鲁棒EKF在脉冲星导航系统中的应用

针对脉冲星导航系统的滤波问题,传统的扩展卡尔曼滤波(EKF)算法存在不能克服系统模型存在不确定性参数以及乘性噪声等缺陷,提出一种鲁棒EKF算法。首先,分析了状态预测误差方程和估计误差方程,利用统计学原理,得到了状态预测方差矩阵和状态估计方差矩阵计算等式。由于系统模型存在不确定性参数,状态预测协方差矩阵和状态估计协方差矩阵无法计算;因此,利用4个重要矩阵不等式,分析并找到预测方差矩阵和状态估计方差矩阵的上界。最后,利用状态估计误差协方差矩阵上界设计状态增益矩阵,使得状态估计协方差矩阵的迹最小。将该算法对脉冲星导航系统进行仿真,仿真结果验证了所提算法的有效性。     

Performance Bounds for Continuous-time Filters in the Presence of Modeling Errors

We are concerned with obtaining bounds on the performance of Kalman-type, linear, continuous-time filters susceptible to modeling errors. Limiting the discussion to stationary performance, we obtain bounds on the performance index, the mean square error of estimates for suboptimal and optimal (Kalman) filters. The bounds are expressed in terms of the model matrices and the range of errors of the matrices. The results are useful to a designer in comparing the performance of a suboptimal filter with that of the optimal filter when he has information on the range of modeling errors. The tightness of the bounds is shown by an application of the results in the estimation of the motion of an aircraft carrier at sea.     

基于稀疏表示的双基地MIMO雷达多目标定位及幅相误差估计

 基于稀疏表示理论,提出一种新的双基地多输入多输出(MIMO)雷达收发角度及幅相误差估计算法。利用接收数据,分别构造发射和接收协方差矩阵,并以列向量化后的发射和接收协方差矩阵为量测信号建立2个一维稀疏线性模型,构造模型求解的 L₂-L₁ 混合范数优化目标函数,通过交替迭代寻优获得目标角度估计和幅相误差估计,最后给出了本文算法的收敛性分析。与现有算法相比,该算法充分利用了目标发射和接收空域的稀疏特性,且能够通过对噪声功率的预估计来抑制噪声。仿真结果表明:在低信噪比(SNR)条件下,本文算法仍能够得到较好的估计精度,且对幅相误差具有一定的稳健性。     

Novel quaternion Kalman filter

This paper presents a novel Kalman filter (KF) for estimating the attitude-quaternion as well as gyro random drifts from vector measurements. Employing a special manipulation on the measurement equation results in a linear pseudo-measurement equation whose error is state-dependent. Because the quaternion kinematics equation is linear, the combination of the two yields a linear KF that eliminates the usual linearization procedure and is less sensitive to initial estimation errors. General accurate expressions for the covariance matrices of the system state-dependent noises are developed. In addition, an analysis shows how to compute these covariance matrices efficiently. An adaptive version of the filter is also developed to handle modeling errors of the dynamic system noise statistics. Monte-Carlo simulations are carried out that demonstrate the efficiency of both versions of the filter. In the particular case of high initial estimation errors, a typical extended Kalman filter (EKF) fails to converge whereas the proposed filter succeeds.     

A quantization architecture for track fusion

Many practical multi-sensor tracking systems are based on some form of track fusion, in which local track estimates and their associated covariances are shared among sensors. Communication load is a significant concern, and the goal of this paper is to propose an architecture for low-bandwidth track fusion. The scheme involves intelligent scalar and vector quantization of the local state estimates and of the associated estimation error covariance matrices. Simulation studies indicate that the communication saving can be quite significant, with only minor degradation of track accuracy.     

Characterization of Kalman filter residuals in the presence ofmismodeling

The mean and covariance of a Kalman filter residual are computed for specific cases in which the Kalman filter model differs from a linear model that accurately represents the true system (the truth model). Multiple model adaptive estimation (MMAE) uses a bank of Kalman filters, each with a different internal model, and a hypothesis testing algorithm that uses the residuals from this bank of Kalman filters to estimate the true system model. At most, only one Kalman filter model will exactly match the truth model and will produce a residual whose mean and standard deviation have already been analyzed. All of the other filters use internal models that mismodel the true system. We compute the effects of a mismodeled input matrix, output matrix, and state transition matrix on these residuals. The computed mean and covariance are compared with simulation results of flight control failures that correspond to mismodeled input matrices and output matrices     

