In this correspondence, the authors develop a novel method based on spherical radial cubature and Gauss-Laguerre quadrature rule for non-linear state estimation problems. The proposed filter, referred as cubature quadrature Kalman filter (CQKF) would be able to overcome inherent disadvantages associated with the earlier reported cubature Kalman filter (CKF). The theory and formulation of CQKF has been presented. Using two well-known non-linear examples, the superior performance of CQKF has been demonstrated. Owing to computational efficiency (compared to the particle and grid-based filter) and enhanced accuracy compared to the extended Kalman filter and the CKF, the developed algorithm may find place in on-board real life applications.

Abstract-The traditional Bayesian approximation framework for filtering in discrete time systems assumes that the measurement is available at every time instant. But in practice, the measurements could be randomly delayed. In the literature, the problem has been examined and solution is provided by restricting the maximum number of delay to one or two time steps. This paper develops an approach to deal with the filtering problems with an arbitrary number of delays in measurement. Pursuing this objective, traditional Bayesian approximation to nonlinear filtering problem is modified by reformulating the expressions of mean and covariances which appear during the measurement update. We use the cubature quadrature rule to evaluate the multivariate integral expressions for the mean vector and the covariance matrix which appear in the developed filtering algorithm. We compare the new algorithm which accounts for delay with the existing CQKF heuristics on two different examples and demonstrate how accounting for a random delay improves the filtering performance.Index Terms-Nonlinear filtering, Bayesian framework of filtering, Random delay in measurements, Cubature quadrature Kalman filter.

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In this paper, an on-going work introducing square-root extension of cubature-quadrature based Kalman filter is reported. The proposed method is named square-root cubature-quadrature Kalman filter (SR-CQKF). Unlike ordinary cubature-quadrature Kalman filter (CQKF), the proposed method propagates and updates square-root of the error covariance without performing Cholesky decomposition at each step. Moreover SR-CQKF ensures positive semi-definiteness of the state covariance matrix. With the help of two examples we show the superior performance of SR-CQKF compared to EKF and square root cubature Kalman filter.

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