The Yau-Yau nonlinear filter has increasingly emerged as a powerful tool to study stochastic complex systems. To leverage it to a wider spectrum of application scenarios, we pack the Yau-Yau filtering ALgorithms (YauYauAL) into a package of computer software. Yau-YauAL was written in R, designed to simplify the implementation of the Yau-Yau filter for solving nonlinear filtering problems. Combining R's accessibility with C++ (via Rcpp) for computational efficiency, YauYauAL provides an intuitive Shiny-based interface that enables real-time parameter adjustment and result visualization. At its core, YauYauAL employs finite difference methods to numerically solve the Kolmogorov forward equation, ensuring a stable and accurate solution even for complex systems. YauYauAL's modular design and open-source framework further encourage customization and community-driven development. YauYauAL aims to bridge the gap between theoretical nonlinear filtering methods and practical applications, without requiring expertise in differential equation solving or programming, fostering its broader impact on various scientific fields, such as signal processing, finance, medicine, and biology among a long list.

翻译：Yau-Yau非线性滤波器已日益成为研究随机复杂系统的有力工具。为使其适用于更广泛的应用场景，我们将Yau-Yau滤波算法（YauYauAL）封装为一套计算机软件包。YauYauAL采用R语言编写，旨在简化Yau-Yau滤波器的实现，以求解非线性滤波问题。该软件结合了R语言的易用性与C++（通过Rcpp）的计算效率，提供了一个基于Shiny的直观界面，支持实时参数调整与结果可视化。其核心采用有限差分法对Kolmogorov前向方程进行数值求解，确保即使在复杂系统中也能获得稳定且精确的解。YauYauAL的模块化设计与开源框架进一步促进了定制化与社区驱动的开发。YauYauAL致力于弥合理论非线性滤波方法与实际应用之间的鸿沟，无需用户具备微分方程求解或编程的专业知识，从而推动其在信号处理、金融、医学、生物学等诸多科学领域的更广泛影响。