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     

贝叶斯假设理论检测发动机传感器故障

贝叶斯多重假设检验是将被检测传感器的M个可能状态,作相应M个假设H_i,其先验概率分别为P(H_i)(i=1,2,…,M),故障决策就是从给定观测量M,寻求H_j为真,由贝叶斯风险函数H_i(i=1,2,…,M,i≠j)个假设中的最小值确定最可能发生的假设H_l。      

Multiple-model adaptive estimation using a residual correlationKalman filter bank

We propose a modified multiple model adaptive estimation (MMAE) algorithm that uses the time correlation of the Kalman filter residuals, in place of their scaled magnitude, to assign conditional probabilities for each of the modeled hypotheses. This modified algorithm, denoted the residual correlation Kalman filter bank (RCKFB), uses the magnitude of an estimate of the correlation of the residual with a slightly modified version of the usual MMAE hypothesis testing algorithm to assign the conditional probabilities to the various hypotheses that are modeled in the Kalman filter bank within the MMAE. This concept is used to detect flight control actuator failures, where the existence of a single frequency sinusoid (which is highly time correlated) in the residual of an elemental filter within an MMAE is indicative of that filter having the wrong actuator failure status hypothesis. This technique results in a delay in detecting the flight control actuator failure because several samples of the residual must be collected before the residual correlation can be estimated. However, it allows a significant reduction of the amplitude of the required system inputs for exciting the various system modes to enhance identifiability, to the point where they may possibly be subliminal, so as not to be objectionable to the pilot and passengers     

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.     

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     

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.     

基于混合卡尔曼滤波器组故障传感器定位方法

为了在发动机性能蜕化与传感器故障并存的情况下实现故障传感器的定位与部件蜕化情况的估计,并实现故障诊断基准数据的修正,构建了1种包含了机载模型与线性卡尔曼滤波器的组合结构混合卡尔曼滤波器组。该卡尔曼滤波器组能够在之前所描述的故障/蜕化耦合情况下定位故障传感器,并得到较为准确的部件蜕化估计结果。为了验证了混合卡尔曼滤波器组的有效性,进行了相关仿真。仿真结果表明:混合卡尔曼滤波器组能够在发动机动态过程中遭遇传感器故障与部件蜕化并存的情况下完成故障定位与蜕化估计。     

Enhanced motion and sizing of bank in moving-bank MMAE

The focus of this research is to provide methods for generating precise parameter estimates in the face of potentially significant parameter variations such as system component failures. The standard multiple model adaptive estimation (MMAE) algorithm uses a bank of Kalman filters, each based on a different model of the system. Parameter discretization within the MMAE refers to selection of the parameter values assumed by the elemental Kalman filters, and dynamically redeclaring such discretization yields a moving-bank MMAE. A new online parameter discretization method is developed based on the probabilities associated with the generalized chi-squared random variables formed by residual information from the elemental Kalman filters within the MMAE. This new algorithm is validated through computer simulation of an aircraft navigation system subjected to interference/jamming while attempting a successful precision landing of the aircraft.     

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。     

基于改进容积卡尔曼滤波的惯性/光流组合自主测速方法

针对容积卡尔曼滤波算法在惯性/光流组合测速数据融合时出现由于各系统输出数据频率不一致导致融合精度有限的问题,提出了一种基于多速率残差校正的改进容积卡尔曼滤波算法.通过当前时刻误差估算组合导航系统残差,再使用估算后的残差对速度估计值进行补偿,最终实现惯性/光流组合系统速度测量值的数据融合.实验结果表明,通过提出的改进容积卡尔曼滤波对惯性/光流数据进行融合后,东向速度均方根误差为0.2964m/s,北向速度均方根误差为0.06m/s,与现有其他卡尔曼滤波算法相比,此方法可显著提高惯性/光流组合系统的速度测量精度.     

Analysis of upgraded GPS internal Kalman filter

GPS receivers with provisions for inertial navigation system (INS) aiding are designed with internal Kalman filters that model generic INSs and process the basic GPS pseudorange and deltarange (range-rate) data to produce an output of inertially-smoothed, “GPS-derived” position and velocity. These Kalman filters model only the basic nine INS errors (position, velocity, and tilt) and do not model any INS gyro or accelerometer errors. It was found that a significant performance improvement could be achieved under conditions of degraded GPS satellite availability by augmenting this type of filter with the six INS gyro and accelerometer bias errors. It is, therefore, recommended that serious consideration be given to incorporating these states into the design of the GPS internal Kalman filter     

基于超球体平方根无迹Kalman滤波算法的涡扇发动机气路部件故障诊断

研究了一种超球体平方根无迹Kalman滤波算法用来有效跟踪涡扇发动机气路部件发生渐变性和突变性故障的健康参数.该算法通过超球体单形采样来降低算法的计算量,采用测量残差协方差阵的平方根代替方差阵进行递推运算,提高了算法的计算效率和数值稳定性.分别采用扩展Kalman滤波算法、无迹Kalman滤波算法和超球体平方根无迹Kalman滤波算法对某型涡扇发动机进行仿真,结果表明:超球体平方根无迹Kalman滤波算法的滤波时间减少50%左右,能够实现渐变性和突变性故障中健康参数的准确估计,是一种有效的涡扇发动机气路部件参数估计和故障诊断方法.      

