一种移动环境下的信噪比估计算法及其在多普勒频移估计中的应用

利用移动信道的功率谱特性,提出了一种基于谱分析的平均信噪比估计算法,其实现可以利用FFT(fastfouriertransform),从而有效节省了运算资源。其次结合噪声环境下多普勒频移的理论偏差,提出了基于信噪比估计的改进方法。计算机仿真表明,在一般通信系统的工作信噪比范围,文章的信噪比估计方法具有较高的估计精度,而且基于信噪比估计的改进多普勒频移估计方法在各种移动速度和信噪比下都表现出较高的估计精度。     

Recursive estimation of two-dimensional processes with application to image processing

A low order quarter-plane-causal recursive model is presented to represent the class of 2-D stationary Gaussian processes with power spectra matrices factorable into a quarter-plane-causal and anti-causal parts. This model is used to develop a technique for obtaining optimal 2-D recursive estimators. The approach taken here is similar to Attasi's [8], with no commutability condition imposed on the model. Circumventing this condition allows the modeling of the 2-D processes to be achieved with fewer parameters, and enables one to find the solutions to the problems of blur and color noise which are inherent in most image degraded images. Some simulated examples illustrate these points.This research was supported in part by the U.S. Army Research Grant DAAG29-79-C-0054 and the National Science Foundation Grant ECS-8011911.     

The design of two-dimensional gradient estimators based onone-dimensional operators

Two-dimensional (2-D) gradient estimators are some of the most useful tools in image processing. A computational procedure for the extension of one-dimensional (1-D) gradient estimators to two dimensions (2-D) is presented. The procedure is equivalent to the surface fitting method. It is, however, simpler in design, as the design is 1-D rather than 2-D. Higher order derivative estimators can also be constructed by the same procedure.     

Monte Carlo extrinsic estimators of manifold-valued parameters

Monte Carlo (MC) methods have become an important tool for inferences in non-Gaussian and non-Euclidean settings. We study their use in those signal/image processing scenarios where the parameter spaces are certain Riemannian manifolds (finite-dimensional Lie groups and their quotient sets). We investigate the estimation of means and variances of the manifold-valued parameters, using two popular sampling methods: independent and importance sampling. Using Euclidean embeddings, we specify a notion of extrinsic means, employ Monte Carlo methods to estimate these means, and utilize large-sample asymptotics to approximate the estimator covariances. Experimental results are presented for target pose estimation (orthogonal groups) and signal subspace estimation (Grassmann manifolds). Asymptotic covariances are utilized to construct confidence regions, to compare estimators, and to determine the sample size for MC sampling     

Characterization and estimation of two-dimensional ARMA models

A class of finite-order two-dimensional autoregressive moving average (ARMA) is introduced that can represent any process with rational spectral density. In this model the driving noise is correlated and need not be Gaussian. Currently known classes of ARMA models or AR models are shown to be subsets of the above class. The three definitions of Markov property are discussed, and the class of ARMA models are precisely stated which have the noncausal and semicausal Markov property without imposing any specific boundary conditions. Next two approaches are considered to estimate the parameters of a model to fit a given image. The first method uses only the empirical correlations and involves the solution of linear equations. The second method is the likelihood approach. Since the exact likelihood function is difficult to compute, we resort to approximations suggested by the toroidal models. Numerical experiments compare the quality of the two estimation schemes. Finally the problem of synthesizing a texture obeying an ARMA model is considered.     

On-line estimation of signal and noise parameters with application to adaptive Kalman filtering

This paper presents two algorithms for on-line estimation of the optimal gain of the Kalman filter applied to sensor signals when the signal-to-noise ratio is unknown. First-order spectra of a pure signal and colored measurement noise have been assumed. The proposed adaptive Kalman filtering algorithms have been tested for various spectra of the pure signal and noise, and for various signal-to-noise ratios. The effect of the length of an adaptation step and a sampling frequency on the mean square errors of the pure signal estimation has also been examined. Although the test have been performed for stationary signals, the algorithms presented can also be used successfully for time-varying sensor signals when the signal-to-noise ratios vary very slowly in comparison with the length of the adaptation step.The results are helpful for designers who synthesize optimal linear digital filters for sensor signals with first-order spectra and colored measurement noise. The estimation error curves presented enable designers to determine the noise reduction attainable for particular applications of the adaptive Kalman filtering algorithms.     

卫星通信中多普勒频偏的预校正

在低轨道卫星通信中，由于多普勒效应,无线电信号会产生频率偏移现象，这为接收机设计带来了一定的困难。一种新方法可用于消除多普勒频偏的影响：根据卫星与地面接收站之间的相对位置和速度，可预先计算出信号的多普勒频偏。据此实时地修正接收机中数字频率合成器输出的本振频率,以达到消除多普勒频偏的目的。     

Comparing between estimation approaches: admissible and dominating linear estimators

We treat the problem of evaluating the performance of linear estimators for estimating a deterministic parameter vector x in a linear regression model, with the mean-squared error (MSE) as the performance measure. Since the MSE depends on the unknown vector x, a direct comparison between estimators is a difficult problem. Here, we consider a framework for examining the MSE of different linear estimation approaches based on the concepts of admissible and dominating estimators. We develop a general procedure for determining whether or not a linear estimator is MSE admissible, and for constructing an estimator strictly dominating a given inadmissible method so that its MSE is smaller for all x. In particular, we show that both problems can be addressed in a unified manner for arbitrary constraint sets on x by considering a certain convex optimization problem. We then demonstrate the details of our method for the case in which x is constrained to an ellipsoidal set and for unrestricted choices of x. As a by-product of our results, we derive a closed-form solution for the minimax MSE estimator on an ellipsoid, which is valid for arbitrary model parameters, as long as the signal-to-noise-ratio exceeds a certain threshold.     

