一种改进的数字滤波平方定时的频域算法

在数字滤波平方定时的频域算法基础上,采用了前端进行带通滤波和后端实施卡尔曼滤波的处理方法对其进行改进。带通滤波器减小了定时误差估计的方差,而卡尔曼滤波则降低了整个定时误差估计过程中噪声的影响。实验与仿真的结果表明,改进后的方法达到了预期的效果。     

一种基于冗余测量的自适应卡尔曼滤波算法

针对目前自适应滤波算法的不足,在测量系统量测噪声方差未知的情况下,设计了一种基于冗余测量的自适应卡尔曼滤波(RMAKF)算法。通过对系统冗余测量值的一阶、二阶差分序列进行有效的统计分析,可以准确估计系统量测噪声统计特性,进而在滤波过程中自适应调节噪声方差阵R,提高滤波精度。以全球定位系统/惯性导航系统(GPS/INS)松组合导航系统为对象进行了仿真实验,结果表明该算法在测量系统噪声特性未知或发生改变时,可对其进行准确估计,在采用低精度惯性器件情况下,滤波结果较其他主要自适应卡尔曼滤波算法有较明显的改进。     

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。     

Novel Nonlinear Filtering & Prediction Method for Maneuvering Target Tracking

A new nonlinear filtering and prediction (NFP) algorithm with input es?imation is proposed for maneuvering target tracking. In the proposed method, the acceleration level is determined by a decision process, where a least squares (LS) estimator plays a major role in detecting target maneuvering within a sliding window. We first illustrate that the optimal solution to minimize the mean squared error (MSE) must consider a trade-off between the bias and error variance. For the application of target tracking, we then derive the MSE of target positions in a closed form by using orthogonal space decompositions. Then we discuss the NFP estimator, and evaluate how well the approach potentially works in the case of a set of given system parameters. Comparing with the traditional unbiased minimum variance filter (UMVF), Kalman filter, and interactive multiple model (IMM) algorithms, numerical results show that the newly proposed NFP method performs comparable or better in all scenarios with significantly less computational requirements.     

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。     

利用卡尔曼滤波求取直升机气动导数的应用研究

本文主要介绍利用低通滤波、卡尔曼滤波及最小二乘法求取直升机气动导数的方法。本方法的特点是,通过低通滤波使旋翼高频成份的影响减至最小,同时求取试验数据的测量噪声和过程噪声,然后通过卡尔曼滤波使试验数据包含的随机噪声减至最小,最后用最小二乘法求得直升机的气动导数,为了提高卡尔曼滤波的准确度,用最小二乘法由试验数据求取直升机的气动导数作为卡尔曼滤波时的初始导数。计算结果表明,该方法可使试验数据中包含的噪声大大减小,误差带减少70％以上,而计算工作量又远远小于最大似然法。     

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     

空间平台机动变轨自主导航研究

针对空间平台在高轨道机动变轨过程中自主导航的需求,采用了基于Kalman滤波器的捷联惯导与星敏感器的组合导航方案。结合Kalman滤波中协方差更新的误差分配分析方法,分析了影响空间平台状态估计误差的主要因素。采用适用于高轨道的球谐重力模型,运用STK工具包设计了变轨机动轨迹,将该轨迹应用于组合导航方案的仿真验证。仿真结果表明,量测噪声是影响空间平台姿态精度的主要因素,加速度计零偏对变轨过程速度精度有决定性影响,改善两者的精度可以实现空间平台机动变轨的高精度自主导航。     

Digital tracking filters with high order correlated measurement noise

The existing algorithms for the design of digital filters with colored measurement noise involve a restriction on the dimension of the measurement error model. Kalman filter equations and state space partition are used to formulate an optimal tracking filter without such restrictions. The input to the new filter are two consecutive measurements, and it is initialized by using the first available measurements and the error model correlation matrix. Several examples illustrate the filter formulation and initialization.     

