In recent years, the Kalman filter has become the prime approach for estimating parameters that evolve following some dynamic model and prior statistics. In addition, recent contributions are introducing the use of autoregressive models in the state-space formulation to deal with correlated Gaussian-distributed magnitudes. However, the derivation of closed-form expressions for predicting their performance during the design stage is still an open problem. In that regard, in this letter we derive novel approximate closed-form upper bounds to characterize the convergence time of autoregressive Kalman filters. To this end, we extend a batch mode-based approach previously proposed in the literature that reveals the need for a dedicated dual-asymptotic analysis for this kind of techniques. Simulations are provided to show the goodness of the derived results.

中文翻译：

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自回归卡尔曼滤波器收敛时间的渐近分析

近年来，卡尔曼滤波器已成为估计遵循一些动态模型和先验统计的参数的主要方法。此外，最近的贡献是在状态空间公式中引入了自回归模型的使用，以处理相关的高斯分布幅度。然而，在设计阶段推导用于预测其性能的闭式表达式仍然是一个悬而未决的问题。在这方面，在这封信中，我们推导出新颖的近似封闭形式上限来表征自回归卡尔曼滤波器的收敛时间。为此，我们扩展了先前在文献中提出的基于批处理模式的方法，该方法揭示了对此类技术进行专用双渐近分析的必要性。