The proliferation of capable and efficient machine learning (ML) models marks one of the strongest methodological shifts in signal processing (SP) in its nearly 100-year history. ML models support the development of SP systems that represent complex, nonlinear relationships with high predictive accuracy. Adapting these models often requires sequential inference, which differs both theoretically and methodologically from the usual paradigm of ML, where data are often assumed independent and identically distributed. Gaussian processes (GPs) are a flexible yet principled framework for modeling random functions, and they have become increasingly relevant to SP as statistical and ML methods assume a more prominent role. We provide a self-contained, tutorial-style overview of GPs, with a particular focus on recent methodological advances in sequential, incremental, or streaming inference. We introduce these techniques from a signal-processing perspective while bridging them to recent advances in ML. Many of the developments we survey have direct applications to state-space modeling, sequential regression and forecasting, anomaly detection in time series, sequential Bayesian optimization, adaptive and active sensing, and sequential detection and decision-making. By organizing these advances from a signal-processing perspective, we intend to equip practitioners with practical tools and a coherent roadmap for deploying sequential GP models in real-world systems.

翻译：高效能机器学习模型的蓬勃发展标志着信号处理领域近百年发展中最显著的方法论变革之一。此类模型通过表征复杂非线性关系实现高精度预测，推动信号处理系统的发展。这些模型的适配常需序贯推断——该范式在理论与方法论层面均区别于传统机器学习中数据独立同分布的基本假设。高斯过程为随机函数建模提供了兼具灵活性与严谨性的框架，随着统计与机器学习方法在信号处理中占据更核心地位，其相关性日益凸显。本文以自包含的教程形式系统阐述高斯过程，重点聚焦序贯、增量及流式推断领域的最新方法论进展。我们从信号处理视角引入这些技术，同时建立其与机器学习前沿研究的桥梁。所综述的诸多进展可直接应用于状态空间建模、序贯回归与预测、时序异常检测、序贯贝叶斯优化、自适应与主动感知，以及序贯检测与决策制定。通过以信号处理视角整合这些进展，我们旨在为实践者提供实用工具与连贯路线图，助力其在真实系统中部署序贯高斯过程模型。