估算马尔可夫状态转移矩阵下的船舶行为预测

Prediction of Ship Behaviors Based on the Estimation of Markov State Transition Matrix

摘要: 目前，马尔可夫模型已被应用于多个领域的预测，如天气、交通等。在水上交通备受关注的今天，如何利用马尔可夫模型对该领域问题进行探究也是一重要问题。本文利用马尔可夫模型对恶劣天气条件下的船舶行为进行预测，用1组数据估算马尔可夫模型状态转移概率矩阵，随后使用估算所获的状态转移概率矩阵对另外3组数据进行预测并计算预测误差，所得的预测平均误差分别约为4.72%、2.33%、2.36%。此外，本文还利用线性化绝对值的方法，找到了另一种线性规划模型，利用该模型也可对状态转移概率矩阵进行估算求解，利用同样数据进行数值实验，所得的预测平均误差分别约为4.42%、2.4%、2.18%。

Abstract: Currently, the Markov model has been extensively applied to various prediction domains, including weather forecasting and traffic analysis. Given the increasing attention on water transportation, it is crucial to investigate how the Markov model can address challenges in this field. The Markov model is employed to predict ship behaviors in adverse weather conditions. The state transition probability matrix of the Markov model is estimated using a specific dataset. Subsequently, the estimated state transition probability matrix is used to predict the other three sets of data and calculate the prediction errors. The obtained average prediction errors are approximately 4.72%, 2.33%, and 2.36% respectively. Furthermore, the method of linearizing absolute values is employed to formulate another linear programming model for the determination of the state transition probability matrix. Using the same dataset for numerical validation, and the obtained average prediction errors were approximately 4.42%, 2.4%, and 2.18% respectively.