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.     

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     

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。     

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。     

Coordinate Conversion and Tracking for Very Long Range Radars

The problem of tracking with very long range radars is studied in this paper. First, the measurement conversion from a radar's r-u-v coordinate system to the Cartesian coordinate system is discussed. Although the nonlinearity of this coordinate transformation appears insignificant based on the evaluation of the bias of the converted measurements, it is shown that this nonlinearity can cause significant covariance inconsistency in the conventionally converted measurements (CM1). Since data association depends critically on filter consistency, this issue is very important. Following this, it is shown that a suitably corrected conversion (CM2) eliminates the inconsistency. Then, initialized with the converted measurements (using CM2), four Cartesian filters are evaluated. It is shown that, among these filters, the converted measurement Kalman filter with second order Taylor expansion (CM2KF) is the only one that is consistent for very long range tracking scenarios. Another two approaches, the range-direction-cosine extended Kalman filter (ruvEKF) and the unscented Kalman filter (UKF) are also evaluated and shown to suffer from consistency problems. However, the CM2KF has the disadvantage of reduced accuracy in the range direction. To fix this problem, a consistency-based modification for the standard extended Kalman filter (E1KF) is proposed. This leads to a new filtering approach, designated as measurement covariance adaptive extended Kalman filter (MCAEKF). For very long range tracking scenarios, the MCAEKF is shown to produce consistent filtering results and be able to avoid the loss of accuracy in the range direction. It is also shown that the MCAEKF meets the posterior Carmer-Rao lower bound for the scenarios considered.     

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。     

基于改进联邦Kalman滤波的组合校准方法研究

联邦滤波器广泛应用于多传感器信息融合领域,联邦滤波中的信息分配原则影响滤波精度.针对联邦Kalman滤波器进行改进,采用基于估计协方差阵奇异值动态确定信息分配系数.对子滤波器进行重置时,采用新的重置方法,保证了子滤波器误差协方差阵的对称性,确保Kalman滤波器的一致收敛稳定性.新的联邦滤波算法允许每个状态分量拥有不同的动态信息分配因子,从而改进了联邦滤波信息融合的精度.设计了SINS/GPS/电子罗盘组合导航系统,仿真结果说明,与传统联邦滤波算法相比,改进的联邦滤波器估计精度得到了提高,可以更好地对SINS误差进行校准,提高系统的精度.     

Sequential nonlinear tracking using UKF and raw range-rate measurements

The three-dimensional (3D) converted measurements filtering (CMF) with both converted position and raw range-rate measurement is proposed to solve the Doppler radar target tracking, where the error between radar-target range and range rate are correlated. Firstly, not using pseudomeasurement constructed by product of range and range rate to reduce the high nonlinearity, the raw range-rate measurements are utilized by unscented Kalman filter (UKF), where the converted errors of the position and the range rate are decorrelated, then linear part (position measurements) and nonlinear part (range-rate measurement) are sequentially processed by Kalman filter (KF) and UKF. Secondly, based on the assumption of small measurement error, the mean and covariance of converted measurement errors are derived by second-order Taylor series expansion. Finally, the influence of the correlated coefficient rho between the range and range rate, and the range-rate noise deviation sigma_r are taken into account and extreme values of rho and sigma_r are used in Monte Carlo simulations. The results show that the proposed method is, in a sense, effective and practical     

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UKF的大失准角船舶行进间对准技术研究

由于标准卡尔曼滤波只适用于线性系统,通常在SINS/GPS组合导航初始对准过程中,先通过基于惯性系的粗对准方法,将失准角转化为小量,然后再进行卡尔曼滤波精对准。由于杆臂效应,使用的基准信息存在一定误差,导致初始对准精度降低。因此,首先设计UKF的大失准角初始对准算法;其次将基准信息杆臂在UKF方程中建模,对杆臂误差进行补偿;最后通过仿真验证算法的可行性,并利用海试实验数据对UKF算法与传统动基座算法进行对比,实验结果表明该方法具有明显优势。     

陆用惯性导航系统非线性对准方法

以某型自行火炮炮载惯性导航系统为研究对象。为解决大方位失准角造成的系统非线性问题,在对大失准角误差模型进行详细分析的基础上,提出了基于快速正交搜索（FOS）和卡尔曼滤波（KF）的非线性参数估计方法。利用事先训练好的非线性误差模型进行对准,既能消除线性姿态误差,又可以对非线性姿态误差起到良好的抑制作用。仿真结果表明,FOS/KF方法的对准精度和实时性远优于扩展卡尔曼滤波（EKF）。对比试验结果表明,单独使用EKF时的方位角误差最大达到14.99°,而FOS/KF可以使方位角误差保持在0.8°以内。FOS/KF方法的估计精度不随系统非线性程度的变化而变化,并且不需要进行粗对准,简化了对准过程,提高了载体机动性。     

航空发动机气路故障诊断的平方根UKF方法研究

设计了适用于双轴涡扇发动机健康参数估计的平方根UKF滤波算法,解决了线性卡尔曼滤波器估计结果准确性依赖于线性模型精度;常规UKF算法中由于计算误差及噪声信号影响引起误差协方差矩阵负定而导致滤波结果发散等问题.提出了根据测量残差变化改进滤波收敛速度与稳定性的方法.发动机渐变与突变故障模式下仿真结果表明,平方根UKF估计算法收敛速度快,稳定性强,精度高,是一种有效的发动机气路部件健康参数估计与故障诊断方法.      

