基于自然梯度提升的空间物体轨道状态预测误差不确定性估计方法

针对空间监视环境中基于动力学模型的轨道状态预测方法精度不够,基于机器学习的误差补偿模型可靠性不足,以及SSA应用中对不确定性建模的需求,将轨道状态预测误差估计问题重新表述为概率预测问题,提出一种对物理模型的轨道状态预测误差进行建模的方法.该方法将轨道状态变量误差的概率分布参数作为梯度提升算法的学习目标,以量化轨道状态误差估计中的不确定性.由于参数所对应的概率分布函数位于黎曼空间,利用基于Fisher信息矩阵的自然梯度代替标准梯度,推导自然梯度的计算公式,并给出状态预测误差的条件概率分布.实验结果表明,与仅采用物理动力学方法的状态预测相比,采用所提出机器学习误差估计方法后,轨道状态各分量的均方根误差至少降低约60%.同时,与其他常用不确定性估计方法相比,所提出方法可以得到更好的负对数似然值,因此能够有效估计状态预测误差的不确定性,提高将机器学习方法用于空间态势感知任务时的可靠性.     

Modified UBB-based input estimation method for nonlinear manoeuvring target tracking problem

The input detection and estimation methods in the manoeuvring target tracking (MTT) application need algorithms for manoeuvring detection and covariance resetting. This algorithm causes an improper delay in target states tracking. In this paper, for solving this problem, unknown but bounded approach for uncertainties modelling is used and a different state space model is developed. In this model, target acceleration is treated as an augmented state in the corresponding state equation. By using interval mathematics, the linearisation error is bounded by an ellipsoidal set and considered in the model development. In augmented state equations, the MTT problem converted to non-manoeuvring target tracking problem. Therefore, the set membership filter is rearranged and used for simultaneous target state and manoeuvre estimation. Furthermore, estimated convex set boundedness is analysed and an upper bound for the estimation error is calculated. The theoretical development of the proposed method is verified with numerical simulations, which contain examples of tracking various manoeuvring targets. The simulation result of the proposed method is compared with traditional input estimation methods. The comparison shows the acceptable performance of the proposed method in the simultaneous estimation of the target acceleration and state vector for the manoeuvring and non-manoeuvring scenarios.     

Team-optimal distributed MMSE estimation in general and tree networks

We construct team-optimal estimation algorithms over distributed networks for state estimation in the finite-horizon mean-square error (MSE) sense. Here, we have a distributed collection of agents with processing and cooperation capabilities. These agents observe noisy samples of a desired state through a linear model and seek to learn this state by interacting with each other. Although this problem has attracted significant attention and been studied extensively in fields including machine learning and signal processing, all the well-known strategies do not achieve team-optimal learning performance in the finite-horizon MSE sense. To this end, we formulate the finite-horizon distributed minimum MSE (MMSE) when there is no restriction on the size of the disclosed information, i.e., oracle performance, over an arbitrary network topology. Subsequently, we show that exchange of local estimates is sufficient to achieve the oracle performance only over certain network topologies. By inspecting these network structures, we propose recursive algorithms achieving the oracle performance through the disclosure of local estimates. For practical implementations we also provide approaches to reduce the complexity of the algorithms through the time-windowing of the observations. Finally, in the numerical examples, we demonstrate the superior performance of the introduced algorithms in the finite-horizon MSE sense due to optimal estimation.     

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.     

Large and small scale sensitivity analysis of optimum estimation algorithms

This paper presents the derivation and evaluation of algorithms for error analysis, large and small scale sensitivity of optimum filtering and fixed interval smoothing solutions to linear estimation problems. Model errors as well as ignorance of plant and measurement noise covariance matrices are considered. Results are presented for a simple scalar problem and for the problem of state estimation in an inertial navigation system operating in the free inertial mode.     

不平衡多分类问题的连续AdaBoost算法研究

现有AdaBoost系列算法一般没有考虑类的先验分布.针对该问题,基于最小化训练错误率,通过把符号函数表示的训练错误率的极值问题转变成一种指数函数的极值问题,提出了不平衡分类问题连续AdaBoost算法,给出了该算法的近似误差估计.基于同样的方法,对二分类问题连续AdaBoost算法的合理性给出了一种全新的解释和证明,并推广到多分类问题,得到了多分类问题连续AdaBoost算法,其具有与二分类连续AdaBoost算法完全类似的算法流程.经分析该算法与Bayes统计推断方法等价,并且其训练错误率随着训练的分类器个数增加而减小.理论分析和基于UCI数据集的实验结果表明了不平衡多分类算法的有效性.在连续AdaBoost算法中,不平衡分类问题常被转换成平衡分类问题来处理,但当先验分布极度不平衡时,使用提出的不平衡分类问题连续AdaBoost算法比一般连续AdaBoost算法有更好效果.     