基于ATSUKF算法的卫星姿控系统故障估计

针对卫星姿态控制过程中可能发生的执行机构或敏感器故障，提出了一种基于无损卡尔曼滤波（UKF）及偏差分离原理的自适应二阶无损卡尔曼滤波（ATSUKF）算法。首先，提出TSUKF算法，通过UKF处理姿态机动时的非线性并通过偏差分离原理将非线性系统的状态及故障分别估计，避免非线性模型的线性化过程同时降低了计算过程中的矩阵维度。然后，在TSUKF算法的基础上提出了ATSUKF算法，通过滑动窗口内的残差计算自适应矩阵，使滤波器在统计特性不准确的情况下仍然具有较快的收敛速度，特别适用于卫星快速机动过程中的姿态与故障估计。数值仿真结果表明，ATSUKF算法相较于TSUKF算法能有效降低统计特性不准对系统造成的不利影响，实现卫星姿态、执行机构/敏感器故障的快速估计。     

多渐消因子Kalman滤波器在SINS初始对准中的应用(英文)

针对系统模型和统计信息不能精确已知的条件下Kalman滤波无法给出最优解这一问题,单一渐消因子Kalman滤波算法对于简单的系统是有效的,但是对于复杂的多变量系统,仅仅利用单个的渐消因子是不够的。本文提出了一种多渐消因子滤波算法,通过利用开窗法计算新息序列协方差的无偏估计获得渐消因子矩阵。利用渐消因子矩阵调节一步预测均方误差矩阵k|k1P,对不同的滤波通道提供不同的渐消速率。将该方法应用于SINS的初始对准中,仿真和试验结果表明:当真实系统噪声统计特性同设定参数不一致时,对准精度明显高于其他滤波算法。其对不确定性噪声具有较低的敏感度,对系统参数具有较好的滤波效果。因而,在实际应用中具有重要的参考价值。     

Kalman filtering for matrix estimation

A general discrete-time Kalman filter (KF) for state matrix estimation using matrix measurements is presented. The new algorithm evaluates the state matrix estimate and the estimation error covariance matrix in terms of the original system matrices. The proposed algorithm naturally fits systems which are most conveniently described by matrix process and measurement equations. Its formulation uses a compact notation for aiding both intuition and mathematical manipulation. It is a straightforward extension of the classical KF, and includes as special cases other matrix filters that were developed in the past. Beyond the analytical value of the matrix filter, it is shown through various examples arising in engineering problems that this filter can be computationally more efficient than its vectorized version.     

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.     

U-D分解的固定点平滑新算法及其在飞行试验中的应用

 本文根据Rauch固定点平滑公式,提出了一种U-D分解的固定点平滑新算法。这一算法不仅具有良好的数值稳定性和可靠性,而且计算量较少;计算效率是Bryson-Ho Y C固定点平滑计算效率的1.5倍以上。将这种新算法用于飞机运动状态初值的确定,提高了飞机气动参数辨识精度。     

Error Covariance Analysis of a Karhunen-Loeve Collocation Estimator

An error covariance analysis of a two-dimensional gravity compensation technique (KLC) employing a Karhunen-Loeve gravity disturbance model and the linear least-square collocation algorithm for its estimation is presented, without actually using any data. Its performance is compared with another gravity compensation technique (KLE), whose error covariance analysis was previously presented by Gupta. From the mismodeling analysis, KLC appears to be superior to KLE.     

受地效影响飞机起飞着陆运动模型的参数辨识

利用基于最小模型误差法和线性不连续跳跃多重打靶法建立的非线性辨识法，辨识了飞机起飞着陆过程的非线性动态模型。对于包含复杂非线性项的动态系统，本方法可以从实际试验测量的系统非线性数据，确定飞机处于地面效应影响运动过程的系统模型，而不需要预先详细描述系统的非线性形式。算例表明该方法对于原始近似动态系统的状态估计是足够精确的。     

Estimation of the covariance matrix for dependent signal samples:polarization diversity systems

The problem of the estimation of covariance matrices in multichannel radar system when signal samples are statistically dependent is addressed. An optimal maximum likelihood (ML) estimate is derived. Probability characteristics and sensitivity to signal models of the estimate are evaluated for a polarization diversity system     

