Bias‐eliminating least‐squares identification of errors‐in‐variables models with mutually correlated noises

This paper proposes a bias‐eliminating least‐squares (BELS) approach for identifying linear dynamic errors‐in‐variables (EIV) models whose input and output are corrupted by additive white noise. The method is based on an iterative procedure involving, at each step, the estimation of both the system parameters and the noise variances. The proposed identification algorithm differs from previous BELS algorithms in two aspects. First, the input and output noises are allowed to be mutually correlated, and second, the estimation of the noise covariances is obtained by exploiting the statistical properties of the equation error of the EIV model. Copyright © 2012 John Wiley & Sons, Ltd.     

Identification of a class of dynamic errors-in-variables models

Dynamic errors-in-variables (EV) models are a new type of linear system models and have found extensive practical applications. One common and important concern with EV models is how to remove noise-induced bias in parameter estimators. In this paper some significant extensions to the newly established bias-eliminated least-squares (BELS) method are made, so that this BELS method can be applied to unbiased identification of a general class of dynamic EV models where input noise is white noise and output noise is correlated noise but the noise statistics are unknown a priori. Though still based on the bias correction principle, this method is very meaningful in that it presents a novel and efficient way of utilizing signal-processing techniques to draw much more useful information from sampled data in order to get desirable identification results. The performance of the proposed method is illustrated by numerical examples.     

Robust centralized and weighted measurement fusion white noise deconvolution estimators for multisensor systems with mixed uncertainties

Estimating the input signal of a system is called deconvolution or input estimation. The white noise deconvolution has important applications in oil seismic exploration, communications, and signal processing. This paper addresses the design of robust centralized fusion (CF) and weighted measurement fusion (WMF) white noise deconvolution estimators for a class of uncertain multisensor systems with mixed uncertainties, including uncertain‐variance multiplicative noises in measurement matrix, missing measurements, and uncertain‐variance linearly correlated measurement and process white noises. By introducing the fictitious noise, the considered system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case system with the conservative upper bounds of uncertain noise variances, the robust CF and WMF time‐varying white noise deconvolution estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the Lyapunov equation approach, their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using the information filter, their equivalence is proved. Their accuracy relations are proved. The computational complexities are analyzed and compared. Compared with the CF algorithm, the WMF algorithms can significantly reduce the computational burden when the number of sensors is larger. The corresponding robust fused steady‐state white noise deconvolution estimators are also presented. A simulation example with respect to the multisensor IS‐136 communication systems shows the effectiveness and correctness of the proposed results.     

基于改进鲁棒自适应UKF的配电网动态状态估计方法

配电网动态状态估计中状态方程的过程噪声统计参数是未知而且时变的,因此在状态估计过程中需要在线对过程噪声统计参数进行实时估计,而且不准确的噪声参数将会导致无迹卡尔曼滤波器的滤波性能下降甚至滤波发散。文中研究了基于改进鲁棒自适应无迹卡尔曼滤波器的配电网动态状态估计方法,其噪声参数统计估值器由一个有偏的和一个无偏的估值器组成,可以提高在状态估计过程中噪声参数估计的准确性,同时确保过程噪声方差矩阵的半正定性,从而保证算法的鲁棒性。通过对IEEE 33节点系统进行仿真验证,结果表明所提方法在系统平稳运行、负荷发生剧烈变动或者初始噪声参数值设置不当的情况下,均能保证较高的状态估计精度。     

A self-tuning automatic voltage regulator

A self-tuning automatic voltage regulator (AVR) for a synchronous generator is presented. The regulator proposed improves the system stability; it is simple and can handle stochastic load changes. The algorithm for the proposed AVR combines a least-squares estimator with a minimum variance control strategy computed from an estimated model. It is shown that if the parameter estimates converge, the control law obtained is in fact the minimum variance control law that would be computed if the parameters of the system were known. The algorithm proposed has been tested by simulation and also by implementation on a minicomputer. Results show that, in general, the system performance is improved with a self-tuning regulator.     

Distributed fusion white noise deconvolution estimators

The white noise deconvolution or input white noise estimation problem has important applications in oil seismic exploration, communication and signal processing. By combining the Kalman filtering method with the modern time series analysis method, based on the autoregressive moving average (ARMA) innovation model, new distributed fusion white noise deconvolution estimators are presented by weighting local input white noise estimators for general multisensor systems with different local dynamic models and correlated noises. The new estimators can handle input white noise fused filtering, prediction and smoothing problems, and are applicable to systems with colored measurement noise. Their accuracy is higher than that of local white noise deconvolution estimators. To compute the optimal weights, the new formula for local estimation error cross-covariances is given. A Monte Carlo simulation for the system with Bernoulli-Gaussian input white noise shows their effectiveness and performance.     

