基于滚动时域估计的带约束运动目标跟踪*

针对实际的运动目标跟踪问题中存在的各种物理约束,采用基于在线滚动优化原理的滚动时域估计方法,将跟踪滤波问题转换为带约束的有限时域优化问题,并通过引入到达代价函数,有效减少了优化问题求解所需的计算量。最后,对实际的目标跟踪问题进行了滚动时域估计仿真研究。Monte Carlo仿真结果表明,滚动时域估计能有效提高跟踪精度,并且能在采样周期之内完成求解,满足在线估计的需要。     

滚动时域估计在连续搅拌釜式反应器中的应用研究

针对连续搅拌釜式反应器的多变量、非线性、带约束等特点,设计一种基于滚动优化原理的滚动时域估计方法.对比扩展卡尔曼滤波和滚动时域估计两种方法,在滚动时域估计中采用扩展卡尔曼滤波近似代替到达代价函数,并通过改变滚动时域窗口的大小有效地减小估计过程中的误差.仿真结果表明:滚动时域估计优于扩展卡尔曼滤波,能够有效地处理带约束化工过程中非线性系统状态估计问题.     

一种滚动时域估计方法在目标跟踪中的应用

针对目标跟踪问题中存在的约束问题 ,拓展模型预测控制 (MPC)的在线滚动优化原理 ,介绍了一种能够将有约束的滤波问题转换为最优状态估计问题的滚动时域估计 (MHE)方法 ,并通过引入一个到达代价 (arrivecost)函数 ,有效地缩减了滤波所需的计算量 ,最后 ,将此方法应用于目标跟踪问题 ,仿真研究表明该估计器具有较好的效果     

基于UKF的滚动时域估计方法研究

在实际工业过程中,模型参数往往具有一定的时变性和非线性。为了能够有效地实施过程操作优化,常常要对过程模型参数进行在线估计。滚动时域估计方法是解决非线性系统模型参数在线估计的1种实用方法。滚动时域估计方法的关键问题之一是抵达成本(Arrival Cost)的计算,针对简化计算抵达成本带来的精度问题,提出采用无迹卡尔曼滤波(UKF)算法来近似估算目标函数中的抵达成本。最后,将基于UKF的滚动时域估计方法应用于2个例子中。结果表明,基于UKF的滚动时域估计方法具有较好的估计效果。     

滚动时域状态估计中极小化问题的求解

滚动时域状态估计(MHSE)方法的基本思想是:将控制系统的状态估计问题转化为有限时域内的优化问题,通过获得的优化解对系统状态进行估计。针对带约束的线性离散系统的状态估计问题,介绍了MHSE方法的研究及应用现状。基于惩罚函数法建立惩罚因子,将约束条件融合到适应度函数中,通过粒子群优化(PSO)算法求解MHSE方法中的极小化问题。基于Matlab编程,实现了二阶仿真算例。仿真结果表明,PSO算法能够有效地求解MHSE方法中的极小化问题,使得2种状态的估计值和真实值之间的均方差分别为0.075 0、0.204 1。PSO算法能够有效地求解二阶仿真算例,以获取滚动时域估计方法中极小化问题的最优解,为基于MHSE方法进行状态估计的研究与应用提供了参考。下一步的研究方向是提高估计精度,以及复杂约束条件下高阶系统的极小化问题的求解。     

基于通信与观测联合优化的多无人机协同目标跟踪控制

为了提高目标跟踪任务的执行效能,提出一种基于通信与观测联合优化的多无人机协同运动目标跟踪控制方法.建立以信息成功传递概率描述的通信链路模型,采用扩展信息滤波实现目标状态融合估计与预测,使用Fisher信息矩阵对无人机观测所获取的信息进行表征.通过将信息成功传输概率引入到优化指标函数中,建立多无人机协同目标跟踪运动控制的滚动时域优化模型,实现通信与观测的联合优化,而这种联合优化体现在提高无人机与地面站之间信息成功传输概率与降低目标状态估计不确定性之间的折中.与不考虑通信优化的跟踪控制对比表明,所提方法可以提高跟踪过程中各架无人机与地面站之间的信息传输概率,使目标状态的全局融合估计结果更精确、更有效.     

带非线性约束的自适应高斯和卡尔曼滤波目标跟踪算法

无线传感网络中运动目标状态通常满足某种非线性状态约束,为了提高对传感网络中运动目标的跟踪精度,降低非高斯噪声对状态估计的影响,避免高斯项数在迭代过程中的冗余累积,提出一种带非线性约束的权值自适应高斯和卡尔曼滤波算法.算法在每个时刻计算目标当前状态的高斯子项集合,并对每个高斯子项分别以无迹卡尔曼滤波进行状态估计.设计了一种高斯子项权值自适应策略动态调节子项权值,以实现无约束状态下的全局估计.将目标的非线性状态约束引入滤波器结构中时,考虑将其看作一类无约束状态估计的约束投影问题,通过状态约束信息先验来修正运动目标的状态估计.仿真结果表明,该算法与目前的非线性约束卡尔曼滤波相比具有更高的跟踪精度.     

