Cubature Kalman filters: Derivation and extension

This paper focuses on the cubature Kalman filters （CKFs） for the nonlinear dynamic systems with additive process and measurement noise. As is well known, the heart of the CKF is the third-degree spherical–radial cubature rule which makes it possible to compute the integrals encountered in nonlinear filtering problems. However, the rule not only requires computing the integration over an n-dimensional spherical region, but also combines the spherical cubature rule with the radial rule, thereby making it difficult to construct higher-degree CKFs. Moreover, the cubature formula used to construct the CKF has some drawbacks in computation. To address these issues, we present a more general class of the CKFs, which completely abandons the spherical–radial cubature rule. It can be shown that the conventional CKF is a special case of the proposed algorithm. The paper also includes a fifth-degree extension of the CKF. Two target tracking problems are used to verify the proposed algorithm. The results of both experiments demonstrate that the higher-degree CKF outperforms the conventional nonlinear filters in terms of accuracy.

An Approximate High Gain Observer for Speed-sensorless Estimation of Induction Motors

Rotor speed estimation for induction motors is a key problem in speed-sensorless motor drives. This paper performs nonlinear high gain observer design based on the full-order model of the induction motor. Such an effort appears nontrivial due to the fact that the full-model at best admits locally a non-triangular observable form(NTOF), and its analytical representation in the NTOF can not be obtained. This paper proposes an approximate high gain estimation algorithm, which enjoys a constructive design, ease of tuning, and improved speed estimation and tracking performance. Experiments demonstrate the effectiveness of the proposed algorithm.

Adaptive Gaussian sum squared-root cubature Kalman filter with split-merge scheme for state estimation

The paper deals with state estimation problem of nonlinear non-Gaussian discrete dynamic systems for improvement of accuracy and consistency. An efficient new algorithm called the adaptive Gaussian-sum square-root cubature Kalman filter（AGSSCKF） with a split-merge scheme is proposed. It is developed based on the squared-root extension of newly introduced cubature Kalman filter（SCKF） and is built within a Gaussian-sum framework. Based on the condition that the probability density functions of process noises and initial state are denoted by a Gaussian sum using optimization method, a bank of SCKF are used as the sub-filters to estimate state of system with the corresponding weights respectively, which is adaptively updated. The new algorithm consists of an adaptive splitting and merging procedure according to a proposed split-decision model based on the nonlinearity degree of measurement. The results of two simulation scenarios（one-dimensional state estimation and bearings-only tracking） show that the proposed filter demonstrates comparable performance to the particle filter with significantly reduced computational cost.

Robust Control for Static Loading of Electro-hydraulic Load Simulator with Friction Compensation

Load simulator is a key test equipment for aircraft actuation systems in hardware-in-the-loop-simulation. Static loading is an essential function of the load simulator and widely used in the static/dynamic stiffness test of aircraft actuation systems. The tracking performance of the static loading is studied in this paper. Firstly, the nonlinear mathematical models of the hydraulic load simulator are derived, and the feedback linearization method is employed to construct a feed-forward controller to improve the force tracking performance. Considering the effect of the friction, a LuGre model based friction compensation is synthesized, in which the unmeasurable state is estimated by a dual state observer via a controlled learning mechanism to guarantee that the estimation is bounded. The modeling errors are attenuated by a well-designed robust controller with a control accuracy measured by a design parameter. Employing the dual state observer is to capture the different effects of the unmeasured state and hence can improve the friction compensation accuracy. The tracking performance is summarized by a derived theorem. Experimental results are also obtained to verify the high performance nature of the proposed control strategy.