状态空间模型中递归贝叶斯推断和非线性跟踪的嵌套高斯滤波器
Nested Gaussian filters for recursive Bayesian inference and nonlinear tracking in state space models
摘要：
我们引入了一种新的顺序方法来校准的固定参数和跟踪的状态空间系统的随机动态变量。所提出的方法是基于嵌套混合滤波（NHF）框架[1]，它结合了两层滤波器，一个在另一个里面，以计算静态参数和状态变量的联合后验概率分布。特别是，我们探讨了使用确定性采样技术的高斯近似在第一层的算法，而不是在原来的程序中采用的蒙特卡罗方法。由此产生的计划降低了计算成本，使算法可能更好地适用于高维状态和参数空间。我们描述了一个具体的例子，新的方法，然后研究其性能和效率的随机Lorenz 63模型与不确定参数的算法。
英文摘要：
We introduce a new sequential methodology to calibrate the fixed parameters and track the stochastic dynamical variables of a state-space system. The proposed method is based on the nested hybrid filtering (NHF) framework of [1], that combines two layers of filters, one inside the other, to compute the joint posterior probability distribution of the static parameters and the state variables. In particular, we explore the use of deterministic sampling techniques for Gaussian approximation in the first layer of the algorithm, instead of the Monte Carlo methods employed in the original procedure. The resulting scheme reduces the computational cost and so makes the algorithms potentially better-suited for high-dimensional state and parameter spaces. We describe a specific instance of the new method and then study its performance and efficiency of the resulting algorithms for a stochastic Lorenz 63 model with uncertain parameters.
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