二阶中心差分粒子滤波FastSLAM算法

为改善SLAM算法中非线性系统状态估计精度不高,计算繁杂的问题,本文创新性地提出了基于二阶中心差分滤波并融合最新观测数据来产生建议分布函数的新算法。新算法基于二阶sterling插值公式处理SLAM中的非线性系统问题,无须计算雅可比矩阵,容易实现。此外,该算法使用Cholesky分解技术,在SLAM概率估计中直接依据协方差平方根因子进行传播,保证协方差矩阵正定性的同时减小了局部线性化的截断误差。仿真试验表明,在粒子数相同的情况下,二阶中心差分FastSLAM(SOFastSLAM)在不同噪声条件下的估计精度均优于FastSLAM2.0、UFastSLAM算法,且用时最少,证实了SOFastSLAM算法的优越性。     

Fuzzy Set-Membership Filtering for Discrete-Time Nonlinear Systems

In this article, the problem of state estimation is addressed for discrete-time nonlinear systems subject to additive unknown-but-bounded noises by using fuzzy set-membership filtering. First, an improved T-S fuzzy model is introduced to achieve highly accurate approximation via an affine model under each fuzzy rule. Then, compared to traditional prediction-based ones, two types of fuzzy set-membership filters are proposed to effectively improve filtering performance, where the structure of both filters consists of two parts: prediction and filtering. Under the locally Lipschitz continuous condition of membership functions, unknown membership values in the estimation error system can be treated as multiplicative noises with respect to the estimation error. Real-time recursive algorithms are given to find the minimal ellipsoid containing the true state. Finally, the proposed optimization approaches are validated via numerical simulations of a one-dimensional and a three-dimensional discrete-time nonlinear systems.      

Optimal event‐triggered transmission scheduling for privacy‐preserving wireless state estimation

We consider a remote state estimation problem in the presence of an eavesdropper over packet dropping links. A smart sensor transmits its local estimates to a legitimate remote estimator, in the course of which an eavesdropper can randomly overhear the transmission. This problem has been well studied for unstable dynamical systems, but seldom for stable systems. In this article, we target at stable and marginally stable systems and aim to design an event‐triggered scheduling strategy by minimizing the expected error covariance at the remote estimator and keeping that at the eavesdropper above a user‐specified lower bound. To this end, we model the evolution of the error covariance as an infinite recurrent Markov chain and develop a recurrence relation to describe the stationary distribution of the state at the eavesdropper. Monotonicity and convergence properties of the expected error covariance are further investigated and employed to solve the optimization problem. Numerical examples are provided to validate the theoretical results.     

双线性状态空间系统的状态观测器设计

针对受过程噪声和量测噪声干扰的双线性状态空间系统,研究其状态估计算法.借助双线性系统的特殊结构,将其等价表示为线性时变模型,推导基于Kalman滤波的状态估计算法.针对线性时变模型中存在的未知变量,基于辅助模型辨识思想,通过构造一个辅助模型,将未知变量用该模型的输出代替,提出基于辅助模型的双线性系统状态估计算法.构造双线性状态观测器,引入delta算子极小化状态估计误差协方差矩阵,从而得到最优状态估计增益,并提出基于delta算子的双线性系统状态估计算法.所提出的算法能够避免线性化过程带来的估计精度差的问题,提高双线性系统的状态估计精度.通过仿真实验验证了所提出算法的有效性,并对比分析了不同噪声情况下所提出算法的估计效果.     

粒子滤波在卫星轨道确定中的应用

卫星轨道确定问题中可能存在初始估计信息误差较大、状态及测量误差分布不是高斯分布等问题,为了寻求一个能采用解决这两种问题的方法,本文采用了“采样-重要性-重采样”SIR(Sampling Importance Resampling)粒子滤波算法作为滤波方法,以地磁场矢量为测量量,对低地球轨道卫星的轨道数据进行自主的估计.为了避免该滤波算法中的采样贫乏的问题,采用了一个崎岖化方法来克服采样贫乏问题.最后给出了此方法应用到了卫星轨道确定问题中的数字仿真实例.     

