Comparison of two measurement fusion methods forKalman-filter-based multisensor data fusion

Currently there exist two commonly used measurement fusion methods for Kalman-filter-based multisensor data fusion. The first (Method I) simply merges the multisensor data through the observation vector of the Kalman filter, whereas the second (Method II) combines the multisensor data based on a minimum-mean-square-error criterion. This paper, based on an analysis of the fused state estimate covariances of the two measurement fusion methods, shows that the two measurement fusion methods are functionally equivalent if the sensors used for data fusion, with different and independent noise characteristics, have identical measurement matrices. Also presented are simulation results on state estimation using the two measurement fusion methods, followed by the analysis of the computational advantages of each method     

Optimal and self-tuning information fusion Kalman multi-step predictor

Based on the optimal fusion algorithm weighted by matrices in the linear minimum variance (LMV) sense, a distributed optimal information fusion for the steady-state Kalman multi-step predictor is given for discrete linear stochastic control systems with multiple sensors and correlated noises, where the same sample period is assumed. When the noise statistics information is unknown, the distributed information fusion estimators for the noise statistics parameters are presented based on the correlation functions and the weighting average approach. Further, a self-tuning information fusion multi-step predictor is obtained. It has a two-stage fusion structure. The first-stage fusion is to obtain the fused noise statistics information. The second-stage fusion is to obtain the fused multi-step predictor. A simulation example shows the effectiveness.     

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.      

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.     

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     

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。     

Fusion of distributed extended forgetting factor RLS state estimators

For single-target multisensor systems, two fusion methods are presented for distributed recursive state estimation of dynamic systems without knowledge of noise covariances. The estimator at every local sensor embeds the dynamics and the forgetting factor into the recursive least squares (RLS) method to remedy the lack of knowledge of noise statistics, developed before as the extended forgetting factor recursive least squares (EFRLS) estimator. It is proved that the two fusion methods are equivalent to the centralized EFRLS that uses all measurements from local sensors directly and their good performance is shown by simulation examples.     

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。     

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。     

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.     

基于自校正Broyden拟牛顿法的航空发动机模型数值计算

以Broyden拟牛顿法为基础结合计算发散判断和校正机制,提出自校正Broyden拟牛顿法.该算法结合牛顿法(Newton-Raphson method)平方收敛和Broyden拟牛顿法超线性收敛特性,通过自适应调整计算步长和校正函数,在非线性系统中具有更好的计算性能.以变循环发动机部件级模型为对象,应用自校正Broyden拟牛顿法进行稳态及动态仿真计算,并与牛顿法和Broyden拟牛顿法作对比.结果表明:自校正Broyden拟牛顿法对恶劣的初始计算条件适应性更高,计算速度更快且收敛能力性更强,动态计算中部件模型计算调用次数为牛顿法的15%,模型动态误差低于Broyden拟牛顿法的15%,同时也低于牛顿法的28%,动态计算最大残差量低于其他两种算法的25%.验证结果表明了自校正Broyden拟牛顿法的优越性.      

A Polynomial Prediction Filter Method for Estimating Multisensor Dynamically Varying Biases

The estimation of the sensor measurement biases in a multisensor system is vital for the sensor data fusion. A solution is provided for the estimation of dynamically varying multiple sensor biases without any knowledge of the dynamic bias model pa- rameters. It is shown that the sensor bias pseudomeasurement can be dynamically obtained via a parity vector. This is accom- plished by multiplying the sensor uncalibrated measurement equations by a projection matrix so that the measured variable is eliminated from the equations. Once the state equations of the dynamically varying sensor biases are modeled by a polynomial prediction filter, the dynamically varying multisensor biases can be obtained by Kalman filter. Simulation results validate that the proposed method can estimate the constant biases and dynamic biases of multisensors and outperforms the methods reported in literature.     

Canonical transform for tracking with kinematic models

A canonical transform is presented that converts a coupled or uncoupled kinematic model for target tracking into a decoupled dimensionless canonical form. The coupling is due to non-zero off-diagonal terms in the covariance matrices of the process noise and/or the measurement noise, which can be used to model the coupling of motion and/or measurement between coordinates. The decoupled dimensionless canonical form is obtained by simultaneously diagonalizing the noise covariance matrices, followed by a spatial-temporal normalization procedure. This canonical form is independent of the physical specifications of an actual system. Each subsystem corresponding to a canonical coordinate is characterized by its process noise standard deviation, called the maneuver index as a generalization of the tracking index for target tracking, which characterizes completely the performance of a steady-state Kalman filter. A number of applications of this canonical form are discussed. The usefulness of the canonical transform is illustrated via an example of performance analysis of maneuvering target tracking in an air traffic control (ATC) system.     

Efficient numerical algorithm for steady-state Kalman covariance

A stable, quadratically convergent numerical algorithm is presented for computing the steady-state covariance and gain matrices of the Kalman filter. The method is more rapidly convergent than standard Riccati integration techniques and is easier to implement than existing eigenvalue-eigenvector algorithms. The quadratic convergence is proved analytically and illustrated by a numerical example     

A new adaptive Kalman filter for navigation systems of carrier-based aircraft

The features of carrier-based aircraft’s navigation systems during the approach and landing phases are investigated. A new adaptive Kalman filter with unknown state noise statistics is proposed to improve the accuracy of the INS/GNSS integrated navigation system. The adaptive filtering algorithm aims to estimate and adapt the unknown state noise covariance Q in high dynamic conditions, when the measurement noise covariance R is assumed to be known empirically in advance. The new adaptive Kalman ...     

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.     

The modeling and estimation of asynchronous multirate multisensor dynamic systems

An asynchronous data fusion problem based on a kind of multirate multisensor dynamic system is studied. The system is observed by multirate sensors independently, with the state model known at the finest scale. Under the assumption that the sampling rates of sensors decrease successively by any positive integers, the discrete dynamic system models are established based on each single sensor and an asynchronous multirate multisensor state fusion estimation algorithm is presented. Theoretically, the estimate is proven to be unbiased and the optimal in the sense of linear minimum covariance, the fused estimate is better than the Kalman filtering results based on each single sensor, and the accuracy of the fused estimate will decrease if any of the sensors' information is neglected. The feasibility and effectiveness of the algorithm are shown through simulations.     

基于速度积分匹配的旋转调制惯导系统动基座对准方法

卫星导航信息辅助动基座对准过程中,速度噪声会影响对准精度和快速性,制约了旋转调制惯导角秒级高精度快速对准的实现.针对这一问题,提出了一种基于旋转调制惯导速度积分匹配的快速动基座对准方法,通过建立旋转调制惯导动基座对准误差方程和卡尔曼滤波观测模型,以消除动基座对准对载机特殊运动的要求.最后,在实验室静态环境和车载环境下,分别开展了速度积分匹配和速度十位置组合导航动基座对准仿真实验.仿真结果表明,提出的速度积分匹配方法具有误差估计量收敛速度快的特点,在对准精度不降低的情况下相对组合导航匹配方式能有效缩短动基座对准时间,并能基于旋转调制惯导取消动基座对准对载机的机动需求.     

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.     

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.