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。      

Robust adaptive filtering method for SINS/SAR integrated navigation system

This paper presents a new robust adaptive filtering method for SINS/SAR (Strap-down Inertial Navigation System/Synthetic Aperture Radar) integrated navigation system. This method adopts the principle of robust estimation to adaptive filtering of observational data. A robust adaptive filter is developed to adaptively determine the covariance matrix of observation noise, and adaptively adjust the covariance matrix of system state noise according to the adaptive factor constructed based on predicted residuals. Experimental results and comparison analysis demonstrate that the proposed method cannot only effectively resist disturbances due to system state noise and observation noise, but it can also achieve higher accuracy than the adaptive Kalman filtering method.     

基于联邦滤波结构的INS／GPS组合导航系统数据融合研究

为了研究平台式惯导INS（interial navigation system）和全球定位系统GPS（globe position system）组合导航联邦滤波器的实现,使用速度局部滤波器和位置局部滤波器,分别对INS／GPS组合导航系统的向东速度、向北速度,以及对经度和纬度进行卡尔曼滤波,然后将位置数据和速度数据输入主滤波进行数据融合。以无人机的向东匀速水平飞行为背景,运用联邦卡尔曼滤波器算法,使用matelab进行仿真分析。可以证明联邦滤波器算法简单,易于实现,并且可以提高导航系统精度．实际应用中此方法可行。     

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。     

Hierarchical adaptive Kalman filtering for interplanetary orbitdetermination

A modular and flexible approach to adaptive Kalman filtering has recently been introduced using the framework of a mixture-of-experts regulated by a gating network. Each expert is a Kalman filter modeled with a different realization of the unknown system parameters. The unknown or uncertain parameters can include elements of the state transition matrix, observation mapping matrix, process noise covariance matrix, and measurement noise covariance matrix. The gating network performs on-line adaptation of the weights given to individual filters based on performance. The mixture-of-experts approach is extended here to a hierarchical architecture which involves multiple levels of gating. The proposed architecture provides a multilevel hypothesis testing capability. The utility of the hierarchical architecture is illustrated via the problem of interplanetary navigation (Mars Pathfinder) using simulated radiometric data. It serves as a useful tool for assisting navigation teams in the process of selecting the parameters of the navigational filter over various operating regimes. It is shown that the scheme has the capability of detecting changes in the system parameters and switching filters appropriately for optimal performance. Furthermore, the expectation-maximization (EM) algorithm is shown to be applicable in the proposed framework     

自适应高阶容积卡尔曼滤波在目标跟踪中的应用

针对传统容积卡尔曼滤波(CKF)在系统状态发生突变时估计精度下降的问题,将强跟踪滤波(STF)算法与高阶容积卡尔曼滤波(HCKF)算法相结合,提出了一种自适应高阶容积卡尔曼滤波(AHCKF)方法。该算法采用高阶球面-相径容积规则,可获得高于传统CKF的估计精度,同时在HCKF算法中引入STF,通过渐消因子在线修正预测误差协方差阵,强迫残差序列正交,提高了算法的鲁棒性,增强了算法应对系统状态突变等不确定因素的能力。将提出的AHCKF算法应用于具有状态突变的机动目标跟踪问题并进行数值仿真,仿真结果表明,AHCKF算法在系统状态发生突变的情况下表现出良好的滤波性能,有效地避免了状态突变造成的滤波精度下降,较传统的CKF、HCKF、交互式多模型-容积滤波(IMM-CKF)和自适应容积卡尔曼滤波(ACKF)算法有更强的鲁棒性和系统自适应能力。     

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。     

Fallacies in computational testing of matrix positivedefiniteness/semidefiniteness

The status of computational tests for establishing matrix positive semidefiniteness and positive definiteness is reviewed. Two pervasive real-time tests that have been used for many years in varied applications to ensure that computed covariances encountered in Kalman filter applications are positive definite and discussed. Structural representations of covariance matrices are reviewed as a prelude to constructing a counterexample and demonstrating that it refutes these real-time tests. It is maintained that the latter are bogus approaches despite the fact that they are pervasive. It is suggested that such bogus tests arose as an attempt to fill the need for a quick check (over the entire mission time) of the massive number of matrices computationally encountered in real-time applications