Marginalized particle filter for spacecraft attitude estimation from vector measurements

An algorithm based on the marginalized particle filters （MPF） is given in details in this paper to solve the spacecraft attitude estimation problem： attitude and gyro bias estimation using the biased gyro and vector observations. In this algorithm, by marginalizing out the state appearing linearly in the spacecraft model, the Kalman filter is associated with each particle in order to reduce the size of the state space and computational burden. The distribution of attitude vector is approximated by a set of particles and estimated using particle filter, while the estimation of gyro bias is obtained for each one of the attitude particles by applying the Kalman filter. The efficiency of this modified MPF estimator is verified through numerical simulation of a fully actuated rigid body. For comparison, unscented Kalman filter （UKF） is also used to gauge the performance of MPE The results presented in this paper clearly derfionstrate that the MPF is superior to UKF in coping with the nonlinear model.     

基于Marginalized粒子滤波的卫星姿态估计算法

针对具有矢量观测的卫星姿态估计问题。提出一种基于Marginalized粒予滤波（MPF）的算法．采用Rao-Blackwellization技术,将卫星模型状态向量中的线性状态部分（陀螺漂移）和非线性状态部分（卫星姿态）分开处理,从而使得估计的方差降低．以较少的运算量获得较好的估计效果．通过引入解决含等式约束条件的估计问题方法,保证了姿态四元数的归一化．将所提出的方法应用于某型号卫星．仿真验证了用该算法处理卫星姿态估计问题的优越性．     

自适应混合滤波算法在微型飞行器姿态估计中的应用

针对低成本惯性测量单元(IMU)存在漂移和噪声干扰等问题,提出了一种具有自适应参数调节的混合滤波算法。采用四元数法进行系统模型的描述,用梯度下降法对加速度计测得的数据进行处理,再通过互补滤波器将其与陀螺仪测量值进行融合,形成混合滤波算法。同时,考虑到飞行姿态的复杂性,进行参数λ的自适应调节,因而改进后的混合滤波算法,能保证各种飞行姿态变化情况下实时姿态的最优估算。实际系统在线实时性能测试表明,提出的算法简单,估计精度高,易于在嵌入式系统中实现,具有较高推广应用价值。     

基于CDKF的飞机姿态角估计

针对扩展卡尔曼滤波(Extend Kalman Filter ,EKF)在飞机姿态估计中存在着计算复杂、线性化误差大等缺点,将一种基于Stirling内插公式的非线性滤波算法—中心差分卡尔曼滤波算法(Central Difference Kalman Filter, CDKF)应用于由低精度高噪声传感器组成的低成本飞机姿态估计系统中。首先建立基于四元数的飞机姿态数学模型,然后用CDKF方法进行姿态估计,并通过实测数据进行验证。实验结果表明, CDKF方法不仅有效地提高了飞机姿态估计的精度和稳定性;而且不需要模型的具体解析形式,避免了复杂的Jacobian矩阵的计算,算法更简单,也更容易实现,优于常用的EKF方法。     

Computing point estimates from a non-Gaussian posterior distribution using a probabilistic k-means clustering approach

The Kalman filter algorithm gives an analytical expression for the point estimates of the state estimates, which is the mean of their posterior distribution. Conventional Bayesian state estimators have been developed under the assumption that the mean of the posterior of the states is the ‘best estimate’. While this may hold true in cases where the posterior can be adequately approximated as a Gaussian distribution, in general it may not hold true when the posterior is non-Gaussian. The posterior distribution, however, contains far more information about the states, regardless of its Gaussian or non-Gaussian nature. In this study, the information contained in the posterior distribution is explored and extracted to come up with meaningful estimates of the states. The need for combining Bayesian state estimation with extracting information from the distribution is demonstrated in this work.     

Spacecraft relative rotation tracking without angular velocity measurements

We present a solution to the problem of tracking relative rotation in a leader-follower spacecraft formation using feedback from relative attitude only. The controller incorporates an approximate-differentiation filter to account for the unmeasured angular velocity. We show uniform practical asymptotic stability (UPAS) of the closed-loop system. For simplicity, we assume that the leader is controlled and that we know orbital perturbations; however, this assumption can be easily relaxed to boundedness without degrading the stability property. We also assume that angular velocities of spacecraft relative to an inertial frame are bounded. Simulation results of a leader-follower spacecraft formation using the proposed controller structure are also presented.     

