Low-cost adaptive square-root cubature Kalman filter forsystems with process model uncertainty

A novel low-cost adaptive square-root cubature Kalmanfilter （LCASCKF） is proposed to enhance the robustness of processmodels while only increasing the computational load slightly.It is well-known that the Kalman filter cannot handle uncertainties ina process model, such as initial state estimation errors, parametermismatch and abrupt state changes. These uncertainties severelyaffect filter performance and may even provoke divergence. Astrong tracking filter （STF）, which utilizes a suboptimal fading factor,is an adaptive approach that is commonly adopted to solvethis problem. However, if the strong tracking SCKF （STSCKF）uses the same method as the extended Kalman filter （EKF） tointroduce the suboptimal fading factor, it greatly increases thecomputational load. To avoid this problem, a low-cost introductorymethod is proposed and a hypothesis testing theory is applied todetect uncertainties. The computational load analysis is performedby counting the total number of floating-point operations and it isfound that the computational load of LCASCKF is close to that ofSCKF. Experimental results prove that the LCASCKF performs aswell as STSCKF, while the increase in computational load is muchlower than STSCKF.

Underwater square-root cubature attitude estimator by use of quaternion-vector switching and geomagnetic field tensor

This paper presents a kind of attitude estimation algorithm based on quaternion-vector switching and square-root cubature Kalman filter for autonomous underwater vehicle(AUV).The filter formulation is based on geomagnetic field tensor measurement dependent on the attitude and a gyro-based model for attitude propagation. In this algorithm, switching between the quaternion and the three-component vector is done by a couple of the mathematical transformations. Quaternion is chosen as the state variable of attitude in the kinematics equation to time update, while the mean value and covariance of the quaternion are computed by the three-component vector to avoid the normalization constraint of quaternion. The square-root forms enjoy a continuous and improved numerical stability because all the resulting covariance matrices are guaranteed to stay positively semidefinite. The entire square-root cubature attitude estimation algorithm with quaternion-vector switching for the nonlinear equality constraint of quaternion is given. The numerical simulation of simultaneous swing motions in the three directions is performed to compare with the three kinds of filters and the results indicate that the proposed filter provides lower attitude estimation errors than the other two kinds of filters and a good convergence rate.

基于IST-RSCKF-MB的雷达多目标跟踪算法

针对多目标跟踪(MTT)算法存在较大的计算量问题,将改进渐消因子的强跟踪(IST)引入快速平方根容积卡尔曼滤波(RSCKF)中,并联合新息自相关矩阵和Murty算法确定最佳假设的多伯努利(MB)算法,提出改进强跟踪平方根容积卡尔曼多伯努利(IST-RSCKF-MB)的雷达多目标跟踪算法。仿真结果显示,所提出算法的运算效率和滤波精度比平方根容积卡尔曼多伯努算法、改进强跟踪平方根容积卡尔曼多伯努利混合算法、扩展卡尔曼多伯努利算法和无迹卡尔曼多伯努利算法均有不同程度提高,误差率分别减少0.36%、4.71%、14.75%和0.17%,适用于嵌入式目标跟踪算法实现。

SCKF-STF-CN:a universal nonlinear filter for maneuver target tracking

Square-root cubature Kalman filter (SCKF) is more effective for nonlinear state estimation than an unscented Kalman filter.In this paper,we study the design of nonlinear filters based on SCKF for the system with one step noise correlation and abrupt state change.First,we give the SCKF that deals with the one step correlation between process and measurement noises,SCKF-CN in short.Second,we introduce the idea of a strong tracking filter to construct the adaptive square-root factor of the prediction error covariance with a fading factor,which makes SCKF-CN obtain outstanding tracking performance to the system with target maneuver or abrupt state change.Accordingly,the tracking performance of SCKF is greatly improved.A universal nonlinear estimator is proposed,which can not only deal with the conventional nonlinear filter problem with high dimensionality and correlated noises,but also achieve an excellent strong tracking performance towards the abrupt change of target state.Three simulation examples with a bearings-only tracking system are illustrated to verify the efficiency of the proposed algorithms.