基于滚动时域的无人机动态航迹规划

针对带有动力学约束的多旋翼无人机航迹规划问题,提出了一种基于滚动时域控制和快速粒子群优化(RHC-FPSO)方法。该方法引入了基于VORONOI图的代价图方法说明从航迹端点到达目标点的距离估计。根据滚动时域和人工势场法的思想,将路径规划问题转化为优化问题,以最小距离和其他性能指标为代价函数。设计评价函数准则,按照评价准则使用变权重粒子群优化算法求解。针对无人机靠近危险区飞行的问题,将斥力场引入到代价函数中,提升其安全性。仿真实验结果显示,使用文中方法可以有效地在满足约束条件下穿过障碍物区域,以及在复杂环境下可以动态计算。     

单目视觉系统自运动的滚动时域估计算法

单目视觉系统的自运动估计是计算机视觉领域中的一个关键问题。针对包含有建筑、树木等一般景物特征的应用环境,提出一种单目摄像机位姿估计的滚动时域位姿估计算法。首先分析极线约束方程的不同形式,建立多帧图像闭环之间的时空相关位姿约束,归纳全局最优模型。然后,采用滚动时域方法实现时域窗口内多时刻摄像机位姿的优化估计,实现算法复杂程度和精度的折衷。另外,在室外复杂应用环境下,对常规极约束、冗余极约束和滚动时域冗余极约束这3种位姿估计优化算法进行实验对比,验证该方法的有效性。     

一种双无人机协同跟踪地面移动目标方法

针对通信延时情况下双无人机协同跟踪地面移动目标问题进行研究, 构建了基于分布式遗传算法和滚动时域优化结合的目标跟踪航迹规划算法模型。考虑到通信延时会增加目标状态信息数据融合时的误差, 导致无人机跟踪任务效果变差, 结合递推最小二乘滤波和加权最小二乘估计设计了融合方法, 来融合处理目标状态信息; 考虑到无人机对目标的观测效果与未来时刻的目标状态信息密切相关, 采用递推最小二乘滤波预测目标的状态信息, 结合分布式遗传算法和滚动时域优化设计了双无人机目标跟踪航迹规划算法。适应度函数考虑了无人机和目标之间的距离、无人机之间的通信距离、无人机之间的通信角度。仿真结果表明：该协同跟踪方法能够较好地完成跟踪任务; 与一架无人机跟踪相比误差明显减小, 并且可以减小通信延时带来的跟踪误差。     

A fast moving horizon estimation algorithm based on nonlinear programming sensitivity

Moving horizon estimation (MHE) is an efficient optimization-based strategy for state estimation. Despite the attractiveness of this method, its application in industrial settings has been rather limited. This has been mainly due to the difficulty to solve, in real-time, the associated dynamic optimization problems. In this work, a fast MHE algorithm able to overcome this bottleneck is proposed. The strategy exploits recent advances in nonlinear programming algorithms and sensitivity concepts. A detailed analysis of the optimality conditions of MHE problems is presented. As a result, strategies for fast covariance information extraction from general nonlinear programming algorithms are derived. It is shown that highly accurate state estimates can be obtained in large-scale MHE applications with negligible on-line computational costs.     

Simultaneous state and input estimation of hybrid systems with unknown inputs

This paper addresses the problem of the simultaneous state and input estimation for hybrid systems when subject to input disturbances. The proposed algorithm is based on the moving horizon estimation (MHE) method and uses mixed logical dynamical (MLD) systems as equivalent representations of piecewise affine (PWA) systems. So far the MHE method has been successfully applied for the state estimation of linear, hybrid, and nonlinear systems. The proposed extension of the MHE algorithm enables the estimation of unknown inputs, or disturbances, acting on the hybrid system. The new algorithm is shown to improve the convergence characteristics of the MHE method by reducing the delay of convergent estimates, while assuring convergence for every possible sequence of input disturbances. To ensure convergence the system is required to be incrementally input observable, which is an extension to the classical incremental observability property.     

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.     

