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This paper proposes a state estimation method for a sampled-data descriptor system by the Kalman filtering method. The sampled-data descriptor system is firstly discretized to obtain a discrete-time nonsingular model. Based on the discretized nonsingular system, a strong tracking unscented Kalman filter (STUKF) algorithm is designed for the state estimation. Then, a defined suboptimal fading factor is proposed and added to the prediction covariance for decreasing the weight of the prior knowledge on the conventional UKF filtering solution. Finally, a simulation example is given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We need to predict mathematical model of the system and a priori knowledge of the noise statistics when traditional simultaneous localization and mapping (SLAM) solutions are used. However, in many practical applications, prior statistics of the noise are unknown or time-varying, which will lead to large estimation errors or even cause divergence. In order to solve the above problem, an innovative cubature Kalman filter-based SLAM (CKF-SLAM) algorithm based on an adaptive cubature Kalman filter (ACKF) was established in this paper. The novel algorithm estimates the statistical parameters of the unknown system noise by introducing the Sage-Husa noise statistic estimator. Combining the advantages of the CKF-SLAM and the adaptive estimator, the new ACKF-SLAM algorithm can reduce the state estimated error significantly and improve the navigation accuracy of the SLAM system effectively. The performance of this new algorithm has been examined through numerical simulations in different scenarios. The results have shown that the position error can be effectively reduced with the new adaptive CKF-SLAM algorithm. Compared with other traditional SLAM methods, the accuracy of the nonlinear SLAM systemis significantly improved. It verifies that the proposed ACKF-SLAM algorithm is valid and feasible. [ABSTRACT FROM AUTHOR]