A new look at Akaike’s Bayesian information criterion for inverse ill-posed problems

Akaike’s Bayesian information criterion (ABIC) has been widely used in inverse ill-posed problems. Little has been done to investigate its statistical aspects. We present an alternative derivation of the marginal distribution of measurements for ABIC under the assumption of normal distributions and show that the principle of ABIC is to statistically estimate the variances of measurements and prior data by maximizing the marginal distribution of measurements. The determination of the regularization parameter with ABIC is essentially equivalent to estimating the relative weighting between measurements and prior data. We prove that ABIC theoretically would produce a biased estimate of the variance of measurements. Since the prior mean is generally unknown but arbitrarily treated as zero in inverse ill-posed problems, ABIC is shown to fail to produce any reasonable estimate for the prior variance. Although ABIC is constructed under the Bayesian framework, it essentially plays more or less the same role as biased regularization from the frequentist’s point of view. ABIC error evaluation cannot be performed under the Bayesian framework but should be more appropriately done with the frequentist’s standpoint in terms of mean squared errors. ABIC is sensitive to prior distributions. In the case of non-informative prior distribution, ABIC leads to the conventional weighted least squares (LS) estimate of parameters and cannot be used to solve inverse ill-posed problems. It is not linked to the regularization parameter but only straightforwardly produces an unbiased estimator for the noise level of measurements, which is only applicable numerically for well-posed problems but not for inverse ill-posed problems. Numerical simulated examples are used to demonstrate the statistical performances of ABIC.     

Direction of arrival tracking for signals with known waveforms based on block least squares techniques

In this paper, we address the problem of tracking DOA of multiple moving targets with known signal source waveforms and unknown gains in the presence of Gaussian noise using a nonuniform linear array. Herein, we make use of the fact that the output of each sensor can be described as a linear regression model whose coefficients each contain a pair of DOA and gain information corresponding to one target. These coefficients are determined by solving a linear least squares (LS) problem and then updated recursively based on a block QR decomposition recursive least squares (QRD-RLS) technique or a block regularized LS technique. Since the coefficients from different sensors have the same amplitude but variable phase information for the same signal, along with simple algebraic manipulations the well-known generalized least squares (GLS) are used to obtain an asymptotically-optimal DOA estimate without requiring a search over a large region of the parameter space. Computer simulations show that the proposed DOA tracking techniques when applied to a sparse antenna array can provide a better tracking performance than some of the existing methods do.     

Auxiliary model based least squares parameter estimation algorithm for feedback nonlinear systems using the hierarchical identification principle

This paper presents a decomposition based least squares estimation algorithm for a feedback nonlinear system with an output error model for the open-loop part by using the auxiliary model identification idea and the hierarchical identification principle and by decomposing a system into two subsystems. Compared with the auxiliary model based recursive least squares algorithm, the proposed algorithm has a smaller computational burden. The simulation results indicate that the proposed algorithm can estimate the parameters of feedback nonlinear systems effectively.     

非线性协整的非参数检验方法

本文基于非参数回归模型的局部核权最小二乘法提出变量间非线性协整的一种非参数检验方法。     

复值型数据Improper线性回归模型的估计(英文)

复随机变量称为"improper"随机变量,若它的"伪"协方差阵不为0,否则称为"proper"随机变量.研究了误差服从独立同分布的improper复高斯分布的线性回归模型.利用极大似然方法和2阶段最小二乘方法来估计回归系数.模拟表明,这2种方法与经典复版本的最小二乘法有不同之处,并将该方法用于实际风信号数据的处理.     

基于偏最小二乘回归的城市生活用水量预测研究

以城市生活用水量为预测研究对象,选取6个社会经济发展因素作为主要变量因子,建立偏最小二乘回归模型。研究分析表明,各变量因子间存在较强的多重共线性,采用偏最小二乘回归模型能有效克服各类因子变量间的多重共线性对模型拟合精度及其预测能力的影响,取得更接近现实的预估结果(平均相对误差为2.7%)。研究还发现,数据序列的长度和变量近期的变化信息也会对模型的预测精度产生重要的影响。     

A novel approach to dictionary construction for automatic modulation classification

In almost all the work carried out in the area of automatic modulation classification (AMC), the dictionary of all possible modulations that can occur is assumed to be fixed and given. In this paper, we consider the problem of discovering the unknown digital amplitude-phase modulations when the dictionary is not given. A deconvolution based framework is proposed to estimate the distribution of the transmitted symbols, which completely characterizes the underlying signal constellation. The method involves computation of the empirical characteristic function (ECF) from the received signal samples, and employing constrained least squares (CLS) filtering in the frequency domain to reveal the unknown symbol set. The decoding of the received signals can then be carried out based on the estimate of the signal constellation. The proposed method can be implemented efficiently using fast Fourier transform (FFT) algorithms. In addition, we show that the distribution estimate of the transmitted symbols can be refined if the signal constellation is known to satisfy certain symmetry and independence properties.     

