Filtering of systems with nonlinear measurements with an application to target tracking

This paper studies the problem of recursive state estimation of stochastic linear systems with nonlinear measurements. The main idea is to rewrite the measurement map in a linear form by considering, as system output, a vector of “virtual” measurements. The result is a linear system with a non‐Gaussian and nonstationary output noise. State estimation is therefore obtained using a Kalman filter or, alternatively, a quadratic filter, suitably designed for non‐Gaussian systems. This work provides two sufficient conditions for the application of the virtual measurement approach and shows its effectiveness in the case of the maneuvering target tracking problem.     

Optical tomography system based on charge-coupled device linear image sensors: Particle size measurement

This paper discussed an optical tomography system based on charge-coupled device (CCD) linear image sensors. The developed system consists of a lighting system, a measurement section and a data acquisition system. Four CCD linear image sensors are configured around a flow pipe with an octagonal-shaped measurement section, for a four projections system. The four CCD linear image sensors consisting of 2048 pixels with a pixel size of 14 μm by 14 μm are used to produce a high-resolution system. A simple optical model is mapped into the system's sensitivity matrix to relate the optical attenuation due to variations of optical density within the measurement section. A reconstructed tomographic image is produced based on the model using MATLAB software. The designed instrumentation system is calibrated and tested through different particle size measurements from different projections.     

Minimum variance estimation for linear uncertain systems with one-step correlated noises and incomplete measurements

This paper deals with state estimation problem for linear uncertain systems with correlated noises and incomplete measurements. Multiplicative noises enter into state and measurement equations to account for the stochastic uncertainties. And one-step autocorrelated and cross-correlated process noises and measurement noises are taken into consideration. Using the latest received measurement to compensate lost packets, the modified multi-step random delays and packet dropout model is adopted in the present paper. By augmenting system states, measurements and new defined variables, the original system is transformed into the stochastic parameter one. On this basis, the optimal linear estimators in the minimum variance sense are designed via projection theory. They depend on the variances of multiplicative noises, the one-step correlation coefficient matrices together with the probabilities of delays and packet losses. The sufficient condition on the existence of steady-state estimators is then given. Finally, simulation results illustrate the performance of the developed algorithms.     

微张力测量模型设计与实验研究

对差分结构的霍尔式张力测量模型进行了研究,基于线性霍尔元件和悬臂梁设计了挠度参变量和转角参变量两种微张力测量模型.应用悬臂梁系统将待测张力转换为位移和转角的变化,并以它们为中间参变量,建立了张力与霍尔电压的线性关系,实现了用线性霍尔元件以磁敏的方式测量张力.模型的对称互补式设计,不仅抵消了非线性变量对测量的影响,还能提高信号输出幅度.模型的差分式电压输出,能够抑制共模干扰和零点漂移.两种模型均能实现单一线性变量测量,实验结果符合理论结论.对比实验研究表明,挠度参变量微张力测量模型的灵敏度和线性度均优于转角参变量微张力测量模型,论述了设计原理并给出了理论计算.     

具有不同观测丢失率多传感器随机不确定系统的加权观测融合估计

本文研究了具有丢失观测的多传感器线性离散随机不确定系统的最优线性估计问题,其中不同的传感器具有不同的丢失率.首先将乘性噪声转化为加性噪声,然后基于矩阵满秩分解和加权最小二乘理论,提出了具有较小计算负担的加权观测融合估计算法.分析了加权观测融合估计算法的稳态特性,给出了稳态存在的一个充分条件.所提出的加权观测融合估值器与集中式融合估值器具有相同的精度,即具有全局最优性.仿真研究验证了算法的有效性.     

一般相关噪声下线性系统固定延迟平滑算法

针对机动目标跟踪中固定延迟平滑估计算法的精度问题,当具有一般相关过程噪声和量测噪声时,提出了离散线性系统最优固定延迟平滑估计算法.该算法通过将延迟区间内全部量测进行集中式扩维.并对误差传递进行分析,从而精确地给出了误差间的相关性.在线性无偏最小方差意义下对系统状态进行递推估计,新算法在噪声的高斯分布假设下是最优的.仿真实验结果表明了该算法的有效性.     

Study of observability of motion of an orbital group of navigation space system using intersatellite range measurements. I

The problem of specification of reference ephemeris (reference motion) using intersatellite range measurements on a given interval between spacecrafts of the space navigation system is formulated; observability for this problem is analyzed. Observability is the possibility of unambiguous determination of motion parameters of the orbital group of the space navigation system using known inter-satellite measurements on a given measurement interval. Linear approximate model describing the dependence between measurements and specified parameters are obtained for investigation of observability properties. In the framework of linear model problems of observability of motion of two any spacecrafts of the navigation system are studied using intersatellite range measurements.     

