An adaptive ARMA four-line lattice filter for spectral estimationwith frequency weighting

A method for designing an adaptive four-line lattice filter which can perform frequency-weighting spectral estimation, which provides more accurate spectral estimation for some frequency bands than for others, is proposed. Using a suitable frequency-weighting function, denoted as an ARMA (autoregressive moving-average) model, an estimated spectrum is obtained by arbitrarily weighing some frequency bands more heavily than others. if the frequency-weighting function has the property of a low-pass filter, the spectrum of the reference model can be estimated accurately with a reduced ARMA order in the low-frequency band. Spectra of time-varying models can be estimated with an exponentially weighted sliding window, and the input signal of the reference model can be estimated by assumption. The order-update and the time-update recursive formulas and the frequency-weighting method for the filter are described. The algorithm is verified by experimental results     

2D ARMA lattice modelling using two-channel AR lattice approach

A new method to obtain a 2D ARMA lattice model of 2D digital systems using a two-channel AR lattice filter is reported. The approach is based on recently developed orthogonal 2D lattice structures for the AR modelling of random fields     

基于ARMA-AKF的HRG随机误差建模分析

针对半球谐振陀螺(HRG)随机误差影响惯性测量单元测量精度的问题,提出了一种改进的基于自回归滑动平均(ARMA)模型和自适应滤波(AKF)的随机误差处理方法。该文对预处理的数据进行了自相关和偏相关特性分析,判断随机误差的适用模型,以及利用贝叶斯信息准则(BIC)准则估计ARMA模型的阶数,通过长自回归模型计算残差法获取模型参数,引入加权自适应因子在线调整一步预测误差阵和量测噪声矩阵用于改进滤波方程,并比较了5项主要误差系数值。结果表明,改进的算法能够有效抑制随机误差,为HRG的随机误差建模补偿提供了新方法。     

Parametric modeling of somatosensory evoked potentials

In this paper, we examine methods of characterizing somatosensory evoked potentials (SEP's) in both the time and frequency domains. We have found that the truncated impulse response (TIR) method produced an accurate time domain model of the SEP signals at model orders greatly reduced from the original state space matrix. The TIR method was valuable for smoothing signals that were slightly corrupted by noise. In this case, the simulated data sequence was close to the original data sequence in the mean squared error sense. For signals that were greatly corrupted by noise, the TIR method was not able to perform as well. Therefore, the TIR method was not a feature extraction method but was valuable for data simulation. In the frequency domain, we have used the autoregressive moving average model (ARMA) to parameterize the SEP signal. An overdetermined set of Yule-Walker equations was created to determine the autoregressive (AR) parameters of the original data with the model order established by the singular value decomposition. From these AR parameters, a residual time series was generated which was used to find the moving average parameters. The resulting ARMA model was used to produce a simulated data sequence. The frequency domain characteristics of the simulated sequence and the corresponding power spectral density of the ARMA filter were very close to the periodogram of the original data sequence. Accurate parameterization was achieved for the SEP waveforms at low filter lengths.     

Multichannel ARMA modeling by least squares circular latticefiltering

The paper makes an attempt to develop least squares lattice algorithms for the ARMA modeling of a linear, slowly time-varying, multichannel system employing scalar computations only. Using an equivalent scalar, periodic ARMA model and a circular delay operator, the signal set for each channel is defined in terms of circularly delayed input and output vectors corresponding to that channel. The orthogonal projection of each current output vector on the subspace spanned by the corresponding signal set is then computed in a manner that allows independent AR and MA order recursions. The resulting lattice algorithm can be implemented in a parallel architecture employing one processor per channel with the data flowing amongst them in a circular manner. The evaluation of the ARMA parameters from the lattice coefficients follows the usual step-up algorithmic approach but requires, in addition, the circulation of certain variables across the processors since the signal sets become linearly dependent beyond certain stages. The proposed algorithm can also be used to estimate a process from two correlated, multichannel processes adaptively allowing the filter orders for both the processes to be chosen independently of each other. This feature is further exploited for ARMA modeling a given multichannel time series with unknown, white input     

Maximum likelihood estimation of the parameters of nonminimum phaseand noncausal ARMA models

The well-known prediction-error-based maximum likelihood (PEML) method can only handle minimum phase ARMA models. This paper presents a new method known as the back-filtering-based maximum likelihood (BFML) method, which can handle nonminimum phase and noncausal ARMA models. The BFML method is identical to the PEML method in the case of a minimum phase ARMA model, and it turns out that the BFML method incorporates a noncausal ARMA filter with poles outside the unit circle for estimation of the parameters of a causal, nonminimum phase ARMA model     