利用硅藻-pH转换函数定量重建Llyn Hir湖pH的变化（英文）

PCA、DCA和CCA分析显示,可以利用英国威尔士地区34个湖泊表层沉积物的现代硅藻组合和pH数据,建立硅藻-pH转换函数.根据RMSE和残差分析,选用了WA_Cla_X和WAPLS_C2_X模型,同时选取WA_Cla作为对照.我们在Llyn Hir湖中心钻取岩芯,对顶部14.5cm进行了化石硅藻种群组合的分析,利用这些资料,根据这三个硅藻-pH转换函数模型,定量重建了该湖1956-1995年pH的变化过程.结果显示,1985年为了改善该湖酸化状况,向湖中施加石灰引起湖水pH明显增高,这种显著效果维持了六年,此后逐渐减弱乃至消失.利用硅藻-pH转换函数重建的湖泊pH变化结果与湖泊pH实际监测结果相当吻合,说明了虽然施加石灰可在较短时期内减弱湖泊酸化程度,但是不能根治湖泊酸化.     

A hierarchical least squares identification algorithm for Hammerstein nonlinear systems using the key term separation

Mathematical models are basic for designing controller and system identification is the theory and methods for establishing the mathematical models of practical systems. This paper considers the parameter identification for Hammerstein controlled autoregressive systems. Using the key term separation technique to express the system output as a linear combination of the system parameters, the system is decomposed into several subsystems with fewer variables, and then a hierarchical least squares (HLS) algorithm is developed for estimating all parameters involving in the subsystems. The HLS algorithm requires less computation than the recursive least squares algorithm. The computational efficiency comparison and simulation results both confirm the effectiveness of the proposed algorithms.     

Auxiliary model based recursive generalized least squares identification algorithm for multivariate output-error autoregressive systems using the decomposition technique

This paper focuses on the parameter estimation problem of multivariate output-error autoregressive systems. Based on the decomposition technique and the auxiliary model identification idea, we derive a decomposition based auxiliary model recursive generalized least squares algorithm. The key is to divide the system into two fictitious subsystems, the one including a parameter vector and the other including a parameter matrix, and to estimate the two subsystems using the recursive least squares method, respectively. Compared with the auxiliary model based recursive generalized least squares algorithm, the proposed algorithm has less computational burden. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithms.     

抗差估计在提高GPS RTK高程拟合精度中的应用

介绍了GPSRTK高程拟合的理论方法和数学模型,常规的方法是以最小二乘估计值为初值,但不宜发现和处理粗差。为了提高高程拟合精度,采用抗差估计理论在GPSRTK高程拟合的精度分析方法,通过选择综合抗差估计阶段的权函数,不断地迭代,直至权无限趋近于零。     

A combined time and frequency domain method for model reduction of discrete systems

A new combined time and frequency domain method for the model reduction of discrete systems in z-transfer function is presented. First, the z-transfer functions are transformed into the w-domain by the bilinear transformation, z = (1+w)/(1?w). Then, four model reduction methods—Routh approximation, Hurwitz polynomial approxima- tion, stability equation, and retaining dominant poles—are used respectively to reduce the order of the denominator polynomials in the w-domain. Least squares estimate is then used to find the optimal coefficients in the numerator polynomials of the reduced models so that the unit step response errors are reduced to a minimum. The advantages of the proposed method are that both frequency domain and time domain characteristics of the original systems can be preserved in the reduced models, and the reduced models are always stable provided the original models are stable.     

Traffic modeling for communications networks: A multifractal approach based on few parameters

In this work, in order to model network traffic processes, an efficient multifractal model is proposed based on fewer parameters than other models present in the literature, called 2PEMV. The 2PEMV model (2-Parameter Exponential Modeling for Multipliers’ Variance) is based on a multiplicative cascade in the wavelet domain capable of synthesizing communication network traffic traces which present characteristics such as self-similarity and wide Multifractal Spectrum Width (MSW). For such a purpose, in the 2PEMV model, the energy decay of the wavelet coefficients is captured by means of an exponential modeling for the multipliers’ variance along the cascade scales. The performance of the 2PEMV model to represent the network traffic characteristics is evaluated in comparison to other models present in the literature through simulations that are carried out using real communication network traffic traces.     

