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.     

非线性非高斯模型的高斯和PHD滤波算法(英文)

A new multi-target filtering algorithm, termed as the Gaussian sum probability hypothesis density （GSPHD） filter, is proposed for nonlinear non-Gaussian tracking models. Provided that the initial prior intensity of the states is Gaussian or can be identified as a Gaussian sum, the analytical results of the algorithm show that the posterior intensity at any subsequent time step remains a Gaussian sum under the assumption that the state noise, the measurement noise, target spawn intensity, new target birth intensity, target survival probability, and detection probability are all Gaussian sums. The analysis also shows that the existing Gaussian mixture probability hypothesis density （GMPHD） filter, which is unsuitable for handling the non-Gaussian noise cases, is no more than a special case of the proposed algorithm, which fills the shortage of incapability of treating non-Gaussian noise. The multi-target tracking simulation results verify the effectiveness of the proposed GSPHD.     

涡轴发动机自适应混合诊断模型高斯加权聚类方法

针对整个飞行包线内涡轴发动机健康参数估计问题,提出基于高斯加权聚类的机载自适应混合模型建立方法.机载自适应混合模型由卡尔曼滤波器和神经网络组成,由于飞行数据样本庞大,采用高斯加权模型对涡轴发动机飞行数据进行实时聚类,利用聚类数据更新神经网络权重,并实现自适应混合模型工作范围的自动扩展.仿真结果表明了该方法的有效性,采用...     

Optimal Detection of a Signala with Time-Varying Carrier Phase

The problem considered in this paper is the detection of a signal known except for time-varying carrier phase in white Gaussian noise. The method of attacking this problem is to model the time-varying carrier phase as a Markov process. Fourier transform techniques are then applies to yield a simple time-wise adaptive form for the phasetracking detector. Optimal accounting for the time variations in phase is accomplished via a simple algorithm which serves to update the detector memory. Furthermore, it is shown that this memory updating operation is a discrete linear filter whose impulse response is a simple function of the previous memory state and the Markov transitional statistics on the phase. A priori knowledge regarding the phase is summarized in the initial impulse response of the updating filter.     

基于混合粒子滤波的激光惯导系统误差的补偿

针对激光陀螺捷联惯导系统在动态尤其是高动态环境下的姿态误差显著增大的问题,提出了一种基于改进高斯混合粒子滤波的纯方位跟踪算法。算法基于混合粒子的卡尔曼滤波和粒子滤波的特点,用有限的高斯模型来近似后验状态密度、系统噪声和观测噪声的分布通过EM的算法设计实现模型的降阶,一定程度上克服了EM算法迭代的结果需要依赖初始值、可能收敛到局部最大点或可能收敛到参数空间边界的缺点,从而改善了粒子携带信息的衰减问题。通过仿真与试验结合,在纯动态应用环境下的姿态与定位精度补偿效果,与传统Kalman滤波相比,算法在保持高精度估计能力的同时,具有较强的鲁棒性,是解决非线性系统状态估计问题的一种有效方法。     

Joint parameter and state estimation for stochastic uncertain system with multivariate skew t noises

Due to the pulse interference, measurement outliers and artificial modeling errors, the multivariate skew t noise widely exists in the real environment. However, to date, little attention has been paid to the state estimation for systems in which the process noise and the measurement noise are both modeled as the heavy-tailed and skew non-Gaussian noise. In this paper, the multivariate skew t distribution is utilized to model the heavy-tailed and skew non-Gaussian noise. Then a probabilistic gra...     

Adaptive robust cubature Kalman filtering for satellite attitude estimation

This paper is concerned with the adaptive robust cubature Kalman filtering problem for the case that the dynamics model error and the measurement model error exist simultaneously in the satellite attitude estimation system. By using Hubel-based robust filtering methodology to correct the measurement covariance formulation of cubature Kalman filter, the proposed filtering algorithm could effectively suppress the measurement model error. To further enhance this effect and reduce the impact of the dynamics model error, two different adaptively robust filtering algorithms, one with the optimal adaptive factor based on the estimated covariance matrix of the predicted residuals and the other with multiple fading factors based on strong tracking algorithm, are developed and applied for the satellite attitude estimation. The quaternion is employed to represent the global attitude parameter, and three-dimensional generalized Rodrigues parameters are introduced to define the local attitude error. A multiplicative quaternion error is derived from the local attitude error to maintain quaternion normalization constraint in the filter. Simulation results indicate that the proposed novel algorithm could exhibit higher accuracy and faster convergence compared with the multiplicative extended Kalman filter, the unscented quaternion estimator, and the adaptive robust unscented Kalman filter.     

