Optimal robust non-fragile Kalman-type recursive filtering with finite-step autocorrelated noises and multiple packet dropouts

In this paper, the optimal robust non-fragile Kalman-type recursive filtering problem is studied for a class of uncertain systems with finite-step autocorrelated measurement noises and multiple packet dropouts. The system state, measurement output and filter parameters are all subject to stochastic uncertainties or multiplicative noises, where the measurement noises are finite-step autocorrelated. When there exist multiple packet dropouts in the system output, the original system is converted into an auxiliary stochastic uncertain system by the augmentation of system states and measurements. The process noises and measurement noises of the auxiliary system are shown to be finite-step autocorrelated and cross-correlated. Then, a robust non-fragile Kalman-type recursive filter is designed that is optimal in the minimum-variance sense. The proposed filter is not only robust against the uncertainties in the system model and measurement model, but also non-fragile against the implementation error with the filter parameters. Simulation results are employed to demonstrate the effectiveness of the proposed method.     

Observer-type Kalman innovation filter for uncertain linear systems

An observer-type of Kalman innovation filtering algorithm to find a practically implementable "best" Kalman filter, and such an algorithm based on the evolutionary programming (EP) optima-search technique, are proposed, for linear discrete-time systems with time-invariant unknown-but-hounded plant and noise uncertainties. The worst-case parameter set from the stochastic uncertain system represented by the interval form with respect to the implemented "best" filter is also found in this work for demonstrating the effectiveness of the proposed filtering scheme. The new EP-based algorithm utilizes the global optima-searching capability of EP to find the optimal Kalman filter and state estimates at every iteration, which include both the best possible worst case Interval and the optimal nominal trajectory of the Kalman filtering estimates of the system state vectors. Simulation results are included to show that the new algorithm yields more accurate estimates and is less conservative as compared with other related robust filtering schemes     

Joint parameter and state estimation for stochastic uncertain system with multivariate skew t noises

Due to the pulse interference, measurement outliers and artificial modeling errors, the multivariate skew t noise widely exists in the real environment. However, to date, little attention has been paid to the state estimation for systems in which the process noise and the measurement noise are both modeled as the heavy-tailed and skew non-Gaussian noise. In this paper, the multivariate skew t distribution is utilized to model the heavy-tailed and skew non-Gaussian noise. Then a probabilistic gra...     

Polynomial networks based adaptive attitude tracking control for NSVs with input constraints and stochastic noises

This paper proposes a backstepping technique and Multi-dimensional Taylor Polynomial Networks (MTPN) based adaptive attitude tracking control strategy for Near Space Vehicles (NSVs) subjected to input constraints and stochastic input noises. Firstly, considering the control input has stochastic noises, and the attitude motion dynamical model of the NSVs is actually modeled as the Multi-Input Multi-Output (MIMO) stochastic nonlinear system form. Furthermore, the MTPN is used to estimate the unknown system uncertainties, and an auxiliary system is designed to compensate the influence of the saturation control input. Then, by using backstepping method and the output of the auxiliary system, a MTPN-based robust adaptive attitude control approach is proposed for the NSVs with saturation input nonlinearity, stochastic input noises, and system uncertainties. Stochastic Lyapunov stability theory is utilized to analysis the stability in the sense of probability of the entire closed-loop system. Additionally, by selecting appropriate parameters, the tracking errors will converge to a small neighborhood with a tunable radius. Finally, the numerical simulation results of the NSVs attitude motion show the satisfactory flight control performance under the proposed tracking control strategy.     

An alternate algorithm for discrete-time filtering

The discrete-time Kalman filter is an optimal estimator for the states of a linear, stochastic system. It assumes that measurements are linear combinations of the states, and all disturbances are Gaussian. The influence diagram, a decision analysis tool that provides an algorithm for discrete-time filtering equivalent to the Kalman filter when the influence diagram represents Gaussian random variables, is discussed. The influence diagram algorithm is a factored form of the Kalman filter, similar to other factored forms such as the U-D filter. Compared with the Kalman filter, it offers improved numerical properties. Compared with other factored forms, it offers a reduced computational load     

The Tracking Index: A Generalized Parameter for ? ? ? and ? ? ? ? Target Trackers

A generalized, optimal filtering solution is presented for the target tracking problem. Applying optimal filtering theory to the target tracking problem, the tracking index, a generalized parameter proportional to the ratio of the position uncertainty due to the target maneuverability to that due to the sensor measurement, is found to have a fundamental role not only in the optimal steady-state solution of the stochastic regulation tracking problem, but also in the track initiation process. Depending on the order of the tracking model, the tracking index solution yields a closed form, consistent set of generalized tracking gains, relationships, and performances. Using the tracking index parameter, an initializing and tracking procedure in recursive form, realizes the accuracy of the Kalman filter with an algorithm as simple as the well-known ? ? ? filter or ? ? ? ? ? filter depending on the tracking order.     