Computing arrival cost parameters in moving horizon estimation using sampling based filters

Moving horizon estimation (MHE) is a numerical optimization based approach to state estimation, where the joint probability density function (pdf) of a finite state trajectory is sought, which is conditioned on a moving horizon of measurements. The joint conditional pdf depends on the a priori state pdf at the start of the horizon, which is a prediction pdf based on historical data outside the horizon. When the joint pdf is maximized, the arrival cost is a penalty term based on the a priori pdf in the MHE objective function. Traditionally, the a priori pdf is assumed as a multivariate Gaussian pdf and the extended Kalman filter (EKF) and smoother are used to recursively update the mean and covariance. However, transformation of moments through nonlinearity is poorly approximated by linearization, which can result in poor initialization of MHE. Sampling based nonlinear filters completely avoid Taylor series approximations of nonlinearities and attempt to approximate the non-Gaussian state pdf using samples and associated weights or probability mass points. The performance gains of sampling based filters over EKF motivate their use to formulate the arrival cost in MHE. The a priori mean and covariance are more effectively propagated through nonlinearities and the resulting arrival cost term can help to keep the horizon small. It is also possible to find closed-form approximations to the non-Gaussian a priori pdf from the sampling based filters. Thus, more realistic nonparametric arrival cost terms can be included by avoiding the Gaussian assumption. In this paper the use of the deterministic sampling based unscented Kalman filter, the class of random sampling based particle filter and the aggregate Markov chain based cell filter are discussed for initializing MHE. Two simulation examples are included to demonstrate the benefits of these methods over the traditional EKF approach.     

Distributed moving horizon estimation for nonlinear constrained systems

In this paper we consider a nonlinear constrained system observed by a sensor network and propose a distributed state estimation scheme based on moving horizon estimation (MHE). In order to embrace the case where the whole system state cannot be reconstructed from data available to individual sensors, we resort to the notion of MHE detectability for nonlinear systems, and add to the MHE problems solved by each sensor a consensus term for propagating information about estimates through the network. We characterize the error dynamics and provide conditions on the local exchanges of information in order to guarantee convergence to zero and stability of the state estimation error provided by any sensor. Copyright © 2010 John Wiley & Sons, Ltd.     

Distributed moving horizon state estimation for nonlinear systems with bounded uncertainties

In this work, we propose a distributed moving horizon state estimation (DMHE) design for a class of nonlinear systems with bounded output measurement noise and process disturbances. Specifically, we consider a class of nonlinear systems that are composed of several subsystems and the subsystems interact with each other via their subsystem states. First, a distributed estimation algorithm is designed which specifies the information exchange protocol between the subsystems and the implementation strategy of the DMHE. Subsequently, a local moving horizon estimation (MHE) scheme is designed for each subsystem. In the design of each subsystem MHE, an auxiliary nonlinear deterministic observer that can asymptotically track the corresponding nominal subsystem state when the subsystem interactions are absent is taken advantage of. For each subsystem, the nonlinear deterministic observer together with an error correction term is used to calculate a confidence region for the subsystem state every sampling time. Within the confidence region, the subsystem MHE is allowed to optimize its estimate. The proposed DMHE scheme is proved to give bounded estimation errors. It is also possible to tune the convergence rate of the state estimate given by the DMHE to the actual system state. The performance of the proposed DMHE is illustrated via the application to a reactor-separator process example.     

A homotopy-based moving horizon estimation

Moving horizon estimation (MHE) solves a constrained dynamic optimisation problem. Including nonlinear dynamics into an optimal estimation problem generally comes at the cost of tackling a non-convex optimisation problem. Here, a particular model formulation is proposed in order to convexify a class of nonlinear MHE problems. It delivers a linear time-varying (LTV) model that is globally equivalent to the nonlinear dynamics in a noise-free environment, hence the optimisation problem becomes convex. On the other hand, in the presence of unknown disturbances, the accuracy of the LTV model degrades and this results in a less accurate solution. For this purpose, some assumptions are imposed and a homotopy-based approach is proposed in order to transform the problem from convex to non-convex, where the sequential implementation of this technique starts with solving the convexified MHE problem. Two simulation studies validate the efficiency and optimality of the proposed approach with unknown disturbances.     

Observer-enhanced distributed moving horizon state estimation subject to communication delays

In this work, we focus on distributed moving horizon estimation (DMHE) of nonlinear systems subject to time-varying communication delays. In particular, a class of nonlinear systems composed of subsystems interacting with each other via their states is considered. In the proposed design, an observer-enhanced moving horizon state estimator (MHE) is designed for each subsystem. The distributed MHEs exchange information via a shared communication network. To handle communication delays, an open-loop state predictor is designed for each subsystem to provide predictions of unavailable subsystem states (due to delays). Based on the predictions, an auxiliary nonlinear observer is used to generate a reference subsystem state estimate for each subsystem. The reference subsystem state estimate is used to formulate a confidence region for the actual subsystem state. The MHE of a subsystem is only allowed to optimize its subsystem state estimate within the corresponding confidence region. Under the assumption that there is an upper bound on the time-varying delays, the proposed DMHE is proved to give decreasing and ultimately bounded estimation error. The theoretical results are illustrated via the application to a reactor–separator chemical process.