A nonlinear IMM algorithm for maneuvering target tracking

In target tracking, the measurement noise is usually assumed to be Gaussian. However, the Gaussian modeling of the noise may not be true. Noise can be non-Gaussian. The non-Gaussian noise arising in a radar system is known as glint noise. The distribution of glint noise is long tailed and will seriously affect the tracking performance. We develop a new algorithm that can effectively track a maneuvering target in the glint environment The algorithm incorporates the nonlinear Masreliez filter into the interactive multiple model (IMM) method. Simulations demonstrate the superiority of the new algorithm     

鲁棒Kalman滤波及其在水下组合导航中的应用

在水下捷联惯导(SINS)/多普勒计程仪(DVL)组合导航系统中,当外部辅助信息受到野值等非高斯噪声污染时,选取调节因子γ为固定值将会降低基于Huber方法的鲁棒Kalman滤波(HRKF)算法的精度和鲁棒性.针对此问题,提出了一种基于马氏距离(MD)算法的调节因子自适应的鲁棒Kalman滤波(HRAKF)算法.首先利...     

Finite-dimensional filters with nonlinear drift. V: solution to Kolmogorov equation arising from linear filtering with non-Gaussian initial condition

Despite its usefulness, the Kalman-Bucy filter is not perfect. One of its weaknesses is that it needs a Gaussian assumption on the initial data. Recently Yau and Yau introduced a new direct method to solve the estimation problem for linear filtering with non-Gaussian initial data. They factored the problem into two parts: (1) the on-line solution of a finite system of ordinary differential equations (ODEs), and (2) the off-line calculation of the Kolmogorov equation. Here we derive an explicit closed-form solution of the Kolmogorov equation. We also give some properties and conduct a numerical study of the solution.     

混合高斯测量噪声下的多模型滤波

就带有混合高斯测量噪声的离散时间系统 ,提出了一种简化的多模型滤波。理论分析证明该滤波方法用较少的计算量得到了与交互多模型滤波相同的估计性能。为满足应用要求 ,给出了该滤波器的数值鲁棒实现方法。一个关于仅有方位测量的制导例子验证了该滤波算法的有效性。     

组合导航系统中一种基于特征值分解的自适应信息融合滤波算法

基于分散滤波理论的联合滤波算法,可以有效地降低组合导航系统的计算负担,并且增强系统的容错性能。给出了一种联合滤波算法中信息分配系数的自适应计算方法,能够使联合系统根据导航过程中各传感器的信息质量的变化合理地反馈全局信息。仿真结果表明,该算法可以有效地降低由于导航子系统降级带来的滤波误差。     

一种基于NGA-QPF的航天器姿态估计方法

针对航天器姿态确定中的非线性非高斯的滤波问题,提出一种基于遗传算法的粒子滤波的航天器姿态估计方法。该方法将姿态四元数作为采样粒子进行粒子滤波,并将小生境遗传算法（NGA）引入粒子滤波算法中,以改善粒子滤波的性能;用遗传算法单独进行陀螺偏差估计,以减少粒子滤波的状态维数。该姿态估计方法保持了四元数的归一化性质,通过引入小生境遗传算法解决了重采样阶段的粒子退化问题,并且由于单独估计陀螺偏差避免了粒子滤波状态的扩展。该方法能够在较少粒子的情况下实现高效率高精度的定姿,仿真结果说明了方法的有效性。     

改进的Sage-Husa自适应滤波算法在MEMS航姿参考系统中的应用

针对经典Kalman滤波和扩展Kalman滤波融合算法存在的计算量大、精度低、实时性差的缺点,引入了改进的Sage-Husa自适应扩展Kalman滤波算法。该算法对经典扩展Kalman滤波算法进行了自适应改进,并在此基础上利用加权渐消记忆法获取了遗忘因子,并通过预测残差得出了最优解。同时,用调整有偏增益估计的措施来保证系统噪声预测方差矩阵与噪声预测方差矩阵的对称性和正定性,对滤波器发散进行了有效的抑制,减少了算法的计算量。实验结果表明,该算法有效改善了可靠性、精确性及自适应能力。     

