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 and for a stochastic volatility model with real data.

我们引入了一种新的顺序方法来校准固定参数并跟踪状态空间系统的随机动态变量。所提出的方法基于 [1] 的嵌套混合过滤 (NHF) 框架，该框架结合了两层过滤器，一层在另一层内，以计算静态参数和状态变量的联合后验概率分布。特别是，我们探索了在算法的第一层中使用确定性采样技术进行高斯近似，而不是原始程序中使用的蒙特卡罗方法。由此产生的方案降低了计算成本，因此使算法可能更适合高维状态和参数空间。