Statistical signal processing applications usually require the estimation of some parameters of interest given a set of observed data. These estimates are typically obtained either by solving a multi-variate optimization problem, as in the maximum likelihood (ML) or maximum a posteriori (MAP) estimators, or by performing a multi-dimensional integration, as in the minimum mean squared error (MMSE) estimators. Unfortunately, analytical expressions for these estimators cannot be found in most real-world applications, and the Monte Carlo (MC) methodology is one feasible approach. MC methods proceed by drawing random samples, either from the desired distribution or from a simpler one, and using them to compute consistent estimators. The most important families of MC algorithms are the Markov chain MC (MCMC) and importance sampling (IS). On the one hand, MCMC methods draw samples from a proposal density, building then an ergodic Markov chain whose stationary distribution is the desired distribution by accepting or rejecting those candidate samples as the new state of the chain. On the other hand, IS techniques draw samples from a simple proposal density and then assign them suitable weights that measure their quality in some appropriate way. In this paper, we perform a thorough review of MC methods for the estimation of static parameters in signal processing applications. A historical note on the development of MC schemes is also provided, followed by the basic MC method and a brief description of the rejection sampling (RS) algorithm, as well as three sections describing many of the most relevant MCMC and IS algorithms, and their combined use. Finally, five numerical examples (including the estimation of the parameters of a chaotic system, a localization problem in wireless sensor networks and a spectral analysis application) are provided in order to demonstrate the performance of the described approaches.

在给定一组观测数据的情况下，统计信号处理应用程序通常需要估计一些感兴趣的参数。这些估计值通常是通过解决最大似然（ML）或最大后验（MAP）估计器中的多元优化问题，或通过执行最小均方误差（MMSE）中的多维积分来获得的）估算器。不幸的是，在大多数实际应用中找不到这些估算器的分析表达式，并且蒙特卡洛（MC）方法是一种可行的方法。MC方法首先从所需分布或较简单的分布中抽取随机样本，然后使用它们来计算一致的估计量。MC算法最重要的族是Markov链MC（MCMC）和重要性采样（IS）。一方面，MCMC方法从建议密度中抽取样本，然后通过接受或拒绝那些候选样本作为链的新状态，从而构建遍历马尔可夫链，该马尔可夫链的固定分布为所需分布。另一方面，IS技术从简单的建议密度中抽取样本，然后为它们分配适当的权重，以某种适当的方式衡量其质量。在本文中，我们对MC方法进行了全面的回顾，以评估信号处理应用中的静态参数。还提供了有关MC方案开发的历史注释，其后是基本MC方法和拒绝采样（RS）算法的简要说明，以及三个部分描述了许多最相关的MCMC和IS算法及其结合使用。最后，