航空发动机气路故障诊断的SANNWA-PF算法

针对航空发动机非线性、非高斯的特点,提出一种用于航空发动机气路故障诊断的自适应神经网络权值调整粒子滤波（SANNWA PF）算法。该算法根据粒子分布情况确定分裂和调整的粒子数目,进而根据粒子权重采用正态分布的方式进行分裂,采用反向传插(BP)神经网络进行权值调整,缓解了粒子的退化和贫化,具有更强的自适应性能和跟踪能力。通过一维非线性跟踪模型和航空发动机气路故障诊断仿真研究表明:SANNWA PF算法具有良好的非高斯性能,相对粒子滤波一维非线性追踪模型估计精度提高约21%,航空发动机气路故障诊断在高斯噪声和非高斯噪声下分别提高约30%和26%,诊断速度分别提高约7倍和10倍。      

SINS/GNSS integrated navigation system based on maximum versoria filter

In the missile-borne Strapdown Inertial Navigation System/Global Navigation Satellite System (SINS/GNSS) integrated navigation system, due to the factors such as the high dynamics, the signal blocking by obstacles, the signal intefereces, etc., there always exist pulse interferences or measurement information interruptions in the satellite receiver, which make nonstationary measurement process. The traditional Kalman Filter (KF) can tackle the state estimation problem under Gaussian white noise, but its performance will be significantly reduced under non-Gaussian noises. In order to deal with the non-Gaussian conditions in the actual missile-borne SINS/GNSS integrated navigation systems, a Maximum Versoria Criterion Extended Kalman Filter (MVC-EKF) algorithm is proposed based on the MVC and the idea of M-estimation, which assigns a smaller weight to the anomalous measurements so as to suppress the influence of anomalous measurements on the state estimation while maintaining a relatively low calculation cost. Finally, the integrated navigation simulation experiments prove the effectiveness and robustness of the proposed algorithm.     

Design of a practical tracking algorithm with radar measurements

The extended Kalman filter (EKF) has been widely used as a nonlinear filtering method for radar tracking problems. However, it has been found that if cross-range measurement errors of the target position are large, the performance of the conventional EKF degrades considerably due to nonnegligible nonlinear effects. A new filtering algorithm for improving the tracking performance with radar measurements is developed based on the fact that correct evaluation of the measurement error covariance is possible in the Cartesian coordinate system. The proposed algorithm may be viewed as a modification of the EKF in which the variance of the range measurement errors is evaluated in an adaptive manner. The filter structure facilitates the incorporation of the sequential measurement processing scheme, and this makes the resulting algorithm favorable to both estimation accuracy and computational efficiency. Computer simulation results show that the proposed method offers superior performance in comparison to previous methods. Moreover, our developed algorithm provides some useful insight into the radar tracking problem     

Matched subspace CFAR detection of hovering helicopters

A constant false alarm rate (CFAR) strategy for detecting a Gaussian distributed random signal against correlated non-Gaussian clutter is developed. The proposed algorithm is based on Scharf's matched subspace detector (MSD) and has the CFAR property with respect to the clutter amplitude probability density function (apdf), provided that the clutter distribution belongs to the compound-Gaussian family and the clutter covariance matrix is known to within a scale factor. Analytical expressions of false alarm and detection probabilities are derived. An application to the problem of detecting hovering helicopters against vegetated ground clutter is reported     

自主姿态测量最优算法研究

针对利用地球重力场和磁场矢量观测进行自主姿态测量的应用问题,提出了一种新的最优递推估计算法。该算法采用卡尔曼滤波框架,利用加权统计线性回归并结合自适应滤波技术进行测量更新,与现有方法相比,在提高测量精度的同时,增加了同步提供姿态速率信息的功能。仿真结果表明,新算法的姿态估计精度比目前常用的直接计算方法提高近两倍。     

Target racking with glint noise

In tracking targets, there can be an uncertainty associated with the measurements in addition to their inaccuracy, which is usually modeled by aDditive Gaussian noise. However, the Gaussian modeling of the noise may not be true. Noise can be non-Gaussian. The non-Gaussian noise arising in a radar system is known as glint noise. The distribution of glint noise is long tailed and will seriously affect the tracking performance. An algorithm is developed which can significantly improve the tracking performance when glint noise is present