MAP moving horizon estimation for threshold measurements with application to field monitoring

This paper deals with state estimation of a spatially distributed system given noisy measurements from pointwise-in-time-and-space threshold sensors spread over the spatial domain of interest. A maximum a posteriori probability (MAP) approach is undertaken and a moving horizon (MH) approximation of the MAP cost function is adopted. It is proved that, under system linearity and log-concavity of the noise probability density functions, the proposed MH-MAP state estimator amounts to the solution, at each sampling interval, of a convex optimization problem. Moreover, a suitable centralized solution for large-scale systems is proposed with a substantial decrease of the computational complexity. The latter algorithm is shown to be feasible for the state estimation of spatially dependent dynamic fields described by partial differential equations via the use of the finite element spatial discretization method. A simulation case study concerning estimation of a diffusion field is presented in order to demonstrate the effectiveness of the proposed approach. Quite remarkably, the numerical tests exhibit a noise-assisted behavior of the proposed approach in that the estimation accuracy results optimal in the presence of measurement noise with non-null variance.     

Variance analysis of robust state estimation in power system using influence function

An analytical equation is derived using influence function approximation to calculate the variance of the state estimate for traditional robust state estimators such as the Quadratic-Constant, Quadratic-Linear, Square-Root, Schweppe-Huber Generalized-M and Multiple-Segment estimator. The equation gives insights into the precision of the estimation. Using the equation, the variance of a state estimate can be expressed as a function of measurement noise variances enabling the selection of sensors for a specified estimator precision. It can also be used to search for the optimum estimator parameters to give the minimum sum of variances. The well-known Weighted-Least-Squares variance formula is a special case of the equation and simulations on the IEEE 14-bus system are given to show the usefulness of the equation.     

产生标准高斯白噪声序列的方法

高斯白色噪声序列在科学研究与工程领域得到广泛的应用，如系统辨识与仿真，电气与通信工程、生物医学工程等。然而，在已有的商业软件包中难以找到确实能产生标准高斯白噪声序列的程序段。该文提出了在计算机上产生标准高斯白噪声序列的新方法，可有效地产生N(0，1)分布并具有良好白色性能的高斯随机序列，其计算方法主要有两个部分组成：首先应用改进的Marsaglia-Bray方法产生标准正态分布的随机序列；然后，在均方误差最小的准则下，应用双随机交换最小化方法对序列进行白化处理。所得序列的幅值分布与给定的理论正态分布相一致，且序列具有优良的白色化随机性能。     

An adaptive estimation method using instrumental variables and deconvolution

The performance of the methods of recursive instrumental variables (RIV) and minimum variance deconvolution (MVD) is examined when the methods are interwoven so as to provide adaptive estimation of the ARMA model parameters of a system driven by white unmeasurable noise. It is shown that the methods have some similar properties which permit their successful combination in most cases. The asymptotic properties of the resulting estimation approach are evaluated in terms of the ARMA model parameters or the pole-zero locations, the signal-to-noise ratio and the frequency bandwidth of the system impulse response. An analysis of the second-order ARMA model and various simulation examples are presented which illustrate the derived results. The method has been successfully applied to the problem of adaptive seismic signal deconvolution.     

Frequency estimation by demodulation of two complex signals

This paper presents a method for frequency estimation in a power system by demodulation of two complex signals. In power system analysis, the αβ-transform is used to convert three phase quantities to a complex quantity where the real part is the in-phase component and the imaginary part is the quadrature component. This complex signal is demodulated with a known complex phasor rotating in opposite direction to the input. The advantage of this method is that the demodulation does not introduce a double frequency component. For signals with high signal to noise ratio, the filtering demand for the double frequency component can often limit the speed of the frequency estimator. Hence, the method can improve fast frequency estimation of signals with good noise properties. The method loses its benefits for noisy signals, where the filter design is governed by the demand to filter harmonics and white noise. The method has been previously published, but not explored to its potential. The paper presents four examples to illustrate the strengths and weaknesses of the method     

Filtering,smoothing and prediction using a control‐loop spectral factorization method for coloured noise

A method for the linear least‐squares estimation of random signals contaminated with random noise that uses a new method of spectral factorization is shown. It is shown that the optimal filter can be written entirely in terms of the two spectral factors of signal plus noise and noise‐alone, and can be applied to the general case of coloured and white additive noise. The method of spectral factorization used is novel and uses control‐system methodology. Copyright © 2012 John Wiley & Sons, Ltd.     

Static state estimation with DC models and linear programming

A decoupled state estimation algorithm is proposed in which the measurement model is based on linear approximation of the power flow equations and the solution method is based on linear programming. The decoupled least-squares DC-estimator and the undecoupled least-absolute-value estimator are numerically compared. As an overall reference, the classic undecoupled least-squares estimator is used. The error-detecting capabilities and the accuracy of the estimated state of all four types of estimators are treated.     