LMS与RLS自适应滤波算法对比研究

自适应滤波算法根据采用优化准则的不同,通常分为两类最基本算法:最小均方误差(LMS)类算法和递归最小二乘(RLS)类算法。本文重点介绍了最小均方误差算法和递归最小二乘算法,并将这两类算法在MATLAB上进行仿真,并对结果作出比较和分析。     

Walsh series approach to lumped and distributed system identification

This paper considers the problem of identifying the parameters of dynamic systems from input-output records. Both lumped-parameter and distributed-parameter systems, deterministic and stochastic, are studied. The approach adopted is that of expanding the system variables in Walsh series. The key point is an operational matrix P which relates the coefficient matrix Г of the Walsh series of a given function with the coefficient matrix of its first derivative. Using this operational matrix P one overcomes the necessity to use differentiated data, a fact that usually is avoided either by integration of the data or by using discrete-time models. Actually, the original differential input-output model is converted to a linear algebraic (or regression) model convenient for a direct (or a least squares) solution. A feature of the method is that it permits the identification of unknown initial conditions simultaneously with the parameter identification. The results are first derived for single-input single-output systems and then are extended to multi-input multi-output systems. The case of non-constant parameters is treated by assuming polynomial forms. Some results are also included concerning the identification of state-space and integral equation models. The theory is supported by two examples, which give an idea of how effective the method is expected to be in the real practice.     

A control algorithm for systems with dead time

A least squares control algorithm for single-input single-output (SISO) systems is developed. The algorithm allows for a delay with large dead time and uses proportional- integral-derivative actions in their parallel form to achieve steady-state without error. Optimization of the controller parameters is achieved and the parameters of the controller are determined from the solution of a set of linear simultaneous equations. The control strategy is to optimize the controller parameters such that a desired well-behaved trajectory is obtained. The controller is shown to be robust and the algorithm is shown to function as well without or with large dead time, to have low sensitivity to changes in the dead time, and to allow an adaptive estimation of changing system parameters. The application of the developed algorithm to control the glucoregulatory system, based on a 4th-order digital model, is presented in two cases: free time delay and with large dead time.     

Fading performance evaluation of a semi-blind adaptive space–time equaliser for frequency selective MIMO systems

A semi-blind adaptive space–time equaliser (STE) has recently been proposed based on a concurrent gradient-Newton (GN) constant modulus algorithm (CMA) and soft decision-directed (SDD) scheme for dispersive multiple-input multiple-output (MIMO) systems that employ high-throughput quadrature amplitude modulation signalling. A minimum number of training symbols, approximately equal to the dimension of the STE, is used to provide a rough initial estimate of the STE's weight vector. The concurrent GN based CMA and SDD blind adaptive scheme is then adopted to adapt the STE. This semi-blind STE has a complexity similar to that of the training-based recursive least squares (RLS) algorithm. For stationary MIMO channels, it has been demonstrated that this semi-blind adaptive STE is capable of converging fast to the optimal minimum mean square error STE solution. In this contribution, we investigate the performance of this semi-blind adaptive STE operating in Rayleigh fading MIMO systems. Our results obtained show that the tracking performance of this semi-blind adaptive algorithm is close to that of the training-based RLS algorithm. Thus, this semi-blind adaptive STE offers an effective and practical means to successfully operate under the highly dispersive and fading MIMO environment.     

The data-filtering based bias compensation recursive least squares identification for multi-input single-output systems with colored noises

For the multi-input single-output (MISO) system corrupted by colored noise, we transform the original system model into a new MISO output error model with white noise through data filtering technology. Based on the newly obtained model and the bias compensation principle, a novel data filtering-based bias compensation recursive least squares (BCRLS) identification algorithm is developed for identifying the parameters of the MISO system with colored noise disturbance. Unlike the exiting BCRLS method for the MISO system (see, in Section 3), without computing the complicated noise correlation functions, still the proposed method can achieve the unbiased parameters estimation of the MISO system in the case of colored process noises. The proposed algorithm simplifies the implementation of and further expands the application scope of the existing BCRLS method. Three numerical examples clearly illustrate the validity of and the good performances of the proposed method, including its superiority over the BCRLS method and so on.     

参量匹配滤波器和向量自回归滤波器的等价性(英文)

分析了自适应匹配滤波器和向量自回归(VAR)时域白化滤波器.结果表明,通过最小化用误差平方之和估计的均方误差得到的参量滤波器系数和通过相同阶数的多通道最小二乘法得到的VAR滤波器系数是等价的.此外,还分析了VAR滤波器最小二乘估计器的渐进性能,分析了滤波器的运算量和杂波抑制性能.     

On the development of an inertial navigation error-budget system

This paper targets the development of an inertial navigation error-budget system for performance validation before actual field operation. The paper starts by studying the various errors that an inertial measurement unit (IMU) incorporates. A systematic approach of error modeling is proposed. The error models are integrated in time and added to the true measurement of the IMU to obtain the observed measurements. Simulation results are presented to show the contribution of the errors to the final measurement of the IMU. The IMU error model is blended with a GPS measurements’ model and the performance of a GPS/IMU extended Kalman filter (EKF) to IMU errors is shown. The simulated IMU errors are essential to study IMU quality effect on an inertial navigation system's (INS) state estimate accuracy.