Freeway traffic estimation within particle filtering framework

This paper formulates the problem of real-time estimation of traffic state in freeway networks by means of the particle filtering framework. A particle filter (PF) is developed based on a recently proposed speed-extended cell-transmission model of freeway traffic. The freeway is considered as a network of components representing different freeway stretches called segments. The evolution of the traffic in a segment is modelled as a dynamic stochastic system, influenced by states of neighbour segments. Measurements are received only at boundaries between some segments and averaged within possibly irregular time intervals. This limits the measurement update in the PF to only these time instants when a new measurement arrives, while in between measurement updates any simulation model can be used to describe the evolution of the particles. The PF performance is validated and evaluated using synthetic and real traffic data from a Belgian freeway. An unscented Kalman filter is also presented. A comparison of the PF with the unscented Kalman filter is performed with respect to accuracy and complexity.     

非线性间歇过程的迭代学习状态估计

在间歇过程的状态估计中,如何充分利用多批次重复特性信息是一个挑战。迭代学习卡尔曼滤波方法利用卡尔曼滤波沿时间方向估计相邻两批次之间的状态误差,并沿批次方向迭代更新当前状态估计,兼顾了时间和批次两维特性。但是,这种方法只适用于线性系统。针对非线性间歇过程,提出一种迭代学习拟线性卡尔曼滤波器(ILQKF)方法。ILQKF基于间歇过程的标称模型,将实际状态与标称状态之间的误差作为新状态,建立了与误差相关的线性化模型。然后,根据迭代学习卡尔曼滤波方法,对状态误差进行估计,而状态轨迹为误差轨迹与标称轨迹之和,从而估计出非线性间歇过程的状态。啤酒发酵过程的应用仿真验证了ILQKF方法的优越性。     

On the application of a hybrid ellipsoidal-rectangular interval arithmetic algorithm to interval Kalman filtering for state estimation of uncertain systems

Modelling uncertainty is a key limitation to the applicability of the classical Kalman filter for state estimation of dynamic systems. For such systems with bounded modelling uncertainty, the interval Kalman filter (IKF) is a direct extension of the former to interval systems. However, its usage is not yet widespread owing to the over-conservatism of interval arithmetic bounds. In this paper, the IKF equations are adapted to use an ellipsoidal arithmetic that, in some cases, provides tighter bounds than direct, rectangular interval arithmetic. In order for the IKF to be useful, it must be able to provide reasonable enclosures under all circumstances. To this end, a hybrid ellipsoidal-rectangular enclosure algorithm is proposed, and its robustness is evidenced by its application to two characteristically different systems for which it provides stable estimate bounds, whereas the rectangular and ellipsoidal approaches fail to accomplish this in either one or the other case.     

Joint state and parameter estimation in particle filtering and stochastic optimization

In this paper, an adaptive estimation algorithm is proposed for non-linear dynamic systems with unknown static parameters based on combination of particle filtering and Simultaneous Perturbation Stochastic Approxi- mation （SPSA） technique. The estimations of parameters are obtained by maximum-likelihood estimation and sampling within particle filtering framework, and the SPSA is used for stochastic optimization and to approximate the gradient of the cost function. The proposed algorithm achieves combined estimation of dynamic state and static parameters of nonlinear systems. Simulation result demonstrates the feasibilitv and efficiency of the proposed algorithm     

一种利用UKF的高速公路实时交通状态估计方法

把无轨迹卡尔曼滤波器（UKF）和宏观随机交通流模型结合在一起,可以实现对高速公路交通状态的实时估计。高速公路被看作是由等距离的路段首尾相接而成的系统,每个路段中交通变量的更新不光与其自身有关,还受到相邻路段的影响。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UKF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。     

Joint state and parameter estimation in particle filtering and stochastic optimization

In this paper, an adaptive estimation algorithm is proposed for non-linear dynamic systems with unknown static parameters based on combination of particle filtering and Simultaneous Perturbation Stochastic Approximation (SPSA) technique. The estimations of parameters are obtained by maximum-likelihood estimation and sampling within particle filtering framework, and the SPSA is used for stochastic optimization and to approximate the gradient of the cost function. The proposed algorithm achieves combined estimation of dynamic state and static parameters of nonlinear systems. Simulation result demonstrates the feasibility and efficiency of the proposed algorithm.     