捷联式航姿系统中四元素算法Kalman滤波器的实现研究

本文基于四元素算法推导了姿态算法和捷联惯导系统误差模型,并设计了Kalman滤波器。在此基础上分析了误差模型的随机噪声补偿和提出了航向修正。仿真结果表明,本文讨论的这种Kalman滤波器能保证航向精度,具有实际应用意义。     

基于卡尔曼滤波的四元数姿态解算算法研究

针对MEMS惯性测量单元器件特性导致的测量精度低,数据发散和航向角积分漂移等问题,提出一种基于卡尔曼滤波的四元数姿态解算算法。设计了4维卡尔曼滤波器,通过加速度计和磁力计的数据作观测量,对姿态解算过程中的四元数进行线性最优估计,在计算量没有大幅提高的前提下修正了四元数的值,进而完成了对姿态角和姿态矩阵的补偿。通过在无磁转台上进行静态测试以及在测试标定系统上进行动态测试,分析各轴向的补偿效果表明,该方法可以有效增强MIMU的动态跟随性能、明显提升姿态解算精度。     

Spacecraft attitude control using magnetic actuators

The problem of inertial pointing for a spacecraft with magnetic actuators is addressed and an almost global solution to the problem is obtained by means of static attitude and rate feedback. A local solution based on dynamic attitude feedback is also presented. Simulation results demonstrate the practical applicability of the proposed approach.     

一种利用粒子滤波的实时交通状态估计方法

将粒子滤波理论和宏观随机交通流模型结合,对高速公路交通状态进行实时估计。在该方法中,高速公路被看作是由等距离的路段首尾相接而形成的模型,交通传感器通常设置在路段的交界处,而且数量远少于所需估计的交通状态。采用压缩状态空间的形式,将模型参数也作为交通状态而非常量进行估计。仿真结果表明粒子滤波方法能够有效地估计和跟踪交通状态的变化,并且与扩展卡尔曼滤波方法相比具有更高的精确度。     

基于修正的卡尔曼滤波的姿态估计算法研究

研究惯导系统的稳定性问题,其中微惯性测量单元(MIMU)可以为捷联惯导系统提供实时的姿态和航向信息。研究姿态估计提高导航精度,由于陀螺漂移引起姿态误差,单独使用MIMU使姿态精度差。为了克服陀螺误差随时间积累不断增大,无法长时间提供稳定的姿态的缺点,提出采用磁强计修正的卡尔曼滤波四元数姿态估计算法。算法以姿态四元数为状态向量,通过四元数更新方程建立离散滤波状态方程,将加速度计和磁强计输出的六维数据转化为四元数的量测值建立量测方程,有效减少了计算量,补偿陀螺的漂移误差带来的影响。仿真结果表明改进算法提高了捷联惯导系统的精度和稳定性。     

基于EKF的航天器姿态确算法定及精度分析

采用陀螺和星敏感器组合的方式来进行航天器姿态确定。首先建立了陀螺和星敏感器的测量模型,选择以四元数作为描述航天器姿态的参数,详细推导了在小偏差下以误差姿态角和陀螺常值漂移误差为状态量的滤波状态方程,并且以星敏感器的测量残差作为量测量,采用扩展卡尔曼滤波（Extended Kalman Filter, EKF）算法进行姿态确定;然后进行了仿真分析,仿真结果表明：该算法可以达到较高的姿态确定精度;最后对影响姿态确定精度的硬件因素和软件因素进行了定量的数据分析,得出了有一定意义的结论,从而为工程实践提供理论支持。     

基于自适应粒子群优化的代价评估Marginalized粒子滤波

针对量测受扰动情况下粒子重要性权重的精确度量和粒子的有效采样问题,提出了一种基于自适应粒子群优化的代价评估Marginalized粒子滤波。首先,在Marginalized粒子滤波框架下,通过引入代价函数和风险函数,实现了粒子重要性权重评价过程中对最新量测信息的合理利用,以降低传统的依据重要性权重度量方式中对于噪声先验信息的依赖。其次,通过对粒子分布特征信息的提取和利用,构建了粒子极限速度设定的自适应选取策略,给出了一种自适应粒子群优化方法。在此基础上,结合粒子群优化中群体优化机理来提升采样粒子对被估计状态的逼近程度,进而改善重采样后粒子的多样性。理论分析和仿真实验验证了算法的有效性。     

On the choice of importance distributions for unconstrained and constrained state estimation using particle filter