Efficient L-D factorization algorithms for PDA, IMM, and IMMPDAfilters

Efficient algorithms exist for the square-root probabilistic data association filter (PDAF). The same approach is extended to develop square-root versions of the interacting multiple model (IMM) Kalman filter and the IMMPDAF algorithms. The computational efficiency of the method stems from the fact that the terms needed in the overall covariance updates of PDAF, IMM, and IMMPDAF can be obtained as part of the square-root covariance update of an ordinary Kalman filter. In addition, a new square-root covariance prediction algorithm that is substantially faster than the usual modified weighted Gram-Schmidt (MWG-S) algorithm, whenever the process noise covariance matrix is time invariant, is proposed     

涡扇发动机变参数鲁棒H_∞滤波器设计

针对存在建模误差及测量噪声干扰条件下的涡扇发动机性能参数估计问题,标准卡尔曼滤波及其改进算法滤波估计误差收敛速度慢,滤波估计精度低,对不确定测量噪声及建模误差较为敏感,为此本文提出了一种变参数鲁棒H_∞滤波器设计方法。该方法采用仿射参数依赖Lyapunov函数设计满足H_∞性能指标要求的鲁棒滤波器,通过引入凸多胞技术,将参数依赖线性矩阵不等式(Linear Matrix Inequality,LMI)中变参数Lyapunov矩阵与系统系数矩阵之间耦合乘积导致的非凸优化问题,转化为常规LMI约束下的凸优化问题进行求解,降低了线性变参数(Linear Parameter Varying,LPV)鲁棒滤波器设计的保守性,得到了全局解。针对涡扇发动机的仿真结果表明:与扩展卡尔曼滤波器对比,采用该方法设计的滤波器具有较快的动态跟踪速度和较高的滤波精度,ΔFn的稳态估计误差不大于0.1%,ΔFn的相对估计误差不大于2.5%,同时对建模误差和测量噪声干扰具有较强的抑制能力。     

A practical filter error method for aerodynamic parameter estimation of aircraft in turbulence

It is common for aircraft to encounter atmospheric turbulence in flight tests. Turbulence is usually modeled as stochastic process noise in the flight dynamics equations. In this paper, parameter estimation of nonlinear dynamic system with both process and measurement noise was studied, and a practical filter error method was proposed. The linearized Kalman filter of first-order approximation was used for state estimation, in which the filter gain, along with the system parameters and the initial states, constituted the parameter vector to be estimated. The unknown parameters and measurement noise covariance were estimated alternately by a relaxation iteration method, and the sensitivities of observations to unknown parameters were calculated by finite difference approximation. Some practical aspects of the method application were discussed. The proposed filter error method was validated by the flight simulation data of a research aircraft. Then, the method was applied to the flight tests of a subscale aircraft, and the aerodynamic stability and control derivatives were estimated. All the estimation results were compared with the results of the output error method to demonstrate the effectiveness of the approach. It is shown that the filter error method is superior to the output error method for flight tests in atmospheric turbulence.     

SINS/BDS紧组合系统中自适应 两阶段扩展卡尔曼滤波

在实际应用中，以伪距/伪距率为观测量的SINS/BDS紧组合导航系统，存在量测噪声的统计特性与实际不相符的情况，传统扩展卡尔曼滤波（EKF）方法无法有效解决这一问题，从而引起滤波误差增大。提出了一种SINS/BDS紧组合导航系统的GDOP估算及在线估计量测噪声的自适应两阶段EKF（ATEKF）方法，该方法使用经过紧组合修正后的SINS输出的位置，并结合星历数据中提供的卫星位置求解GDOP。在此基础上，利用GDOP值以及新息，实现了紧组合导航系统的量测噪声方差阵（Rk）的在线实时估计，从而达到自适应滤波的效果，改善导航精度。     

