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采用3种方法研究了LTI(Linear time-invariant)状态空间模型中未知参数的估计问题:利用Metropolis-Hastings算法,从后验分布中抽取一定容量的样本,得出其均值和标准差;采用进化算法来最小化对数似然函数,得到全局最优解;采用模拟退火算法来最大化似然函数,得到全局最优解.最后,通过数值实验验证和比较了3种估计算法的有效性.
Three kinds of methods are used to study the estimation of unknown parameters in LTI (Linear time-invariant) state-space model: the Metropolis-Hastings algorithm is used to extract the samples of a certain capacity from the posterior distribution and obtain the mean and standard deviation; Algorithm to minimize the log-likelihood function and get the global optimal solution.Meanwhile, the simulated annealing algorithm is used to maximize the likelihood function to get the global optimal solution.Finally, the validity of the three estimation algorithms is verified and compared through numerical experiments.