Asymptotic Analysis of the Convergence Time of Autoregressive Kalman Filters

• Published in: IEEE signal processing letters Vol. 27; pp. 820 - 824
• Main Authors: Locubiche-Serra, Sergi, Seco-Granados, Gonzalo, Lopez-Salcedo, Jose A.
• Format: Journal Article
• Language: English
• Published: New York IEEE 2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic properties; Autoregressive models; Autoregressive process; Bayesian Cramér-Rao bound; Closed form solutions; Computer simulation; Convergence; convergence time; Dynamic models; Exact solutions; Kalman filter; Kalman filters; Kinematics; Mathematical model; Modeling; Noise measurement; Parameter estimation; Performance prediction; State-space methods; steady state; Upper bounds
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2020.2993174

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.