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。     

基于联合特征的边缘粒子滤波目标跟踪算法研究

针对采用单一特征建立的动态空间模型与实际系统差距较大,从而使估计误差增加的问题,通过将系统的状态参数引入颜色特征模型中,与颜色特征参数一起构成系统状态空间向量,提出了一种联合颜色状态特征的优化目标跟踪算法.应用Rao-Blackwellization算法思想,由Kalman线性滤波方法解析处理线性的颜色特征转移和更新过程;而目标位置参数采用粒子滤波进行估计,提高了视频目标跟踪的精度和实时性.通过与其他相似算法的比较实验结果可以看出,算法在环境亮度发生变化、目标遮挡等情况下,仍能够保持较高的跟踪精度,既提高了跟踪系统的鲁棒性,又保证了算法的实时性,优于传统的单一特征视频跟踪算法.     

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.     

Star-sensor-based predictive Kalman filter for satellite attitude estimation

A real-time attitude estimation algorithm, namely the predictive Kalman filter, is presented . This algorithm can accurately estimate the three-axis attitude of a satellite using only star sensor measurements. The implementation of the filter includes two steps: first, predicting the torque modeling error, and then estimating the attitude. Simulation results indicate that the predictive Kalman filter provides robust performance in the presence of both significant errors in the assumed model and in the initial conditions.     

Drift-free attitude estimation for accelerated rigid bodies

In this paper we study the attitude estimation problem for an accelerated rigid body using gyros and accelerometers. The application in mind is that of a walking robot and particular attention is paid to the large and abrupt changes in accelerations that can be expected in such an environment. We propose a state estimation algorithm that fuses data from rate gyros and accelerometers to give long-term drift free attitude estimates. The algorithm does not use any local parameterization of the rigid body kinematics and can thus be used for a rigid body performing any kind of rotations. The algorithm is a combination of two non-standard, but in a sense linear, Kalman filters between which a trigger based switching takes place. The kinematics representation used makes it possible to construct a linear algorithm that can be shown to give convergent estimates for this nonlinear problem. The state estimator is evaluated in simulations demonstrating how the estimates are long-term stable even in the presence of gyro drift.     

Decentralized adaptive attitude synchronization of spacecraft formation

This paper studies adaptive attitude synchronization of spacecraft formation with possible time delay. By introducing a novel adaptive control architecture, decentralized controllers are developed, which allow for parameter uncertainties and unknown external disturbances. Based upon graph theory, Lyapunov stability theory and time-delay control theory, analytical tools are also provided. A distinctive feature of this work is to address the adaptive attitude synchronization with unknown parameters and coupling time delay in a unified theoretical framework, with general directed information flow. It is shown that arbitrary desired attitude tracking and synchronization with respect to a given reference can be attained. Simulation results are provided to demonstrate the effectiveness of the obtained results.     

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．     

改进粒子滤波与预测滤波相结合的单星敏姿态估计

针对卫星姿态估计的非线性、非高斯特性,提出一种粒子滤波和预测滤波相结合的估计方法,在无角速率测量时,首先利用预测方法在线估计系统模型误差和姿态角速度,再通过改进的规则化粒子滤波器估计姿态四元数.粒子初始化和重要性函数等的设计加快了算法的收敛速度,预测方法的引入有效降低了粒子维数.在某通用小卫星平台上进行仿真,并与扩展卡尔曼滤波(EKF)比较,所得结果表明,算法在不同初始姿态估计时具有较好的稳定性和收敛精度.算法还为粒子滤波和无陀螺定姿的研究提供了参考.     

Applying the unscented Kalman filter for nonlinear state estimation

Based on presentation of the principles of the EKF and UKF for state estimation, we discuss the differences of the two approaches. Four rather different simulation cases are considered to compare the performance. A simple procedure to include state constraints in the UKF is proposed and tested. The overall impression is that the performance of the UKF is better than the EKF in terms of robustness and speed of convergence. The computational load in applying the UKF is comparable to the EKF.     

EKF和互补滤波器在飞行姿态确定中的应用

设计了一种旋翼飞行姿态参考系统,采用基于加速度计和陀螺仪的惯性测量组合(IMU)测量飞行姿态数据。采集实测数据并运用Allan方差分析法分析其噪声特性,建立传感器模型;针对旋翼飞行器分别应用经典扩展Kalman滤波(EKF)算法和互补滤波算法进行姿态解算。在详细阐述2种算法的原理与实现的基础上,进行飞行器平台实验验证。研究结果表明2种算法均有效,且互补滤波器相对经典Kal-man滤波器更为简单、有效。     

非线性交互粒子滤波算法

在非线性非高斯系统状态估计问题中,后验概率密度函数的解析形式难以获得,标准粒子滤波算法采用状态转移概率函数代替后验概率作为重要性采样概率密度函数,而未考虑当前观测数据的影响．针对该问题,首先提出了非线性交互多模型算法;然后应用该算法产生重要性采样概率密度函数,设计了新的非线性交互粒子滤波器．新的概率密度函数融入最新观测数据,更接近系统状态后验概率．比较实验表明了所提出算法的有效性．     

Robust decentralized attitude coordination control of spacecraft formation

The attitude coordination control problem for multiple spacecraft is investigated in this paper. A simple decentralized variable structure coordinated controller is proposed using Lyapunov’s direct method. In the presence of model uncertainties, external disturbances and time-varying delays in the intercommunication, the presented controller can render a spacecraft formation consistent to a prespecified orientation in the globally-convergent sense. By virtue of a corollary of Barbalat’s Lemma, the convergence of the proposed controller for the resulting closed-loop system is proved theoretically. Numerical simulations are also included to demonstrate the performance of the developed controller.     

