基于规划理论的最小二乘法改进及其在Markov跳变系统参数估计中的应用

分析了高斯最小二乘法在Markov跳变系统参数估计中的局限性,即不能够直接解决带有约束条件的拟合问题。而Markov跳变系统的转移概率矩阵要满足列和为1的约束,同时在多次观测值中有部分数据是未知的。根据规划问题为带有约束条件的极值问题,且约束条件中决策变量的个数可以多于目标函数中决策变量个数的特点,将Markov跳变系统参数估计问题转化为非线性规划问题。从求解的角度出发,将非线性规划问题转化为凸规划,同时给出了具体的转化方法。从理论上说明了转化后的凸规划问题在满足库恩-塔克条件的前提下,库恩-塔克点一定为全局最优解。最后给出仿真算例,说明结论的合理性。

Improved least square method based on theory of programming and application in parameters estimating of Markov jumping systems

The authors analyzed the limitations of the least squares of Gauss in parameters estimation for Markov jumping systems：Not able to solve directly the fitting problem with constraint conditions.But the elements for every columns in the transition probability matrix of Markov jumping systems should add up to one,while partly of the data of observations are unknown.According to the programming problem for the extreme value with constraint conditions,and the number of decision variables in the constraint conditions can be more than the number of decision variables in the objective function,the Markov jumping system parameter estimation problem could be turned into a nonlinear programming problem.Starting from solving the angle,the nonlinear programming problem is transformed into a convex programming,and gives a method into specific.In theory that the convex programming problem transformed in order to meet the conditions of the Kuhn-Tucker,Kuhn-Tucker point to the global optimal solution.Finally,a simulation example is given to illustrate the conclusions is rational.