Square root parallel Kalman filtering using reduced-order localfilters

The basic parallel Kalman filtering algorithms derived by H.R. Hashemipour et al. (IEEE Trans. Autom. Control. vol.33, p.88-94, 1988) are summarized and generalized to the case of reduced-order local filters. Measurement-update and time-update equations are provided for four implementations: the conventional covariance filter, the conventional information filter, the square-foot covariance filter, and the square-foot information filter. A special feature of the suggested architecture is the ability to accommodate parallel local filters that have a smaller state dimension than the global filter. The estimates and covariance or information matrices (or their square roots) from these reduced-order filters are collated at a central filter at each step to generate the full-size, globally optimal estimates and their associated error covariance or information matrices (or their square roots). Aspects of computational complexity and the ensuing tradeoff with communication are discussed     

Random Weighting Estimation Method for Dynamic Navigation Positioning

This paper presents a new random weighting estimation method for dynamic navigation positioning.This method adopts the concept of random weighting estimation to estimate the covariance matrices of system state noises and observation noises for controlling the disturbances of singular observations and the kinematic model errors.It satisfies the practical requirements of the residual vector and innovation vector to sufficiently utilize observation information,thus weakening the disturbing effect of the kinematic model error and observation model error on the state parameter estimation.Theories and algorithms of random weighting estimation are established for estimating the covariance matrices of observation residual vectors and innovation vectors.This random weighting estimation method provides an effective solution for improving the positioning accuracy in dynamic navigation.Experimental results show that compared with the Kalman filtering,the extended Kalman filtering and the adaptive windowing filtering,the proposed method can adaptively determine the covariance matrices of observation error and state error,effectively resist the disturbances caused by system error and observation error,and significantly improve the positioning accuracy for dynamic navigation.     

Reconciling steady-state Kalman and alpha-beta filter design

The deterministic design of the alpha-beta filter and the stochastic design of its Kalman counterpart are placed on a common basis. The first step is to find the continuous-time filter architecture which transforms into the alpha-beta discrete filter via the method of impulse invariance. This yields relations between filter bandwidth and damping ratio and the coefficients, α and β. In the Kalman case, these same coefficients are related to a defined stochastic signal-to-noise ratio and to a defined normalized tracking error variance. These latter relations are obtained from a closed-form, unique, positive-definite solution to the matrix Riccati equation for the tracking error covariance. A nomograph is given that relates the stochastic and deterministic designs     

Recursive 3-D motion estimation from a monocular image sequence

Consideration is given to the design and application of a recursive algorithm to a sequence of images of a moving object to estimate both its structure and kinematics. The object is assumed to be rigid, and its motion is assumed to be smooth in the sense that it can be modeled by retaining an arbitrary number of terms in the appropriate Taylor series expansions. Translational motion involves a standard rectilinear model, while rotational motion is described with quaternions. Neglected terms of the Taylor series are modeled as process noise. A state-space model is constructed, incorporating both kinematic and structural states, and recursive techniques are used to estimate the state vector as a function of time. A set of object match points is assumed to be available. The problem is formulated as a parameter estimation and tracking problem which can use an arbitrarily large number of images in a sequence. The recursive estimation is done using an iterated extended Kalman filter (IEKF), initialized with the output of a batch algorithm run on the first few frames. Approximate Cramer-Rao lower bounds on the error covariance of the batch estimate are used as the initial state estimate error covariance of the IEKF. The performance of the recursive estimator is illustrated using both real and synthetic image sequences     

Analytical Results for a Kalman Tracker Using Position and Rate Measurements

Analytical results are presented for determining the steady-state components of the gain and error covariance matrices of the two-state Kalman tracking filter with white noise maneuver capability.     

优化抗差自适应滤波器在深组合导航中的应用

为了提高惯性/卫星深组合导航系统的滤波性能,在抗差自适应滤波算法的 基础上,研究了一种优化抗差自适应滤波算法。该算法通过比较实际预测残差协方差矩 阵和理论协方差阵的差值来生成自适应因子,从而优化抗差自适应滤波。将所研究的算 法应用于惯性/卫星深组合导航系统, 在高动态环境下进行仿真验证, 并与常规卡尔曼 滤波、抗差自适应滤波进行比较。结果表明,优化算法能有效地控制观测异常和动态模 型异常对状态参数估值的影响,所得组合导航位置误差和速度误差明显减小,提高了组 合导航系统的滤波精度。