Robust interacting multiple model algorithms based on multi-sensor fusion criteria

This paper is concerned with the state estimation problem for a class of Markov jump linear discrete-time stochastic systems. Three novel interacting multiple model (IMM) algorithms are proposed based on the H∞ technique, the correlation among estimation errors of mode-conditioned filters and the multi-sensor optimal information fusion criteria. Mode probabilities in the novel algorithms are derived based on the error cross-covariances instead of likelihood functions. The H∞ technique taking the place of Kalman filtering is applied to enhance the robustness of the new approaches. Theoretical analysis and Monte Carlo simulation results indicate that the proposed algorithms are effective and have an obvious advantage in velocity estimation when tracking a maneuvering target.     

Multipartitioning linear estimation algorithms: Continuous systems

The partitioned estimation algorithms of Lainiotis for the linear continuous-time state estimation problem have been generalized in this paper in two important ways. First, the initial condition of the estimation problem can, using the results of this paper, be partitioned into the sum of an arbitrary number of jointly Gaussian random variables; and second, these jointly Gaussian random variables may be statistically dependent. The form of the resulting algorithm consists of an imbedded Kalman filter with partial initial conditions and one correction term for each other partition or subdivision of the initial state vector. Emphasis in this paper is on ways in which this approach, called multipartitioning, can be used to provide added insight into the estimation problem. One significant application is in the parameter identification problem where identification algorithms can be formulated in which the inversion of the information matrix of the parameters is replaced by simple division by scalars. A second use of multipartitioning is to show the specific effects on the filtered state estimate of off-diagonal terms in the initial-state covariance matrix.     

Stochastic control of processes having moving boundaries—An experimental study

A general state estimator requiring only discrete time measurements has been developed for nonlinear distributed parameter systems having moving boundaries. The state estimator has been combined with an optimal linear-quadratic feedback controller to provide a stochastic feedback control scheme for this class of problem. Both the state estimation and control algorithms were implemented in real time for a laboratory casting process and were found to perform well. The state estimation scheme would seem to hold the most interest for industrial applications.     

Performance analysis of digital FM demodulators for fading channels in the threshold region

The quasi-optimum digital FM demodulators for fading channels reported earlier reflected the system performance accurately under high signal to noise ratio conditions. In this paper, the prediction of the system performance for low SNR values is considered. A new set of error variance algorithms is developed from the filter algorithm assuming a Gaussian distribution for the state estimation errors and taking the effect of high frequency terms into consideration. Simulation analysis for an FM system with Rician fading channel shows that these algorithms predict the system performance accurately in the threshold region.     

Cramér–Rao lower bound in nonlinear filtering problems under noises and measurement errors dependent on estimated parameters

This paper derives recurrent expressions for the maximum attainable estimation accuracy calculated using the Cramér–Rao inequality (Cramér–Rao lower bound) in the discretetime nonlinear filtering problem under conditions when generating noises in the state vector and measurement error equations depend on estimated parameters and the state vector incorporates a constant subvector. We establish a connection to similar expressions in the case of no such dependence. An example illustrates application of the obtained algorithms to lowerbound accuracy calculation in a parameter estimation problem often arising in navigation data processing within a model described by the sum of a Wiener sequence and discrete-time white noise of an unknown variance.     

基于误差分布估计的机器人手眼标定方法研究

精确的机器人手眼标定对于机器人的视觉环境感知具有重要的意义。现有算法通常采用最小二乘估计或全局非线性优化求解方法对机器人手眼系统的变换参数进行估计。当系统存在测量粗差时直接采用最小二乘估计会导致标定结果精度的下降;基于全局非线性优化策略的标定算法则由于数据粗差的影响,求解过程易过早收敛也会造成标定精度低。为了解决误差粗差敏感的问题,提出了一种基于误差分布估计的加权最小二乘鲁棒估计方法,以提高机器人手眼标定的精度。首先,通过最小二乘估计计算手眼变换矩阵;之后计算每对坐标对应的误差值;根据误差值的分布概率初始化对应坐标数据的权值;最后采用加权的最小二乘估计重新计算机器人手眼标定矩阵。最后引入迭代估计策略进一步提高手眼标定的精度。设计的机器人手眼标定实验及结果证明,所提算法能够在数据粗差影响下保持较高的标定精度,更适用于机器人的手眼标定问题。     

