In this letter, we propose a class of efficient, accurate, and general methods for solving state-estimation problems with equality and inequality constraints. The methods are based on recent developments in variable splitting and partially observed Markov processes. We first present the generalized framework based on variable splitting, then develop efficient methods to solve the state-estimation subproblems arising in the framework. The solutions to these subproblems can be made efficient by leveraging the Markovian structure of the model as is classically done in so-called Bayesian filtering and smoothing methods. The numerical experiments demonstrate that our methods outperform conventional optimization methods in computation cost as well as the estimation performance.

中文翻译：

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部分观测马尔可夫过程中约束状态估计的变量分裂方法

在这封信中，我们提出了一类有效、准确和通用的方法来解决具有等式和不等式约束的状态估计问题。这些方法基于变量分裂和部分观察到的马尔可夫过程的最新发展。我们首先提出基于变量分裂的广义框架，然后开发有效的方法来解决框架中出现的状态估计子问题。这些子问题的解决方案可以通过利用模型的马尔可夫结构来提高效率，这在所谓的贝叶斯过滤和平滑方法中是经典的。数值实验表明，我们的方法在计算成本和估计性能方面优于传统的优化方法。