ARMA implementation of diffraction operators with inverse-rootsingularities

The integral of a time-domain diffraction operator which has an integrable inverse-root singularity and an infinite tail is numerically differentiated to get a truncated digital form of the operator. This truncated difference operator effectively simulates the singularity but is computationally inefficient and produces a convolutional truncation ghost. The authors therefore use a least-squares method to model an equivalent autoregressive moving-average (ARMA) filter on the difference operator. The recursive convolution of the ARMA filter with a wavelet has no truncation ghost and an error below 1% of the peak diffraction amplitude. Design and application of the ARMA filter reduces computer (CPU) time by 42% over that repaired with direct convolution. A combination of filter design at a coarse spatial sampling, angular interpolation of filter coefficients to a finer sampling, and recursive application reduces CPU time by 83% over direct convolution or 80% over Fourier convolution, which also has truncation error     

多通道ARMA信号信息融合Wiener滤波器

应用Kalman滤波方法,基于白噪声估计理论,在线性最小方差最优信息融合准则下,提出了多通道ARMA信号的两传感器信息融合稳态最优Wiener滤波器、平滑器和预报器;给出了最优加权阵和最小融合误差方差阵.与单传感器情形相比,可提高滤波精度.一个雷达跟踪系统的仿真例子说明了其有效性.     

一种ARMA模型的格型迭代递推辨识法

本文针对ARMA模型的格型迭代法,推出了它的递推算法,并针对本算法提出了相应的判价方法.运用它对ARMA模型和时变ARMR模型进行了汁算机模拟瓣识,结果良好.     

多传感器信息融合稳态最优Wiener反卷积滤波器

应用现代时间序列分析方法,基于ARMA新息模型和Lyapunov方程,提出了单通道ARMA信号的多传 感器信息融合稳态最优Wiener反卷积滤波器。它避免了Riccati方程,可用于设计含未知模型参数和含未知噪声方 差系统的自校正信息融合滤波器。一个仿真例子说明了其有效性。     

Lattice methods for spectral estimation

Lattice forms provide convenient parametrization of rational spectra of stationary processes. A comprehensive summary of lattice algorithms for estimating spectral parameters of AR, MA, and ARMA processes is presented. It is shown that various well-known spectral estimation techniques, such as the Maximum Entropy Method (MEM) and Maximum Likelihood Method (MLM), can be efficiently computed from lattice parameters. Algorithms are presented for the autocorrelation, pre-windowed, and covariance methods of forming the sample covariance matrix.     

Synthesis of grating lattice circuits

The realization of high-performance components based on optical infinite impulse response (IIR) filter design theory is desirable for next-generation global optical networks. Previously proposed IIR filter synthesis methods are matrix factorization techniques for a lattice circuit using ring resonators. The size of ring resonator limits the bandwidth of the lattice filters. In this paper, two configurations of grating lattice filters are synthesized by using a scattering matrix representation for the grating. The grating is one of the most powerful optical elements both in fiber optics and photonic integrated circuits. One configuration is a serial grating lattice filter configuration and the other is a parallel grating lattice filter configuration. The actual frequency response of the synthesized grating lattice filter is calculated to show the design limitation due to the frequency response of the element gratings     

Optimal and self-tuning State estimation for singular stochastic systems: a polynomial equation approach

This paper is concerned with the optimal steady-state estimation for singular stochastic discrete-time systems using a polynomial equation approach. The key to the optimal estimation is the calculation of an optimal estimator gain matrix. The main contribution of the paper is the derivation of a simple method for computing the gain matrix. Our method involves solving one simple polynomial equation which is derived from the uniqueness of the autoregressive moving average (ARMA) innovation model. The approach covers prediction, filtering, and smoothing problems. Further, when the noise statistics of the model are not available, self-tuning estimation is performed by identifying one ARMA innovation model.     

Adaptive prediction of an arma lattice

In the letter, based on a modification of a well-known approximate likelihood estimation technique, a one-step-ahead prediction method using an ARMA lattice structure is obtained.     

ARMA Model Order Determination Using Edge Detection: A New Perspective

An edge detection-based approach to estimate the order of an autoregressive moving average (ARMA) model process is presented. The proposed method performs edge detection to select the ARMA order by extracting the outlines of a data covariance matrix derived from the observed data sequence. The method is based on the minimum eigenvalue (MEV) criterion developed by Liang et al., IEEE Trans. Signal Process., 41(10): 3003-3009, 1993. The algorithm transforms the MEV covariance matrix into an image by normalizing and resizing the original covariance matrix. Then, a search is performed to locate changes in the intensity function, i.e., pixels where the brightness changes abruptly. Examples are presented to demonstrate the performance of this algorithm.     

