Abstract: In accordance with the characteristics of ship navigation positioning data based on time series, the transition probability feature of the Markov chain state is utilized to solve the predictive problem of relatively great random volatility based on autoregressive integrated moving average model. During the process of building the probability matrix of Markov chain state transition, the K-means clustering algorithm is used to divide the differential state interval between predicted value and true value, and then a set of optimized predictive algorithm model is built. The value experiment on the algorithm and its comparison with other algorithms show that this optimized algorithm has better predictive effect when it comes to short-term predication of the ship navigation positioning data. It is better than other algorithms and can be applied to mobile positioning products for ships.

Key words: autoregressive integrated moving average model (ARIMA), Markov chain, K-means, positioning data prediction

摘要： 根据基于时间序列的船舶航行定位数据的特征，在差分自回归移动平均模型的基础上，运用马尔可夫链状态转移概率特性解决非平稳数据的预测问题，在建立马尔可夫链状态迁移概率矩阵过程中，使用K-means聚类算法划分预测值与真实值的差值状态区间，继而构建出优化预测算法。对算法进行了理论分析和数值实验，并与其他算法进行了比较，结果表明，该优化算法在船舶定位数据短时预测领域具有较好的预测效果，优于多个其他算法，可应用于船舶移动定位产品中。

关键词: 差分自回归移动平均模型（ARIMA）, 马尔可夫链, K-means, 定位数据预测