自适应Kalman滤波在多传感器数据融合中应用

文中介绍基于白噪声滤波器和平滑器的改进的Sage和Husa噪声统计估值器及相应的自适应Kalman滤波器,可处理未知常的和时变的噪声统计估计问题.仿真结果验证了改进滤波器在精度和收敛速度上的优越性.     

自适应UKF在北斗伪距定位中的研究

针对北斗伪距定中噪声统计特性未知或者不准确带来的定位精度不高问题,为减小噪声统计特性的不准确在滤波过程中对状态估计带来的影响,采用了无迹卡尔曼滤波(UKF)和噪声统计值估计器相结合的滤波方法,该方法在UKF中引入改进的噪声估计Sage-Husa算法,对系统噪声和观测噪声进行实时估计,抵抗不准确噪声在定位解算时带来的误差;最后在进行状态更新时引入一个收敛因子对每一次滤波状态进行更新,保证算法的收敛性。实验结果表明,该方法与传统的无迹卡尔曼滤波相比,在提升算法收敛速度的同时,将伪距定位的精度提高了40%左右,可用于带有时变噪声和未知噪声的定位系统中。     

基于卡尔曼滤波的高精度弹道滤波算法研究

在弹道轨迹估计中,卡尔曼滤波算法是一种普遍使用的算法,常规卡尔曼滤波算法适用于线性离散系统.对于非线性离散系统模型,为了提高滤波的精度,减小系统模型误差以及未知的量测噪声和过程噪声统计特性对滤波精度的影响,提出了一种带有噪声统计估计器的拟线性最优平滑滤波算法.将该算法应用到弹道系统模型中,对弹道轨迹进行滤波估计.通过计算机建模仿真改进的算法和传统的拟线性最优平滑滤波算法,得到的实验结果表明,改进后的算法可以减小由于系统模型不精确带来的误差,很大程度上提高了弹道轨迹滤波估计的精度.     

双模噪声中信号识别与精确估计

文中给出了双模噪声中信号参量的精确估计，并给出了任意加性白噪声中信号识别与估计的一般方法，且可同时估信号与噪声，具有一定的普遍意义，仿真表明，本识别与估计方法是正确的。     

Robust time‐varying Kalman estimators for systems with packet dropouts and uncertain‐variance multiplicative and linearly correlated additive white noises

This paper is concerned with robust estimation problem for a class of time‐varying networked systems with uncertain‐variance multiplicative and linearly correlated additive white noises, and packet dropouts. By augmented state method and fictitious noise technique, the original system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case system with conservative upper bounds of uncertain noise variance, the robust time‐varying Kalman estimators (filter, predictor, and smoother) are presented. A unified approach of designing the robust Kalman estimators is presented based on the robust Kalman predictor. Their robustness is proved by the Lyapunov equation approach in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Their accuracy relations are proved. The corresponding robust steady‐state Kalman estimators are also presented, and the convergence in a realization between the time‐varying and steady‐state robust Kalman estimators is proved. Finally, a simulation example applied to uninterruptible power system shows the correctness and effectiveness of the proposed results.     

基于VSS-CDFE的三相非平衡电力系统频率无偏估计

为了实现含噪三相非平衡电力系统高精度频率无偏估计,引入了复数域直接频率估计(CDFE)算法,分析其原理并对其进行了改进。CDFE算法基于正弦信号的线性预测,求取误差函数的瞬时平方值关于频率的偏导数,并以该值作为频率估计的更新值。在此基础上,进一步提出变步长CDFE(VSS-CDFE)算法,根据最速下降法则动态更新步长因子来代替CDFE算法的固定步长。仿真分析及实验结果表明,在噪声干扰下,VSS-CDFE算法可以准确地对基于复数建模的三相非平衡电力系统进行频率追踪,其估计均方误差和理论值相吻合。相比CDFE算法,VSS-CDFE算法在相同的收敛速度下,估计均方误差更小,在相同的估计均方误差下,收敛速度更快。     

Fourier series expansions of noisy signals — consistent estimation of the whole spectrum

In this note the problem of estimating the Fourier series coefficients of a deterministic signal measured in a noise is discussed. Firstly, it is shown that if random errors are not taken into account, then the mean square error between the true spectrum and its commonly used estimator is infinite. The method proposed for overcoming this difficulty is based on multiplying the estimates by the geometric sequence. It is shown that if this sequence depends on the number of observations and is appropriately chosen, then consistent estimation of the whole spectrum is possible. The method introduces a bias which is shown to be asymptotically vanishing. For smooth signals an upper bound for the bias is also derived.