转移概率未知条件下随机跳变系统联合估计与辨识方法研究

The joint estimation and identification of stochastic jump systems with unknown transition probability matrix faces challenges in high dimension, deep coupling between estimation and identification, and identification efficiency. This project carries out the research on joint estimation and identification from the following three aspects: 1) decomposing high dimensional parameter identification, 2) constructing an interactive identification framework and 3) recursively solving parameter identification. Base on the approximate Bayesian inference, we propose an interactive expectation-maximization recursive algorithm with the split-merge strategy in order to implement the recursive identification and optimization for model parameters under the rule of interactive identification. In addition, we also propose a recursive identification approach for the probability transition matrix and model parameters based on the variational Bayesian. In this approach, standard forms of conditional expectations can be obtained and an interactive identification rule can be constructed, respectively. As a consequence, the high dimensional parameter identification under the condition of deep coupling between estimation and identification can be solve based on the above researches. In addition, we apply the above approaches into the GNSS-based navigation and then propose a novel multipath mitigation approach in order to improve the precision of the GNSS-based navigation. Finally, the proposed approach is evaluated based on data obtained from a measurement campaign conducted by the small UAV. The project will promote the integration of estimation and identification in stochastic jump systems, enrich and develop theories associated with the expectation-maximization and variational Bayesian and provide a novel approach for the GNSS-based navigation in the multipath environment.

针对转移概率未知条件下随机跳变系统联合状态估计与参数辨识问题所面临的高维数、估计与辨识深度耦合、辨识效率等方面挑战。本项目拟围绕高维参数辨识分解，交互式辨识框架构建以及参数辨识递推求解三个方面开展联合估计与辨识方法研究。在近似贝叶斯推理基础上，研究基于分裂-融合策略的交互式期望最大化递推算法，实现在交互式辨识规则下模型参数递推辨识与优化；研究基于变分贝叶斯的转移概率与模型参数递推辨识方法，完成相应的条件期望标准型推导与辨识交互规则构建。通过上述研究，解决估计与辨识深度耦合下高维参数递推辨识这一关键科学问题。将理论研究结果与GNSS导航技术相结合，提出一类新的抗多径干扰的GNSS导航技术，并开展飞行实验验证。通过本项目研究，促进随机跳变系统估计与辨识的交叉融合，丰富和发展期望最大化与变分贝叶斯理论，为多径干扰下的GNSS精确导航提供新思路与新方法。

针对转移概率未知条件下随机跳变系统联合估计与辨识所面临的高维数、估计与辨识深度耦合等方面问题，首先提出了随机跳变系统高维参数辨识分解方法；其次将变分贝叶斯推断与粒子滤波相结合，提出了系统状态与未知模型参数的交互式辨识框架；然后建立随机跳变系统模式变量先验模型并基于高维参数辨识分解方法和交互式辨识框架，提出了转移概率未知条件下随机跳变系统状态估计与未知参数递推辨识方法；最后将提出的理论方法推广应用至未知高斯混合噪声条件下非线性系统的状态估计与参数辨识等其它非线性系统中。通过本项目研究，促进了变分贝叶斯推断与粒子滤波理论的有机融合，丰富并发展了随机跳变系统估计与辨识理论。