Simultaneous input and state estimation for nonlinear systems with applications to flow field estimation

This paper studies the problem of simultaneous input and state estimation (SISE) for nonlinear dynamical systems with and without direct input–output feedthrough. We take a Bayesian perspective to develop a sequential joint input and state estimation approach. Our scheme gives rise to a nonlinear Maximum a Posteriori optimization problem, which we solve using the classical Gauss–Newton method. The proposed approach generalizes a number of SISE methods presented in the literature. We illustrate the effectiveness of the proposed scheme for nonlinear systems with direct feedthrough in an oceanographic flow field estimation problem involving submersible drogues that measure position intermittently and acceleration continuously.     

Nonlinear state estimation for suspension control applications: a Takagi-Sugeno Kalman filtering approach

A new nonlinear state estimation approach, which combines classical Kalman filter theory and Takagi-Sugeno (TS) modeling, is proposed in this paper. To ensure convergence of the TS observer, conditions are derived that explicitly account for the TS model's confined region of validity. Thereby, the secured domain of attraction (DA) of the TS error dynamics is maximized within given bounds. The TS Kalman filtering concept is then applied to a hybrid vehicle suspension configuration, whose nonlinear dynamics are exactly represented by a continuous-time TS system. The benefit of the novel estimation technique is analyzed in comparison with the well-known EKF and UKF variants in simulations and experiments of a passive and an actively controlled suspension configuration in a quarter-car set-up. Employing a real road profile as disturbance input, the TS Kalman filter shows the highest estimation quality of the concepts studied. Moreover, as its computational complexity adds up to only one third of the one involved with the classical methods, the new approach operates remarkably efficient.     

Geometric particle swarm optimization for robust visual ego-motion estimation via particle filtering

Conventional particle filtering-based visual ego-motion estimation or visual odometry often suffers from large local linearization errors in the case of abrupt camera motion. The main contribution of this paper is to present a novel particle filtering-based visual ego-motion estimation algorithm that is especially robust to the abrupt camera motion. The robustness to the abrupt camera motion is achieved by multi-layered importance sampling via particle swarm optimization (PSO), which iteratively moves particles to higher likelihood region without local linearization of the measurement equation. Furthermore, we make the proposed visual ego-motion estimation algorithm in real-time by reformulating the conventional vector space PSO algorithm in consideration of the geometry of the special Euclidean group SE(3), which is a Lie group representing the space of 3-D camera poses. The performance of our proposed algorithm is experimentally evaluated and compared with the local linearization and unscented particle filter-based visual ego-motion estimation algorithms on both simulated and real data sets.     

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.     

离散系统状态和参数鲁棒滤波分离算法

提出了一种离散系统的鲁棒分离滤波方法.为了对状态向量进行较准确估计,将鲁棒滤波器分为:1)零误差状态估计器;2)不确定矩阵估计器;3)鲁棒合成器.零偏差状态估计器是假定系统的不确定部分为零时的状态估计器;其新息作为不确定部分的估计变量,并由此估计系统的不确定部分;最后,根据系统不确定部分估计误差的上下界,用鲁棒合成器对状态向量的估计值进行鲁棒修正.为了在合成器中得到鲁棒滤波的逼近计算式,通过变换状态估计误差的协方差阵,得到了系统矩阵不确定部分的误差上界不等式逼近,并且得到了估计误差协方差阵逆阵的下界不等式逼近,从而给出了鲁棒合成滤波的完整算法.     

A new state estimation method for high-mix semiconductor manufacturing processes

In semiconductor manufacturing upstream processes may affect the wafer substrate in a manner that alters performance in downstream operations, and the context within which a process is run may fundamentally change the way the process behaves. Incorporating these influences into a control method ultimately leads to better predictability and improved control performance, because one lot of a specific product may take a very different processing path through the fabrication facility than the next lot of that same product. This paper provides a new method for state estimation in a high-mix manufacturing scenario, based on a random walk model. This model, combined with a moving window approach and least squares solution, provides better estimates for simulated processes with a high-mix of tools and products with many low-runners as compared to alternative methods. An approach combining the Kalman filter and the least squares solution is also developed, with improved results in some cases. In the case of manufacturing data, we modify the model parameters and the weights on processing contexts to get better results.     