飞行器气动力参数辨识的一种实用滤波误差方法

提出了一种观测噪声相对于过程噪声较小情况下气动参数识别的实用滤波误差方法，方法不要求已知系统过程噪声和观测噪声方差阵，计算量小，具有一定的应用价值。     

自校准Kalman滤波方法

提出一种自校准Kalman滤波方法(SKF),建立SKF模型及其滤波递推算法.在深空探测、发动机故障诊断等许多工程实际中,由于未知输入(如突风、故障、未知的系统误差等)的影响,传统的Kalman滤波方法在滤波递推过程中会产生较大误差.文中提出的自校准Kalman滤波方法能够自动补偿这种未知输入的影响,提高滤波精度.从某飞行器仿真中可以看到,SKF的滤波误差均值和方差分别比传统的Kalman滤波方法降低了400%和300%以上,有效地改善了滤波效果.并且该方法计算简单,便于工程应用.     

自适应扩展增量 Kalman 滤波方法

基于扩展增量Kalman滤波方法(EIKF)和自适应增量Kalman滤波(AIKF),建立自适应扩展增量Kalman(AEIKF)模型及其分析方法,给出递推算法.在许多实际情况(如深空探测),由于环境因素的影响、测量设备的不稳定性等原因,量测方程往往存在未知的系统误差,并且模型参数也具有不确定性,结果导致较大的Kalman滤波误差,影响滤波的收敛性.提出的AEIKF方法能够成功消除这种未知的系统误差,并能够实时估计变化的噪声统计量,提高Kalman滤波精度.该方法计算简单,便于工程应用.      

Analytical solution of discrete colored noise ECA tracking filter

New analytical solutions of steady-state Kalman gains are presented for a discrete-time tracking filter with correlation in both the measurement noise and the target maneuver. The measurement noise model is a first-order discrete Markov process characterized by a correlation coefficient ρ. The target motion is examined for an exponentially correlated acceleration maneuver type in which the vehicle oscillation such as wind-induced-bending is also considered. The present solution method is based on factorizing the observed spectral density matrix Ψ(z) in frequency domain. The algorithm proposed here gives the Kalman gain matrix directly. For a case when the steady-state error covariance matrix is desired, such gains can be incorporated with the algebraic Riccati equation     

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     

一种基于模型误差预测的UKF方法

UnscentedKalman滤波器（UKF）对本质非线性系统具有估计精度高、收敛速度快和容易实现等优点,但是对系统的模型误差比较敏感。针对这一问题,提出了一种基于模型误差预测的UKF方法,称为PUKF（PredictiveUnscentedKalmanFilter）。它利用非线性预测滤波器（NPF）的模型误差预测过程,能够对不准确的系统模型进行实时修正,弥补了UKF方法的不足。仿真结果表明,相对于原始的UKF方法,新方法从滤波精度、收敛速度和收敛的稳定性等几个方面,显著提高了非线性滤波的性能。PUKF可适用于模型不确定、非线性较强系统的滤波。     

Application of the Kalman-Levy Filter for Tracking Maneuvering Targets

Among target tracking algorithms using Kalman filtering-like approaches, the standard assumptions are Gaussian process and measurement noise models. Based on these assumptions, the Kalman filter is widely used in single or multiple filter versions (e.g., in an interacting multiple model (IMM) estimator). The oversimplification resulting from the above assumptions can cause degradation in tracking performance. In this paper we explore the application of Kalman-Levy filter to handle maneuvering targets. This filter assumes a heavy-tailed noise distribution known as the Levy distribution. Due to the heavy-tailed nature of the assumed distribution, the Kalman-Levy filter is more effective in the presence of large errors that can occur, for example, due to the onset of acceleration or deceleration. However, for the same reason, the performance of the Kalman-Levy filter in the nonmaneuvering portion of track is worse than that of a Kalman filter. For this reason, an IMM with one Kalman and one Kalman-Levy module is developed here. Also, the superiority of the IMM with Kalman-Levy module over only Kalman-filter-based IMM for realistic maneuvers is shown by simulation results.