Recursive state estimation of constrained nonlinear dynamical system has attracted the attention of many researchers in recent years. For nonlinear/non-Gaussian state estimation problems, particle filters have been widely used (Arulampalam et al. [1]). As pointed out by Daum [2], particle filters require a proposal distribution and the choice of proposal distribution is the key design issue. In this paper, a novel approach for generating the proposal distribution based on a constrained Extended Kalman filter (C-EKF), Constrained Unscented Kalman filter (C-UKF) and constrained Ensemble Kalman filter (C-EnkF) has been proposed. The efficacy of the proposed state estimation algorithms using a particle filter is illustrated via a successful implementation on a simulated gas-phase reactor, involving constraints on estimated state variables and another example problem, which involves constraints on the process noise (Rao et al. [10]). We also propose a state estimation scheme for estimating state variables in an autonomous hybrid system using particle filter with Unscented Kalman filter as a proposal and unconstrained Ensemble Kalman filter (EnKF) as a proposal. The efficacy of the proposed state estimation scheme for an autonomous hybrid system is demonstrated by conducting simulation studies on a three-tank hybrid system. The simulation studies underline the crucial role played by the choice of proposal distribution in formulation of particle filters.     

Synchronized multiple spacecraft rotations

The objective of this paper is to present formation control laws for maintaining attitude alignment among a group of spacecraft in either deep space or earth orbit. The paper presents two control strategies based on emergent behavior approaches. Each control strategy considers the desired formation behaviors of convergence to the final formation goal, formation keeping, and the desire to rotate the spacecraft about fixed axes. The first approach uses velocity feedback and the second approach used passivity-based damping. In addition, we prove analytically that our approach guarantees formation keeping throughout the maneuver. Simulation results demonstrate the effectiveness of our approach.     

粒子群优化粒子滤波方法

针对粒子滤波方法存在粒子贫乏以及初始状态未知时需要大量粒子才能进行鲁棒状态预估等问题,将粒子群优化思想引入粒子滤波中．该方法将最新观测值融合到采样过程中,并对采样过程利用粒子群优化算法进行优化．通过优化,可使粒子集朝后验概率密度分布取值较大的区域运动,从而克服了粒子贫乏问题,并极大地降低了精确预估所需的粒子数．实验结果表明,该算法具有较高的预估精度和较好的鲁棒性．     

Bayesian estimation via sequential Monte Carlo sampling—Constrained dynamic systems

Nonlinear and non-Gaussian processes with constraints are commonly encountered in dynamic estimation problems. Methods for solving such problems either ignore the constraints or rely on crude approximations of the model or probability distributions. Such approximations may reduce the accuracy of the estimates since they often fail to capture the variety of probability distributions encountered in constrained linear and nonlinear dynamic systems. This article describes a practical approach that overcomes these shortcomings via a novel extension of sequential Monte Carlo (SMC) sampling or particle filtering. Inequality constraints are imposed by accept/reject steps in the algorithm. The proposed approach provides samples representing the posterior distribution at each time point, and is shown to satisfy the same theoretical properties as unconstrained SMC. Illustrative examples show that results of the proposed approach are at least as accurate as moving horizon estimation, but computationally more efficient and in addition, the approach indicates the uncertainty associated with these estimates.     

动态背景下基于粒子滤波的运动目标跟踪方法

在智能视频监控系统中,实现对动态背景下的运动目标准确跟踪是一个难点问题。使用一种基于粒子滤波的方法来对动态背景下的运动目标进行跟踪。该方法基于贝叶斯估计,利用粒子集来表示概率,通过递推的贝叶斯滤波来近似逼近最优化的估计结果。实验结果证明,该方法可准确跟踪动态背景下的运动目标,是一种有效的目标跟踪方法。     

基于共轭梯度法和互补滤波相结合的姿态解算算法

为了提高姿态解算精度,提出了一种基于共轭梯度和互补滤波相结合的多传感器数据融合策略。系统采用四元数方法进行姿态解算。利用加速度计和磁强计的输出数据,通过共轭梯度方法对姿态四元数进行寻优估计,再将其和利用陀螺仪输出数据更新的四元数进行互补滤波,解算出姿态角。实验测试表明,这种融合策略使姿态检测系统静态性能和和动态性能均有所提高,尤其在姿态剧烈变化时,其性能明显优于卡尔曼滤波和梯度下降法。