On-line state and parameter estimation of EPDM polymerization reactors using a hierarchical extended Kalman filter

A hierarchical extended Kalman filter (EKF) design is proposed to estimate unmeasured state variables and key kinetic parameters in a first principles model of a continuous ethylene–propylene–diene polymer (EPDM) reactor. The estimator design is based on decomposing the dynamic model into two subsystems by exploiting the triangular model structure and the different sampling frequencies of on-line and laboratory measurements directly related to the state variables of each subsystem. The state variables of the first subsystem are reactant concentrations and zeroth-order moments of the molecular weight distribution (MWD). Unmeasured state variables and four kinetic parameters systematically chosen to reduce bias are estimated from frequent and undelayed on-line measurements of the ethylene, propylene, diene and total polymer concentrations. The state variables of the second subsystem are first-order moments of the MWD. Given state and parameters estimates from the first subsystem EKF, the first-order moments and three non-stationary parameters added to the model for bias reduction are estimated from infrequent and delayed laboratory measurements of the ethylene and diene contents and number average molecular weight of the polymer. Simulation tests show that the hierarchical EKF generates satisfactory estimates even in the presence of measurement noise and plant/model mismatch.     

Set membership state and parameter estimation for systems described by nonlinear differential equations

This paper investigates the use of guaranteed methods to perform state and parameter estimation for nonlinear continuous-time systems, in a bounded-error context. A state estimator based on a prediction-correction approach is given, where the prediction step consists in a validated integration of an initial value problem for an ordinary differential equation (IVP for ODE) using interval analysis and high-order Taylor models, while the correction step uses a set inversion technique. The state estimator is extended to solve the parameter estimation problem. An illustrative example is presented for each part.     

多传感器跟踪系统自适应Kalman滤波融合

多传感器目标跟踪的一个实际问题是如何获得目标的过程噪声信息,以获得较好的跟踪性能。针对多传感器分布式估计融合系统,利用这种自适应技术给出了一种自适应Kalman滤波的融合方法,它具有与中心式相近的跟踪性能。计算机模拟结果表明：这种方法具有较优良的性能。     

互补滤波和卡尔曼滤波的融合姿态解算方法

针对捷联惯性测量单元(IMU)噪声大、精度低的缺点和常规的姿态解算算法精度不高等问题,提出了一种互补滤波和卡尔曼滤波相结合的融合算法.该算法基于姿态角微分方程建立系统的状态方程模型,利用互补滤波后的姿态角作为系统的观测量,再应用扩展卡尔曼滤波(EKF)算法融合了陀螺仪、加速度计和电子罗盘的测量数据.为验证该算法有效性,用带有传感器的开发板依次进行静态和动态测试,实验结果表明:结合了互补滤波和卡尔曼滤波的融合算法,在静态时能够抑制姿态角漂移和滤出噪声,在动态时能够快速跟踪姿态的变化,提高了姿态角的解算精度.     

A separated bias identification and state estimation algorithm for nonlinear systems

A computational algorithm for the identification of biases in discrete-time, nonlinear, stochastic systems is derived by extending the separate bias estimation results for linear systems to the extended Kalman filter formulation. The merits of the approach are illustrated by identifying instrument biases using a terminal configured vehicle simulation.     

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.     

Possibilistic Kalman filtering for radar 2D tracking

Standard Kalman filter (SKF) introduced by Kalman in the 60s has gained a non-estimated importance in control as well as in robotics community. Its importance arises from the obtained optimal result in the sense of variance minimization under stochastic, Gaussian and unbiased perturbations, and when the state model as well as the measurement model are precisely known. However, when the last requirement is relaxed such that one or more parameters governing the models are ill-defined and rather given in terms of interval evaluations, Chen et al. (IEEE Trans. Aerospace Electr. Syst. 33 (1) (1997) 251–259) have proposed Interval Kalman Filter (IKF) by extending the arithmetic operations to interval calculus. In this paper, we rather assume that the uncertainty pervading some parameters of the models are given in terms of possibility distributions [21]. This leads to a formulation of possibilistic Kalman Filtering (PKF), which agrees with IKF. The same example of 2D-radar tracking is tackled. Comparisons with IKF are investigated as well the influence of the modelling process on the performance of the filter. Besides, the proposal permits to capture certainty qualified information, which cannot be obtained from IKF.