基于自适应容积卡尔曼滤波方法的涡扇发动机气路部件故障诊断

针对涡扇发动机气路部件故障诊断中参数存在不同的噪声统计特性,提出了一种自适应平方根容积卡尔曼滤波(ASRCKF)器的自适应滤波方法.该方法直接利用基于3阶容积积分方法近似发动机的非线性统计特性,用于替代非线性无迹卡尔曼滤波方法的系统模型,避免了滤波过程参数选取的问题;采用移动窗口法对噪声协方差矩阵进行自适应估计,提高了算法对不同统计特性噪声的自适应能力和滤波精度.通过对发动机气路部件健康参数蜕化过程仿真结果表明:ASRCKF方法相比平方根容积卡尔曼滤波(SRCKF)方法,精度提高40%~50%,对不同噪声信号具有更好的适应能力.      

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     

非线性椭球集员滤波及其在故障诊断中的应用

 针对带有未知但有界噪声的非线性系统,提出一种椭球集员滤波算法,并将其应用于保证故障检测与隔离。对非线性状态方程和量测方程进行泰勒展开之后,通过区间分析的方法给出线性化余项存在区域的盒子外界描述。假设过程和量测噪声由盒子限界,在算法的时间更新和量测更新过程中,分别计算包含椭球与线段的向量和及椭球与带的交的次最小容积椭球。在椭球集员滤波算法的基础之上,给出传感器故障检测与隔离的方法。由于集员滤波是保证状态估计,因而基于集员滤波算法的故障检测与隔离方法也具有保证性,即如果发出故障警报,则一定有故障发生。一个二维非线性系统的例子说明了该方法的有效性。     

R-T-S平滑算法与抗差Kalman在数据后处理中的应用

为了提高组合导航系统后处理精度和数据稳定性,将R-T-S最优固定区间平滑算法引入数据后处理中,在前向Kalman滤波的基础上,进行了后向R-T-S最优固定区间平滑处理,并针对GPS观测值中存在异常的问题,将抗差Kalman滤波算法引入数据后处理中,并对该算法进行实物仿真。结果表明,与传统Kalman滤波相比,R-T-S平滑算法不仅可以提高位置、姿态精度,而且在卫星信号失锁的情况下精度也得到显著改善,并且在不丢星的时刻,抗差Kalman滤波可以有效处理GPS信号中的异常观测值,遏制滤波发散,是一种有效的数据处理方法。     

一种非线性滤波器的误差分析及应用

针对一类具有未建模误差和扰动的非线性系统的状态估计问题,提出一种在线估计并补偿模型误差的非线性滤波算法,该算法利用非线性预测滤波(NPF)基于预测输出残差的方差最小的基本原则估计模型误差,冉利用扩展卡尔曼滤波(EKF)的思想对补偿后的模型进行状态估计;详细推导了状态估计误差及其方差阵的传播模型.以卫星姿态确定系统为例,...     

Spacecraft attitude/rate estimation using vector-aided GPSobservations

A sequential filtering algorithm is presented for spacecraft attitude and attitude-rate estimation from Global Positioning System (GPS) differential carrier phase measurements. A third-order, minimal-parameter method for solving the attitude matrix kinematic equation is used to parameterize the state of the filter, which renders the resulting estimator computationally efficient. Borrowing from tracking theory concepts, the angular acceleration is modeled as an exponentially autocorrelated stochastic process, thus avoiding the use of the uncertain spacecraft dynamic model. The new formulation facilitates the use of aiding vector observations in a unified filtering algorithm, which can enhance the robustness and accuracy of the method. Numerical examples are used to demonstrate the performance of the method     

考虑非高斯相关噪声的视线角速率提取算法

针对捷联导引头敏感信息存在非高斯噪声且状态噪声与观测噪声相关的问题,提出了修正球面坐标系下带有相关噪声解耦的扩展椭球集员滤波（ESMF）算法。首先,通过对弹目相对距离及其变化率的规范化处理,得到修正球面坐标系下的视线角速率提取模型;然后,利用相关噪声解耦方法去除观测方程中耦合的状态噪声项,基于泰勒级数展开推导了相关噪声解耦后的模型线性化表达式,得到包含线性化误差的虚拟噪声椭球集合,并根据最小迹和最小化尺度因子上界的优化方法得到状态更新与观测更新椭球,形成非高斯相关噪声解耦的扩展椭球集员滤波算法。仿真结果表明,所提算法能够在考虑非高斯相关噪声的情况下,实现捷联导引头视线角速率的高精度提取。     

Use of the radial velocity measurement in target tracking

A new sequential filtering algorithm that incorporates the radial velocity measurement into a Kalman filter, in the presence of correlated range and radial velocity measurement errors, is presented. An analysis is given concerning its asymptotic behavior on the basis of analysis of its stochastic controllability and observability. The simulation results verify the analysis and show that the new algorithm is superior to the conventional extended Kalman filter (EKF) and close to an ideal filter.     

