden in stock price fluctuations were contained in these data components. Then， the Kernel Adaptive Filtering （KAF） was used to capture the trading patterns with different scales to predict the future stock return. Experimental results show that compared with those of the prediction model based on Two-Stage KAF （TSKAF）， the Mean Absolute Error （MAE） of the results generated by the proposed method is reduced by 10%， and the Sharpe Ratio （SR） of the results generated by the proposed method is increased by 8.79%， verifying that the proposed method achieves better stock return prediction performance.

It is well known that the Kalman filter can be adopted to make unbiased estimation for system state with the measurement of the noise interference. However, neither the EKF algorithm nor the UKF algorithm can avoid filtering divergence. In terms of the adaptability of RBF neural network (RBFNN), this paper proposed a RBFNN-based algorithm to correct the output of the Kalman filter and further to avoid the output divergence. Both the simulation and the application results show that the output divergence can be effectively avoided by the presented filtering algorithm.

Concerning the clock skew and clock drift problem in wireless sensor networks, some different methods of synchronization time on synchronization accuracy were studied. With the principle of clock synchronization of cluster-shaped network structure, an optimized clock basis algorithm was put forward. And the Kalman filtering method was applied to adjust the nodes’ clock deviation in optimized recursive way. Compared with the general synchronization algorithm of cluster-shaped, the proposed algorithm can not only improve the synchronization accuracy, but also reduce the energy consumption of synchronous nodes. The simulation results show that the algorithm can accurately describe the synchronization precision and is more efficient for clock synchronization.