With the deepening of the research on kernel recursive least squares (KRLS), significant researches have been applied to time series online prediction. However, it usually ignores the extraneous and redundant factors in the raw data, which can cause bias in the prediction. In addition, it usually contains both noise and non-stationary characteristics, resulting in deteriorated prediction accuracy and reduced model efficiency. To ease the above two drawbacks of conventional KRLS, this brief presents a dynamic adaptive sparse kernel recursive least squares (DASKRLS) filtering algorithm. It first uses the online vector projection standard and the approximate linear dependence criterion to effectively constrain kernel matrix dimension, and reduce the computational complexity of the model. After that, the regularized maximum correlation entropy criterion to significant process noise-containing data from the perspective of improving generalization ability. Moreover, the adaptive update mechanism can dynamically track the real-time weight of non-stationary signals. The dynamic sparse process is essentially equivalent to a feature selection process that maintains low-dimensional manifold information. Lorenz benchmarking experiments and real data experiments show that DASKRLS achieves better prediction performance in complex systems with noise and nonstationary.

随着对内核递归最小二乘（KRLS）研究的深入，重要的研究已应用于时间序列在线预测。但是，它通常会忽略原始数据中的无关紧要的因素，这些因素可能会导致预测出现偏差。另外，它通常同时包含噪声和非平稳特性，从而导致预测精度下降和模型效率降低。为了缓解常规KRLS的上述两个缺点，本简介提出了一种动态自适应稀疏内核递归最小二乘（DASKRLS）过滤算法。它首先使用在线矢量投影标准和近似线性相关性准则来有效地约束内核矩阵维，并降低模型的计算复杂性。之后，从提高泛化能力的角度出发，将正则化最大相关熵准则应用于重要的含过程噪声数据。此外，自适应更新机制可以动态跟踪非平稳信号的实时权重。动态稀疏过程本质上等效于保持低维流形信息的特征选择过程。洛伦兹基准测试和真实数据实验表明，DASKRLS在具有噪声和非平稳性的复杂系统中具有更好的预测性能。动态稀疏过程本质上等效于保持低维流形信息的特征选择过程。洛伦兹基准测试和真实数据实验表明，DASKRLS在具有噪声和非平稳性的复杂系统中具有更好的预测性能。动态稀疏过程本质上等效于保持低维流形信息的特征选择过程。洛伦兹基准测试和真实数据实验表明，DASKRLS在具有噪声和非平稳性的复杂系统中具有更好的预测性能。