Application of autoregressive moving average parametric modeling in magnetic resonance image reconstruction

The modeling of data is an alternative to conventional use of the fast Fourier transform (FFT) algorithm in the reconstruction of magnetic resonance (MR) images. The application of the FFT leads to artifacts and resolution loss in the image associated with the effective window on the experimentally-truncated phase encoded MR data. The transient error modeling method treats the MR data as a subset of the transient response of an infinite impulse filter (H(z) = B(z)IA(z)). Thus, the data are approximated by a deterministic autoregressive moving average (ARMA) model. The algorithm for calculating the filter coefficients is described. It is demonstrated that using the filter coefficients to reconstruct the image removes the truncation artifacts and improves the resolution. However, determining the autoregressive (AR) portion of the ARMA filter by algorithms that minimize the forward and backward prediction errors (e.g., Burg) leads to significant image degradation. The moving average (MA) portion is determined by a computationally efficient method of solving a finite difference equation with initial values. Special features of the MR data are incorporated into the transient error model. The sensitivity to noise and the choice of the best model order are discussed. MR images formed using versions of the transient error reconstruction (TERE) method and the conventional FFT algorithm are compared using data from a phantom and a human subject. Finally, the computational requirements of the algorithm are addressed.     

Computation of the exact cramer-rao lower bound for 2-D ARMA parameter Estimation-I: the quarter-plane case

A closed-form expression for computing the exact Cramer-Rao lower bound (CRLB) on unbiased estimates of the parameters of a two-dimensional (2-D) autoregressive moving average (ARMA) model is developed. The formulation is based on a matrix representation of 2-D homogeneous Gaussian random process that is generated uniformly from the related 2-D ARMA model. The formulas derived for the exact Fisher information matrix (FIM) are an explicit function of the 2-D ARMA parameters and are valid for real-valued homogeneous quarter-plane (QP) 2-D ARMA random fields, where data are propagated using only the past values. It is noteworthy that our approach is practical especially for quantifying the accuracy of 2-D ARMA parameter estimates realized with short data records. Computer simulations display the behavior of the derived CRLB expression for some QP causal 2-D ARMA processes, as a function of the number of data points. The extension of this algorithm for the nonsymmetric half-plane (NSHP) case will be presented in a subsequent paper.     

A new recursive pseudo least squares algorithm for ARMA filteringand modeling. II

For pt.I see ibid., vol.40, no.11, p.2766-74 (Nov. 1992). A recursive algorithm for ARMA (autoregressive moving average) filtering has been developed in a companion paper. These recursions are seen to have a lattice-like filter structure. The ARMA parameters, however, are not directly available from the coefficients of this filter. The problem of identification of the ARMA model from the coefficients of this filter is addressed here. Two new update relations for certain pseudoinverses are derived and used to obtain a recursive least squares algorithm for AR parameter estimation. Two methods for the estimation of the MA parameters are also presented. Numerical results demonstrate the usefulness of the proposed algorithms     

基于自适应信息融合的导航系统构成与算法研究

由于组合导航系统应用环境的不确定性,给噪声统计特性的准确描述带来困难,这将造成Kalman滤波器不稳定甚至发散,目前常用的解决办法是直接估计系统噪声与量测噪声的方差阵 Q及R ,进行自适应滤波.但方程的增加将使计算量加大、实时性不能保证.本文在对基于信息融合的INS/GPS组合导航系统进行分析和设计的基础上,探讨了通过ARMA模型自适应参数辨识求解可变增益K,从而求出状态估计值的方法,并对辨识误差协方差的防饱和算法进行了研究.计算机仿真结果表明:该算法对提高导航精度和运算速度是行之有效的,所得结论有一定的工程实用价值.     

The generalized lapped pseudo-biorthogonal transform: oversampled linear-phase perfect reconstruction filterbanks with lattice structures

We investigate a lattice structure for a special class of N-channel oversampled linear-phase perfect reconstruction filterbanks with a decimation factor M smaller than N. We deal with systems in which all analysis and synthesis filters have the same finite impulse response (FIR) length and share the same center of symmetry. We provide the minimal lattice factorization of a polyphase matrix of a particular class of these oversampled filterbanks (FBs). All filter coefficients are parameterized by rotation angles and positive values. The resulting lattice structure is able to provide fast implementation and allows us to determine the filter coefficients by solving an unconstrained optimization problem. We consider next the case where we are given the generalized lapped pseudo-biorthogonal transform (GLPBT) lattice structure with specific parameters, and we a priori know the correlation matrix of noise that is added in the transform domain. In this case, we provide an alternative lattice structure that suppress the noise. We show that the proposed systems with the lattice structure cover a wide range of linear-phase perfect reconstruction FBs. We also introduce a new cost function for oversampled FB design that can be obtained by generalizing the conventional coding gain. Finally, we exhibit several design examples and their properties.