Multi-faults detection and estimation for nonlinear stochastic system based on particle filter and hypothesis test

This paper is concerned with the fault detection and estimation for nonlinear stochastic system with additive multi-faults. The states of system are estimated by the improved particle filter which composed of basic particle filter and preliminary fault estimation. Since the preliminary fault estimation contains noise, the faults are detected by the method of hypothesis testing, while the amplitude of each fault is estimated by the average of the sample of preliminary fault estimation. Meanwhile, the relationship of the sample size, the significance level of two types of error, the amplitude of fault and the variance of the error of preliminary fault estimation are also given. The effectiveness of the proposed method is verified by the simulation of three-vessel water tank system.     

Simplex filter: A novel heuristic filter for nonlinear systems state estimation

This paper introduces a new filter for nonlinear systems state estimation. The new filter formulates the state estimation problem as a stochastic dynamic optimization problem and utilizes a new stochastic method based on simplex technique to find and track the best estimation. The vertices of the simplex search the state space dynamically in a similar scheme to the optimization algorithm, known as Nelder-Mead simplex. The parameters of the proposed filter are tuned, using an information visualization technique to identify the optimal region of the parameters space. The visualization is performed using the concept of parallel coordinates. The proposed filter is applied to estimate the state of some nonlinear dynamic systems with noisy measurement and its performance is compared with other filters.     

State estimation using the particle filter with mode tracking

A particle filter is a data assimilation scheme that employs a fully nonlinear, non-Gaussian analysis step. Unfortunately as the size of the state grows the number of ensemble members required for the particle filter to converge to the true solution increases exponentially. To overcome this Vaswani [Vaswani N. 2008. IEEE Trans Signal Process 56:4583–97] proposed a new method known as mode tracking to improve the efficiency of the particle filter. When mode tracking, the state is split into two subspaces. One subspace is forecast using the particle filter, the other is treated so that its values are set equal to the mode of the marginal pdf. There are many ways to split the state. One hypothesis is that the best results should be obtained from the particle filter with mode tracking when we mode track the maximum number of unimodal dimensions. The aim of this paper is to test this hypothesis using the three dimensional stochastic Lorenz equations with direct observations. It is found that mode tracking the maximum number of unimodal dimensions does not always provide the best result. The best choice of states to mode track depends on the number of particles used and the accuracy and frequency of the observations.     

A variable neighborhood search particle filter for bearings-only target tracking

In this paper a novel filtering procedure that uses a variant of the variable neighborhood search (VNS) algorithm for solving nonlinear global optimization problems is presented. The base of the new estimator is a particle filter enhanced by the VNS algorithm in resampling step. The VNS is used to mitigate degeneracy by iteratively moving weighted samples from starting positions into the parts of the state space where peaks and ridges of a posterior distribution are situated. For testing purposes, bearings-only tracking problem is used, with two static observers and two types of targets: non-maneuvering and maneuvering. Through numerous Monte Carlo simulations, we compared performance of the proposed filtering procedure with the performance of several standard estimation algorithms. The simulation results show that the algorithm mostly performed better than the other estimators used for comparison; it is robust and has fast initial convergence rate. Robustness to modeling errors of this filtering procedure is demonstrated through tracking of the maneuvering target. Moreover, in the paper it is shown that it is possible to combine the proposed algorithm with an interacted multiple model framework.     

基于粒子滤波的非线性系统静态参数估计方法*

针对基于滤波方法的最大似然参数估计步长序列过于单一,算法收敛缓慢并很容易收敛于局部最优解的问题,提出了基于似然权值的在线EM参数估计算法(LWOEM)。通过粒子滤波方法实时估计系统的状态值变化,结合最大似然方法计算静态参数的点估计,然后通过计算更新参数的似然值来动态更新步长序列.与在线EM参数估计算法(OEM)的实验结果比较,表明该算法具有更好的适应性和收敛效果。     

Adaptive attitude tracking control for rigid spacecraft with finite-time convergence

In this paper, the finite-time attitude tracking control problem for rigid spacecraft with external disturbances and inertia uncertainties is addressed. First, a novel fast nonsingular terminal sliding mode surface (FNTSMS) without any constraint is designed, which not only avoids the singularity problem, but also contains the advantages of the nonsingular terminal sliding mode (NTSM) and the conventional sliding-mode together. Second, the proposed FNTSM control laws (FNTSMCLs) by employing FNTSMS associated with adaptation provide finite-time convergence, robustness, faster, higher control precision. The proposed FNTSMCLs in light of novel adaptive control architecture are continuous. Thus, they are chattering-free. Finally, simulation results are presented to illustrate effectiveness of the control strategies. In addition, digital simulations of satellite Hubble Space Telescope (HST) are presented to verify the practical feasibility of the reorientation/ slew maneuvers mission.