室内WiFi定位技术的多参数优化研究

基于WiFi的室内定位技术受天线数量和频道带宽影响,存在定位精度低和跟踪易失败的问题。为此,提出一种多参数室内无源定位技术。通过几何关系解释包括到达角、飞行时间和多普勒频移在内的参数,利用参数模型量化用户运动和信道状态信息间的关系,将多参数估计问题表示为最大似然估计问题,使用广义期望最大化算法将错误的原始参数细化到一定范围内,最终输出目标位置。实验结果表明,该技术平均定位误差为0.7 m,相较于时间与空间信号模型、指纹定位、空间域建模等现有的无源定位技术具有更好的定位精度和稳定性。     

Constrained particle filter approach to approximate the arrival cost in Moving Horizon Estimation

Moving Horizon Estimation (MHE) is an efficient state estimation method used for nonlinear systems. Since MHE is optimization-based it provides a good framework to handle bounds and constraints when they are required to obtain good state and parameter estimates. Recent research in this area has been directed to develop computationally efficient algorithms for on-line application. However, an open issue in MHE is related to the approximation of the so-called arrival cost and of the parameters associated with it. The arrival cost is very important since it provides a means to incorporate information from the previous measurements to the current state estimate. It is difficult to calculate the true value of the arrival cost; therefore approximation techniques are commonly applied. The conventional method is to use the Extended Kalman Filter (EKF) to approximate the covariance matrix at the beginning of the prediction horizon. This approximation method assumes that the state estimation error is Gaussian. However, when state estimates are bounded or the system is nonlinear, the distribution of the estimation error becomes non-Gaussian. This introduces errors in the arrival cost term which can be mitigated by using longer horizon lengths. This measure, however, significantly increases the size of the nonlinear optimization problem that needs to be solved on-line at each sampling time. Recently, particle filters and related methods have become popular filtering methods that are based on Monte-Carlo simulations. In this way they implement an optimal recursive Bayesian Filter that takes advantage of particle statistics to determine the probability density properties of the states. In the present work, we exploit the features of these sampling-based methods to approximate the arrival cost parameters in the MHE formulation. Also, we show a way to construct an estimate of the log-likelihood of the conditional density of the states using a Particle Filter (PF), which can be used as an approximation of the arrival cost. In both cases, because particles are being propagated through the nonlinear system, the assumption of Gaussianity of the state estimation error can be dropped. Here we developed and tested EKF and eight different types of sample based filters for updating the arrival cost parameters in the weighted 2-norm approach (see Table 1 for the full list). We compare the use of constrained and unconstrained filters, and note that when bounds are required the constrained particle filters give a better approximation of the arrival cost parameters that improve the performance of MHE. Moreover, we also used PF concepts to directly approximate the negative of the log-likelihood of the conditional density using unconstrained and constrained particle filters to update the importance distribution. Also, we show that a benefit of having a better approximation of the arrival cost is that the horizon length required for the MHE can be significantly smaller than when using the conventional MHE approach. This is illustrated by simulation studies done on benchmark problems proposed in the state estimation literature.     

Motion estimation using learning automata

Block-matching algorithms (BMAs) are widely employed for motion estimation. BMAs divide input frames into several blocks and minimize an error function for each block to calculate motion vectors. Afterward, each motion vector is applicable for all of the pixels within the block. Since computing the error functions is resource intensive, many fast-search motion estimation algorithms have been suggested to reduce the computational cost. These fast algorithms provide a significant reduction in computation but often converge to a local minimum. A learning automaton is an adaptive decision-making unit that learns the optimal action through repeated interactions with its environment. Learning automata (LA) have been applied successfully to a wide range of applications including pattern recognition, dynamic channel assignment, and social network analysis. In this paper, we apply LA to motion estimation problem, which is one of the basic problems in computer vision. We compare the accuracy and performance of the suggested algorithms with other well-known BMAs. Interestingly, the obtained results indicate high efficiency and accuracy of the proposed methods. The results suggest that simplicity, efficiency, parallel nature, and accuracy of LA-based methods make them a good candidate to solve computer vision problems.