Optimal estimation for continuous-time Markovian jump linear systems with delayed measurements

This paper is to investigate the linear minimum mean square error estimation for continuous-time Markovian jump linear systems with delayed measurements. The key technique applied for treating the measurement delay is the reorganization innovation analysis, by which the state estimation with delayed measurements is transformed into a standard linear mean square filter of an associated delay-free system. The optimal filter is derived based on the innovation analysis method together with geometric arguments in Hilbert space. An analytical solution to the filter is obtained in terms of two Riccati differential equations, and hence is very simple in computation. Computer simulations are carried out to evaluate the performance of the proposed algorithms. The problem of tracking a maneuvering target is addressed.     

有适应力的分布式状态估计方法

为提高智能体系统对攻击的免疫力,研究了测量攻击下的适应力分布式状态估计方法。每个智能体对系统状态进行连续的本地线性测量。由于不同智能体的本地测量模型相互异构,对系统状态可能不具有本地可观测性,且攻击者能够操控部分智能体的测量数据,随意改变其测量结果。而智能体的目标是协同处理本地测量数据,并正确估计出未知的系统状态。因此,该问题的挑战在于在不对真实测量数据和恶意智能体的测量数据进行分辨时,如何设计算法估计得到真实的系统状态。为了解决这个问题,设计了适应性分布式最大后验概率估计算法。在该算法中,只要恶意智能体的数量小于某个特定值,所有智能体都能够收敛到系统状态。首先,根据卡尔曼滤波给出集中式最大后验概率(Maximum A Posteriori,MAP)估计方法,并与分布式一致性结合,进而得到分布式最大后验概率估计方法。然后,考虑到测量攻击,从估计一致性的角度,利用自适应饱和度增益设计了适应性分布式最大后验概率估计方法。最后,通过仿真实验验证算法的有效性。     

On the determination of optimal costly measurement strategies for linear stochastic systems

This paper presents the formulation of a class of optimization problems dealing with selecting, at each instant of time, one measurement provided by one out of many sensors. Each measurement has an associated measurement cost. The basic problem is then to select an optimal measurement policy, during a specified observation time interval, so that a weighted combination of “prediction accuracy” and accumulated “observation cost” is optimized. The current analysis is limited to the class of linear stochastic dynamic systems and measurement subsystems. The problem of selecting the optimal measurement strategy can be transformed into a deterministic optimal control problem. An iterative digital computer algorithm is suggested for obtaining numerical results. It is shown that the optimal measurement policy and the associated “matched” Kalman-type filter can be precomputed, i.e. specified before the measurements actually occur. Numerical results for a third-order system with two possible measurements are presented.     

The reliability and accuracy of an electromagnetic motion analysis system when used conjointly with an accelerometer

The effect of an accelerometer driven electronic postural monitor (Spineangel®) placed within the electromagnetic measurement field of the Polhemus Fastrak? is unknown. This study assessed the reliability and accuracy of Fastrak? linear and angular measurements, when the Spineangel® was placed close to the sensor(s) and transmitter. Bland Altman plots and intraclass correlation coefficient (2,1) were used to determine protocol reproducibility and measurement consistency. Excellent reliability was found for linear and angular measurements (0.96, 95% CI: 0.90–0.99; and 1.00, 95% CI: 1.00–1.00, respectively) with the inclusion of Spineangel®; similar results were found, without the inclusion of Spineangel®, for linear and angular measurements, (0.96, 95% CI: 0.89–0.99; and 1.00, 95% CI: 1.00–1.00, respectively). The greatest linear discrepancies between the two test conditions were found to be less than 3.5 mm, while the greatest angular discrepancies were below 3.5°. As the effect on accuracy was minimal, these findings support the conjoint use of the Fastrak? during validation studies of the Spineangel® device.

Statement of Relevance: Although previous studies have used the Fastrak? as the gold standard measurement system, the influence of an accelerometer driven postural monitor on accuracy has not been reported. The strength of the present study has been to determine the effect of accelerometer placement within the electromagnetic field on the reliability and accuracy of the Fastrak?.     

An application of system identification in metrology

Metrology is advancing by development of new measurement techniques and corresponding hardware. A given measurement technique, however, has fundamental speed and precision limitations. In order to overcome the hardware limitations, we develop signal processing methods based on the prior knowledge that the measurement process dynamics is linear time-invariant.Our approach is to model the measurement process as a step response of a dynamical system, where the input step level is the quantity of interest. The solution proposed is an algorithm that does real-time processing of the sensor's measurements. It is shown that when the measurement process dynamics is known, the input estimation problem is equivalent to state estimation. Otherwise, the input estimation problem can be solved as a system identification problem. The main underlying assumption is that the measured quantity is constant and the measurement process is a low-order linear time-invariant system. The methods are validated and compared on applications of temperature and weight measurement.     

