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.
翻译:我们采用新的顺序方法校准固定参数并跟踪州空间系统的随机动态变量。拟议方法基于[1] [1] 的嵌套混合过滤框架(NHF),这一框架将两层过滤器(一个在另一层内)结合起来,以计算静态参数和状态变量的联合远地点概率分布。特别是,我们探索在算法的第一层使用高萨近似定点抽样技术,而不是在最初程序中使用的蒙特卡洛方法。由此产生的方法降低了计算成本,从而使这些算法有可能更好地适用于高维状态和参数空间。我们描述了新方法的具体实例,然后研究其性能和由此产生的算法效率,用于具有不确定参数的随机Lorenz 63模型。