In this study, a non-linear filtering algorithm for state estimation with symmetric alpha-stable (SαS) noise is presented. The dynamic system model investigated here can be described by a linear state-space equation and a non-linear observation equation. The contribution of this study can be summarised as follows. First, particle filtering approach is employed for coarse estimation of the unknown parameters and then Kalman filter is performed to achieve better estimation. Second, SαS noise is considered as the additive disturbance in the observed signal and Gaussian approximation is used to compute the characteristics. Third, the calculation complexity is analysed according to the proposed algorithm. The proposed method is compared with the standard particle filter, extended Kalman filter and unscented Kalman filter for static parameter estimation of a periodic signal. As a practical application, the proposed method is used in high frequency source localisation based on time difference of arrival measurements.

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Kalman particle filtering algorithm for symmetric alpha-stable distribution signals with application to high frequency time difference of arrival geolocation

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