Stochastic sampling algorithms for state estimation of jump Markov linear systems
Stochastic sampling algorithms for state estimation of jump Markov linear systems
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DOI：
10.1109/9.839943
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发表时间：
2000-02-01
影响因子：
6.8
通讯作者：
Krishnamurthy, V
中科院分区：
文献类型：
--
作者：
Doucet, A;Logothetis, A;Krishnamurthy, V
跳跃马尔可夫线性系统是指参数按有限状态马尔可夫链随时间演化的线性系统。给定一组观测，我们的目的是估计有限状态马尔可夫链的状态和线性系统的连续(在空间)状态。针对马尔可夫链或跳跃马尔可夫线性系统状态估计的条件均值或最大后验概率(MAP)状态估计的计算开销随观测次数呈指数增长的问题，提出了三种基于随机抽样方法的跳跃马尔可夫线性系统状态估计的全局收敛算法。每次迭代的成本与数据长度呈线性关系。第一个提出的算法是产生条件平均状态估计的数据增强(DA)方案。第二种方案是DA的随机退火法(SA)版本，它计算有限状态和连续状态的联合映射序列估计。最后，设计了一个基于SA的Metropolis-Hastings DA方案，给出了有限状态马尔可夫链的MAP估计。给出了上述三种随机算法的收敛结果，并通过计算机仿真对算法的性能进行了评估。研究了基于一组噪声数据估计来自中子传感器的稀疏信号的问题，以及扩频码分多址(CDMA)系统中的窄带干扰抑制问题。
Jump Markov linear systems are linear systems whose parameters evolve with time according to a finite-state Markov chain. Given a set of observations, our aim is to estimate the states of the finite-state Markov chain and the continuous (in space) states of the linear system. The computational cost in computing conditional mean or maximum a posteriori (MAP) state computing conditional mean or maximum a posteriori (MAP) state estimates of the Markov chain or the state of the jump Markov linear system grows exponentially in the number of observations.In this paper, we present three globally convergent algorithms based on stochastic sampling methods for state estimation of jump Markov linear systems. The cost per iteration is linear in the data length. The first proposed algorithm is a data augmentation (DA) scheme that yields conditional mean state estimates. The second proposed scheme is a stochastic annealing (SA) version of DA that computes the joint MAP sequence estimate of the finite and continuous states. Finally, a Metropolis-Hastings DA scheme based on SA is designed to yield the MAP estimate of the finite-state Markov chain is proposed. Convergence results of the three above-mentioned stochastic algorithms are obtained.Computer simulations are carried out to evaluate the performances of the proposed algorithms. The problem of estimating a sparse signal developing from a neutron sensor based on a set of noisy data from a neutron sensor and the problem of narrow-band interference suppression in spread spectrum code-division multiple-access (CDMA) systems are considered.