连续时间系统的定常状态估计器

 对于线性定常的连续时间系统,当系统和测量噪声为平稳白噪声过程时,研究了定常的状态估计器的设计方法。为了改进传统的Kalman-Bucy滤波器的瞬态性能,提出了两种新的性能函数的定义,从而给出了两种便于工程应用的修正的Kalman-Bucy滤波器。     

连续最小阶奇异滤波器

 本文讨论了当动态噪声统计特性未知时,奇异线性定常连续随机系统最小阶滤波器的设计问题。在系统部分观测量能精确测量的情况下,利用广义逆阵方法选择L矩阵,以消除动态噪声对降阶系统的影响,从而推导出缺动态噪声统计特性时的降阶奇异最优滤波器,其阶数为n-m+r。当量测方程奇异假设条件成立及引理有解时,本文证明了最小阶奇异滤波器必定存在。文中举例说明了这一降阶滤波方法的可行性。     

基于UKF的GPS/SINS组合导航直接式滤波算法

基于无迹卡尔曼滤波(UKF)方法,使用姿态、速度、位置等9个导航参数组成状态向量,以GPS系统输出的速度、位置组成6维观测向量,构建直接式结构的UKF滤波器。该滤波器能够直接反映系统导航参数的动态过程,准确显示运动状态演变。针对GPS/SINS组合导航系统的特点,构建了GPS/SINS组合导航直接式卡尔曼滤波仿真验证系统,仿真结果验证了基于UKF的GPS/SINS组合导航直接式滤波算法的有效性,该直接式非线性滤波算法可使惯性组合导航系统的导航精度得到提高。     

LMI approach to the mixed H2/H∞filtering design for discrete-time uncertain systems

The problem of full-order robust filtering design for discrete-time uncertain linear systems is addressed. The uncertain parameters are assumed to belong to convex bounded domains (polytope type uncertainty). The main purpose is to design a stable linear filter such that the filtering error output signal remains bounded. For that, the parameterization of all linear filters assuring quadratic stability with an H_∞ attenuation constraint to the filtering error system is provided in terms of linear matrix inequalities (LMIs). Then, through the definition of an auxiliary cost, an upper bound to the filtering error variance is minimized, providing a mixed H₂/H _∞ guaranteed cost filtering design. Standard optimization procedures with global convergence assured can be used to solve the problem, as illustrated by an example     

传统组合导航中的实用Kalman滤波技术评述

在随机线性系统建模准确的情况下,Kalman滤波是线性最小方差无偏估计。针对传统惯导/卫导组合导航的实际应用,难以精确建模,给出了常用的建模方法、状态量选取原则、离散化方法及滤波快速计算方法。讨论了平方根滤波、自适应滤波、联邦滤波和非线性滤波等技术的适用场合,并给出了使用建议。针对前人研究可观测度中未考虑随机系统噪声的缺陷,提出了更加合理的以初始状态均方误差阵为参考的可观测度定义和分析方法。提出了均方误差阵边界限制方法,可有效抑制滤波器的过度收敛和滤波发散。该讨论可为工程技术人员提供一些有实用价值的参考。     

Exact Bayesian and particle filtering of stochastic hybrid systems

The standard way of applying particle filtering to stochastic hybrid systems is to make use of hybrid particles, where each particle consists of two components, one assuming Euclidean values, and the other assuming discrete mode values. This paper develops a novel particle filter (PF) for a discrete-time stochastic hybrid system. The novelty lies in the use of the exact Bayesian equations for the conditional mode probabilities given the observations. Therefore particles are needed for the Euclidean valued state component only. The novel particle filter is referred to as the interacting multiple model (IMM) particle filter (IMMPF) because it incorporates a filter step which is of the same form as the interaction step of the IMM algorithm. Through Monte Carlo simulations, it is shown that the IMMPF has significant advantage over the standard PF, in particular for situations where conditional switching rate or conditional mode probabilities have small values