直接根据性能指标进行航空发动机LQG/LTR控制器设计

本文提出了一种根据性能指标要求设计航空发动机LQG/LTR控制器的方法。采用这种方法,可根据发动机模型及性能指标要求直接获得卡尔曼滤波器增益,而无需求解Riccati方程。随后的仿真结果表明,所设计的控制系统具有较好的稳定鲁棒性及较好的动态性能。      

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     

Intelligent SINS/RDSS Integrated Algorithms for Land Vehicle Navigation

This is a discussion of the design of strap-down inertial navigation systems (SINS) and radio determination satellite service (RDSS) integrated navigation algorithms. The research aims at testing the effectiveness of artificial intelligence (AI)-aided Kalman filtering (KF) approaches for land vehicle applications. A back-propagation neural network (BPNN)-aided K*F algorithm and a fuzzy inference-based KF algorithm are presented in order to overcome the time delay of RDSS positioning provided by a double-star positioning system in China. Traditional KF causes biased solutions, and indeed, leads to filter instability easily since the time delay of RDSS positioning, in an active mode, is hard to be modeled and sometimes suffers from RDSS outages. Therefore, a fuzzy inference is used to correct the variance matrix of KE measurement noises adaptively; and a trained BPNN corrects the outputs of the Kalman filter. The algorithms proposed herein have been verified on real SINSIRDSS data. collected in land vehicle tests and are compared with other approaches. The results demonstrate that fuzzy inference-based KF algorithms improve the positioning accuracy to over 40 % better than KF algorithms, and BPNN-aided KF algorithms have the same precision as GPS which is the reference station In dynamic experiments without RDSS outages. The test results with RDSS outages indicate that the fuzzy inference-based KF is feasible but with positioning errors of hundreds of meters, so the BPNN-aided KF is designed to efficiently compensate for RDSS outages and improve system performance.     

Steady-State Covariance Matrix Determination for a Three-Dimensional Kalman Tracking Filter

The steady-state components of the covariance matrix of estimation errors after processing an observation have been analytically determined ined for a tree-dimensional Kalman tracking filter.     

Interrelationship of single-filter and multiple-model adaptivealgorithms

An equivalent filter bank structure for multiple model adaptive estimation (MMAE) is developed that uses the residual and state estimates from a single Kalman filter and linear transforms to produce equivalent residuals of a complete Kalman filter bank. The linear transforms, which are a function of the differences between the system models used by the various Kalman filters, are developed for modeling differences in the system input matrix, the output matrix, and the state transition matrix. The computational cost of this new structure is compared with the cost of the standard Kalman filter bank (SKFB) for each of these modeling differences. This structure is quite similar to the generalized likelihood ratio (GLR) structure, where the linear transforms can be used to compute the matched filters used in the GLR approach. This approach produces the best matched filters in the sense that they truly represent the time history of the residuals caused by a physically motivated failure model     

Kalman Filter Behavior in Bearings-Only Tracking Applications

The extended Kalman filter applied to bearings-only target tracking is theoretically analyzed. Closed-form expressions for the state vector and its associated covariance matrix are introduced, and subsequently used to demonstrate how bearing and range estimation errors can interact to cause filter instability (i.e., premature covariance collapse and divergence). Further investigation reveals that conventional initialization techniques often precipitate such anomalous behavior. These results have important practical implications and are not presently being exploited to full advantage. In particular, they suggest that substantial improvements in filter stability can be realized by employing alternative initialization and relinearization procedures. Some candidate methods are proposed and discussed.     

捷联惯导系统大失准角下的初始对准研究

针对捷联惯导系统初始对准过程中的大失准角情况,建立了基于欧拉平台误差角概念的捷联惯导系统(SINS)非线性误差模型,对于具有加性噪声的动态方程,当状态方程为非线性而观测方程为线性时,将一种简化的UKF滤波方法运用到捷联惯导系统初始对准中,并在静基座下对捷联惯导系统大失准角初始对准进行了仿真。仿真结果表明,随着失准角的增大,简化的UKF比EKF估计精度更高,是一种在进行捷联惯导系统大失准角条件下的初始对准时实用方法。     

False alarm effects on estimation in multitarget trackers

An analysis of false alarm effects on tracking filter performance in multitarget track-while-scan radars, using variable correlation gates, is presented. The false alarms considered originate from noise, clutter, and crossing targets. The dimensions of the correlation gates are determined by filter prediction and measurement error variances. Track association is implanted either by means of a distance weighted average of the observations or by the nearest neighbor rule. State estimation is performed by means of a second-order discrete Kalman filter, taking into consideration random target maneuvers. Measurements are made in polar coordinates, while target dynamics are estimated in Cartesian coordinates, resulting in coupled linear filter equations. the effect of false alarms on the observation noise covariance matrix, and hence on state estimation errors, is analyzed. A computer simulation example, implementing radar target tracking with a variable correlation gate in the presence of false alarms, is discussed