Bounding the Parameters of Linear Systems With Input Backlash

In this note we present a two-stage procedure for deriving parameters bounds of linear systems with input backlash when the output measurement errors are bounded. First, using steady-state input-output data, parameters of the nonlinear dynamic block are tightly bounded. Then, given a suitable PRBS input sequence we evaluate tight bounds on the unmeasurable inner signal which, together with noisy output measurements are employed for bounding the parameters of the linear dynamic system     

Optimal state reconstruction algorithms for linear discrete-time systems

This paper deals with optimal time-invariant reconstruction of the state of a linear time-invariant discrete-time system from output measurements. The problem is analysed in two settings, depending on whether or not the present output measurement is available for the estimation of the present state. The results prove complete separation of observer and controller design for the optimal dynamic output feedback control with respect to a quadratic cost.     

Optimal distributed Kalman filtering fusion for a linear dynamic system with cross-correlated noises

In this article, we study the distributed Kalman filtering fusion problem for a linear dynamic system with multiple sensors and cross-correlated noises. For the assumed linear dynamic system, based on the newly constructed measurements whose measurement noises are uncorrelated, we derive a distributed Kalman filtering fusion algorithm without feedback, and prove that it is an optimal distributed Kalman filtering fusion algorithm. Then, for the same linear dynamic system, also based on the newly constructed measurements, a distributed Kalman filtering fusion algorithm with feedback is proposed. A rigorous performance analysis is dedicated to the distributed fusion algorithm with feedback, which shows that the distributed fusion algorithm with feedback is also an optimal distributed Kalman filtering fusion algorithm; the P matrices are still the estimate error covariance matrices for local filters; the feedback does reduce the estimate error covariance of each local filter. Simulation results are provided to demonstrate the validity of the newly proposed fusion algorithms and the performance analysis.     

The design of optimal reduced-order stochastic observers fordiscrete-time linear systems

The minimum-variance-state estimation of linear discrete-time systems with random white-noise input and partially noisy measurements is investigated. An observer of minimal order is found which attains the minimum-variance estimation error. The structure of this observer is shown to depend strongly on the geometry of the system. This geometry dictates the length of the delays that are applied on the measurements in order to obtain the optimal estimate. The transmission properties of the observer are investigated for systems that are left invertible, and free of measurement noise. An explicit expression is found for the transfer-function matrix of this observer, from which a simple solution to the linear discrete-time singular optimal filtering problem is obtained     

The design of optimal reduced order stochastic observers fordiscrete-time linear systems

The minimum variance state estimation of linear discrete-time systems with random white noise input and partially noisy measurements is investigated. An observer of minimal-order that attains the minimum-variance estimation error is found. The structure of this observer is shown to depend strongly on the geometry of the system. This geometry dictates the length of the delays that are applied on the measurements in order to obtain the optimal estimate. The transmission properties of the observer are investigated for systems that are left invertible and free of measurement noise. An explicit expression is found for the transfer function matrix of the observer, from which a simple solution to the linear discrete-time singular optimal filtering problem is obtained     

具有测量数据丢失的大系统鲁棒H∞控制

研究一类具有测量数据丢失的大系统分散H∞控制器设计问题.针对由个子系统构成的线性离散大系统,假设测量数据丢失满足已知概率的Bernoulli分布,采用线性矩阵不等式方法给出了分散H∞控制器存在的充分条件,所设计的控制器使得闭环系统均方指数稳定,且满足指定的H∞性能指标.通过仿真例子验证了该方法的有效性.     

A dual method for parameter identification under deterministicuncertainty

Proposes a numerical method for reduction of a priori bounds on the values of uncertain plant parameters. The method successively eliminates parts of the parameter domain which are inconsistent with the plant measurement. The size of the eliminated parts is determined by a measure of inconsistency evaluated with the help of the support functions of the set of feasible states and of the set of possible measurements. We specify our approach on an identification problem for a linear control system with bounds on the magnitude and/or on the energy for the disturbances in the dynamics and in the measurement     

Robust method for identifying material parameters based on virtual fields in elastodynamics

We develop an inverse method with the purpose of extracting elastic properties of materials in the framework of transient dynamics. To this end, we create a small linear system based on a set of well-chosen time-dependent virtual fields (VF) and measurement data. The parameters are the solutions of this system and can be quickly extracted. We compare this new method with the classical finite element model updating (FEMU) method for different case studies. In our study, the measurements are synthetic, i.e, they are calculated using a fine finite element (FE) model. Uniform white noise is added to model measurement uncertainties. Results, based on Monte Carlo simulations, show that our method is more robust and accurate than the FEMU method for an acceptable noise level. Our new method appears well-adapted to linear elasticity in transient dynamics.