Noise estimation for hyperspectral subspace identification on FPGAs

The Journal of Supercomputing - We present a reliable and efficient FPGA implementation of a procedure for the computation of the noise estimation matrix, a key stage for subspace identification of...     

Nonlinear observer design for state and disturbance estimation

A new systematic framework for nonlinear observer design that allows the concurrent estimation of the process state variables together with key unknown process or sensor disturbances is proposed. The nonlinear observer design problem is addressed within a similar methodological framework as the one introduced in [N. Kazantzis, C. Kravaris, Nonlinear observer design using Lyapunov's auxiliary theorem, Systems Control Lett. 34 (1998) 241; A.J. Krener, M. Xiao, Nonlinear observer design in the Siegel domain, SIAM J. Control Optim. 41 (2002) 932.] for state estimation purposes only. From a mathematical standpoint, the problem under consideration is addressed through a system of first-order singular PDEs for which a rather general set of solvability conditions is derived. A nonlinear observer is then designed with a state-dependent gain that is computed from the solution of the system of singular PDEs. Under the aforementioned conditions, both state and disturbance estimation errors converge to zero with assignable rates. The convergence properties of the proposed nonlinear observer are tested through simulation studies in an illustrative example involving a biological reactor.     

Recursive subspace identification subject to relatively slow time-varying load disturbance

In this paper, a recursive subspace identification method is proposed to identify linear time-invariant systems subject to load disturbance with relatively slow dynamics. Using the linear superposition principle, the load disturbance response is decomposed from the deterministic-stochastic system response in the form of a time-varying parameter. To ensure unbiased estimation of the deterministic system matrices, a recursive least-squares (RLS) identification algorithm is established with a fixed forgetting factor, while another RLS algorithm with an adaptive forgetting factor is constructed based on the output prediction error to quickly track the time-varying parameter of load disturbance response. By introducing a deadbeat observer to represent the deterministic system response, two extended observer Markov parameter matrices are constructed for recursive estimation. Consequently, the deterministic matrices are retrieved from the identified system Markov parameter matrices. The convergence of the proposed method is analysed with a proof. Two illustrative examples are shown to demonstrate the effectiveness and merit of the proposed identification method.     

Algorithms for deterministic balanced subspace identification

New algorithms for identification of a balanced state space representation are proposed. They are based on a procedure for the estimation of impulse response and sequential zero input responses directly from data. The proposed algorithms are more efficient than the existing alternatives that compute the whole Hankel matrix of Markov parameters. It is shown that the computations can be performed on Hankel matrices of the input-output data of various dimensions. By choosing wider matrices, we need persistency of excitation of smaller order. Moreover, this leads to computational savings and improved statistical accuracy when the data is noisy. Using a finite amount of input-output data, the existing algorithms compute finite time balanced representation and the identified models have a lower bound on the distance to an exact balanced representation. The proposed algorithm can approximate arbitrarily closely an exact balanced representation. Moreover, the finite time balancing parameter can be selected automatically by monitoring the decay of the impulse response. We show what is the optimal in terms of minimal identifiability condition partition of the data into “past” and “future”.     

Two-stage bootstrap algorithms for parameter estimation

This paper presents two different algorithms for parameter estimation of dynamic systems. Both algorithms operate in two stages which are coupled together in a bootstrap manner. The effectiveness of the two algorithms is demonstrated by a suitable numerical example. A case study using real daily maximum temperature data of Delhi is also included.     

Entropy-based subspace separation for multiple frequency estimation

A subspace-based algorithm for estimating the order and the frequencies of multiple sinusoids embedded in noise is proposed. The new estimator (referred to as E-MUSIC) uses the entropy of a random variable related to the angles between the signal and noise subspaces as its objective function. Maximizing the entropy tends to achieve uniform angle distribution and thus leads to maximal subspace separation. The entropy-based objective function and the performance of the E-MUSIC algorithm is compared with some reference algorithms in the literature. Simulations which are performed in additive white and colored Gaussian noise show that the E-MUSIC offers an improvement for both model order and multiple frequency estimation. The improvement is more pronounced for high model orders and large SNR values.     

一种完全数据驱动的子空间辨识与鲁棒预测控制器设计

针对线性时变多变量系统,在可能存在输入输出数据噪声的情况下,不需已知系统的先验结构信息,提出一种完全数据驱动的子空间辨识及控制器设计方法.在子空间在线辨识基础上,利用不确定性模型更好地建模被控系统,结合鲁棒控制策略进行预测控制器的设计;将系统建模与鲁棒控制器的设计包含在一个控制系统设计框架内,对模型不确定性具有更好的鲁棒性;最后给出仿真实例验证算法的有效性.     

Criteria for informative experiments with subspace identification

Informative experiments are identification experiments which contain sufficient information for an identification algorithm to discriminate between different models in an intended model set. In this paper, a particular set of identification algorithms, namely subspace based identification, is considered. Criteria for experiments to be informative with these methods in the deterministic setup and the combined deterministic-stochastic setup are presented. It is pointed out that if these criteria are not satisfied, interesting phenomena, in which perfect cancellations of the deterministic components and the stochastic components occur in a subspace projection, may occur. It is further shown that such cancellations can indeed be avoided under mild conditions.     

