Third-Order Kalman Filter: Tuning and Steady-State Performance

Huaqiang Shu (1) , Eric Pierre Simon (2) , Laurent Ros (3)

1 TELICE - IEMN - Télécommunication, Interférences et Compatibilité Electromagnétique - IEMN
2 IEMN - Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520
3 GIPSA-CICS - GIPSA - Communication Information and Complex Systems

This letter deals with the Kalman filter (KF) based on a third-order integrated random walk model (RW3). The resulting filter, noted as RW3-KF, is well suited to track slow time-varying parameters with strong trend behaviour. We first prove that the RW3-KF in steady-state admits an equivalent structure to the third-order digital phase-locked loops (DPLL). The approximate asymptotic mean-squared-error (MSE) is obtained by solving the Riccati equations, which is given in a closed-form expression as a function of the RW3 model parameter: the state noise variance. Then, the closed-form expression of the optimum state noise variance is derived to minimize the asymptotic MSE. Simulation results are given for the particular case where the parameter to be estimated is a Rayleigh channel coefficient with Jakes' Doppler spectrum.

Mots clés: Kalman filter (KF); random walk model (RW).; random walk model (RW); Kalman filter (KF)

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Huaqiang Shu, Eric Pierre Simon, Laurent Ros. Third-Order Kalman Filter: Tuning and Steady-State Performance. IEEE Signal Processing Letters, 2013, 20 (11), pp.1082-1085. ⟨10.1109/LSP.2013.2277668⟩. ⟨hal-00912475⟩