Unknown disturbance inputs estimation based on a state functional observer design

We consider the problem of function of state plus unknown input estimation of a linear time-invariant system using only the measured outputs. Two reduced-order input estimators built upon a state functional observer are proposed. The first is an extension of a state/input estimator, while the second is based on adaptive observer design technique. The proposed estimator can be designed under less restrictive conditions than those of the previous work, and unlike some of the past studies the proposed observer can be designed for certain nonminimum phase systems.     

Conjugate gradient on Grassmann manifolds for robust subspace estimation

Most geometric computer vision problems involve orthogonality constraints. An important subclass of these problems is subspace estimation, which can be equivalently formulated into an optimization problem on Grassmann manifolds. In this paper, we propose to use the conjugate gradient algorithm on Grassmann manifolds for robust subspace estimation in conjunction with the recently introduced generalized projection based M-Estimator (gpbM). The gpbM method is an elemental subset-based robust estimation algorithm that can process heteroscedastic data without any user intervention. We show that by optimizing the orthogonal parameter matrix on Grassmann manifolds, the performance of the gpbM algorithm improves significantly. Results on synthetic and real data are presented.     

含齿隙双电机伺服系统未知参数的两阶段辨识

针对含齿隙的双电机伺服系统,提出一种两阶段辨识法辨识双电机系统未知参数以及齿隙非线性环节的死区参数.针对电机转动惯量、等效粘性摩擦系数以及齿隙大小未知的情况,运用Legendre多项式将双电机伺服系统中的齿隙模型分段化,根据最小二乘法辨识双电机伺服系统参数.最后,通过仿真验证两阶段辨识法的有效性,验证结果表明,两阶段辨识法能够较准确地辨识电机参数和齿隙参数.     

Two-stage identification of closed-loop systems

A two-stage identification method based on modeling error compensation for systems operating in closed loop is presented. The feedback regulator is assumed linear, time-invariant. The model structure and the identification technique described do not suggest any changes in the feedback regulator or in the plant input. Results of identification based on a simulated process are included.     

Links between PPCA and subspace methods for complete Gaussian density estimation

High-dimensional density estimation is a fundamental problem in pattern recognition and machine learning areas. In this letter, we show that, for complete high-dimensional Gaussian density estimation, two widely used methods, probabilistic principal component analysis and a typical subspace method using eigenspace decomposition, actually give the same results. Additionally, we present a unified view from the aspect of robust estimation of the covariance matrix.     

基于子空间辨识的煤气混合加压过程建模方法

本文针对高炉煤气与焦炉煤气混合加压过程,提出一种基于子空间辨识的过程状态与输出关系建模方法.通过分析过程的强耦合特性,以蝶阀前的高炉煤气压力和流量、焦炉煤气压力和流量为过程状态,混合煤气热值和压力为输出,采用子空间辨识方法建立了一个4输入2输出的关系模型.仿真实验表明,建立的模型有效地反映了过程特性,具有较高的辨识精度.     

A subspace fitting method for identification of linear state-spacemodels

A new method is presented for the identification of systems parameterized by linear state-space models. The method relies on the concept of subspace fitting, wherein an input/output data model parameterized by the state matrices is found that best fits, in the least-squares sense, the dominant subspace of the measured data. Some empirical results are included to illustrate the performance advantage of the algorithm compared to standard techniques     

A subspace algorithm for balanced state space system identification

In an earlier paper by Moonen et at. (1989), an algorithm has been introduced for identifying multivariable linear systems directly from input-output data. This new algorithm falls in the class of so-called subspace methods and resembles impulse response based realization algorithms. In this paper, we extend this algorithm by incorporating a balancing step, such that the identified model is always in balanced coordinates. With this modification, one obtains a data driven counterpart for Kung's realization algorithm     

两阶段多层感知的随机脉冲噪声比例预测

目的 基于卷积神经网络（CNN）在图块级上实现的随机脉冲噪声（RVIN）降噪算法在执行效率方面较经典的逐像素点开关型降噪算法有显著优势,但降噪效果如何取决于能否对降噪图像受噪声干扰程度（噪声比例值）进行准确估计。为此,提出一种基于多层感知网络的两阶段噪声比例预测算法,达到自适应调用CNN预训练降噪模型获得最佳去噪效果的目的。方法 首先,对大量无噪声图像添加不同噪声比例的RVIN噪声构成噪声图像集合;其次,基于视觉码本（visual codebook）采用软分配（soft-assignment）编码法提取并筛选若干能反映噪声图像受随机脉冲噪声干扰程度的特征值构成特征矢量;再次,将从噪声图像上提取的特征矢量及对应的噪声比例分别作为多层感知网络的输入和输出训练噪声比例预测模型,实现从特征矢量到噪声比例值的映射（预测）;最后,采用粗精相结合的两阶段实现策略进一步提高RVIN噪声比例的预测准确性。结果 针对不同RVIN噪声比例的失真图像,从预测准确性、实际降噪效果和执行效率3个方面验证提出算法的性能和实用性。实验数据表明,本文算法在大多数噪声比例下的预测误差小于2%,降噪效果（PSNR指标）较其他主流降噪算法高24 dB,处理一幅大小为512×512像素的图像仅需3 s左右。结论 本文提出的RVIN噪声比例预测算法在各个噪声比例下具有鲁棒的预测准确性,在降噪效果和执行效率两个方面较经典的开关型RVIN降噪算法有显著提升,更具实用价值。