Minimum variance in biased estimation: bounds and asymptotically optimal estimators

We develop a uniform Cramer-Rao lower bound (UCRLB) on the total variance of any estimator of an unknown vector of parameters, with bias gradient matrix whose norm is bounded by a constant. We consider both the Frobenius norm and the spectral norm of the bias gradient matrix, leading to two corresponding lower bounds. We then develop optimal estimators that achieve these lower bounds. In the case in which the measurements are related to the unknown parameters through a linear Gaussian model, Tikhonov regularization is shown to achieve the UCRLB when the Frobenius norm is considered, and the shrunken estimator is shown to achieve the UCRLB when the spectral norm is considered. For more general models, the penalized maximum likelihood (PML) estimator with a suitable penalizing function is shown to asymptotically achieve the UCRLB. To establish the asymptotic optimality of the PML estimator, we first develop the asymptotic mean and variance of the PML estimator for any choice of penalizing function satisfying certain regularity constraints and then derive a general condition on the penalizing function under which the resulting PML estimator asymptotically achieves the UCRLB. This then implies that from all linear and nonlinear estimators with bias gradient whose norm is bounded by a constant, the proposed PML estimator asymptotically results in the smallest possible variance.     

Parameter estimation of two-dimensional moving average randomfields

This paper considers the problem of estimating the parameters of two-dimensional (2-D) moving average random (MA) fields. We first address the problem of expressing the covariance matrix of nonsymmetrical half-plane, noncausal, and quarter-plane MA random fields in terms of the model parameters. Assuming the random field is Gaussian, we derive a closed-form expression for the Cramer-Rao lower bound (CRLB) on the error variance in jointly estimating the model parameters. A computationally efficient algorithm for estimating the parameters of the MA model is developed. The algorithm initially fits a 2-D autoregressive model to the observed field and then uses the estimated parameters to compute the MA model. A maximum-likelihood algorithm for estimating the MA model parameters is also presented. The performance of the proposed algorithms is illustrated by Monte-Carlo simulations and is compared with the Cramer-Rao bound     

A novel method for two-dimensional frequency estimation

This paper proposes a novel solution to two-dimensional (2-D) frequency estimation problems. The solution is applicable to the cases where the data length is much larger in one dimension than the other. The method estimates 2-D frequencies based on several one-dimensional (1-D) frequency estimation processes and hence has a low computational complexity. To avoid resolving close frequencies in 1-D processing, we construct matrices to estimate the linear combinations of the 2-D frequencies. Performance evaluation of this method is presented based on the comparison of the Crame/spl acute/r-Rao bound (CRB) and numerical simulations.     

An efficient algorithm for two-dimensional frequency estimation

This paper presents a computationally efficient eigenstructure-based 2D-MODE algorithm for two-dimensional frequency estimation. We derive the theoretical performance of the 2D-MODE estimator and show that it is asymptotically statistically efficient under either the assumption that the number of temporal snapshots is large or the signal-to-noise ratio is high. Numerical examples showing the performance of this algorithm and comparing it with the computationally efficient subspace rotation algorithms are also given. We show that the statistical performance of the 2D-MODE algorithm is better than that of the subspace rotation methods. The amount of computations required by the former is no more than a few times of that needed by the latter for either small numbers of spatial measurements or a single temporal snapshot, which are the cases of interest herein.     

Cumulant-based LP method for two-dimensional spectral estimation

A cumulant-based linear prediction (CBLP) method for two-dimensional (2-D) spectral estimation is presented. The main idea of the method is to compute the coefficients of two different single-quadrant prediction filters by applying the LP theory to a selected 2-D fourth-order mixed cumulant slice of the noisy signal. These coefficients are employed in formulating two different autoregressive spectral models. Both spectral models are combined to obtain the desired spectral estimate. The effectiveness of the proposed CBLP method is demonstrated through computer simulation     

A two-dimensional Prony's method for spectral estimation

The problem of estimating the parameters of a model for bidimensional data made up by a linear combination of damped two-dimensional sinusoids is considered. Frequencies, amplitudes, phases, and damping factors are estimated by applying a generalization of the monodimensional Prony's method to spatial data. This procedure finds the desired quantities after an autoregressive model fitting to the data, a polynomial rooting, and a least-squares problem solution. The autoregressive models involved have a particular nature that simplifies the analysis. In fact, their characteristic polynomial factors into two parts so that many of their properties can be easily determined. Quick estimates of the parameters computed are found by using standard one-dimensional autoregressive estimation methods. An iterative procedure for refining the autoregressive parameters estimates which gives rise to better frequency estimates is also discussed. Some simulation results are reported     

On the spatially causal estimation of two-dimensional pocesses

Autoregressive-Moving Average (ARMA) dynamic models of two-dimensional bistationary processes are obtained and used to clarify the problem of optimum, recursive, spatially causal estimation of such processes. Two specific methods for the realization of optimum or suboptimum estimators are examined. The first is based on a general dynamic model of two-dimensional processes, identifiable via a variant of the Yule-Walker equations used for the identification of stationary time series. This method is computationally tractable. The second leads to a novel and as yet unsolved factorization problem for bivariate spectra.     

Doppler frequency shift estimation for differentially coherent CPM

A communication scheme based on continuous-phase modulated (CPM) signals used in conjunction with trellis-coded modulation (TCM) is considered. To keep the complexity manageable, a detection scheme based on differential detection of CPM signals is used. Methods that estimate the Doppler-induced frequency shift from the receiver signal are studied. Since differential detection transforms a frequency shift into a phase shift, the phase estimation problem is examined first. Three Doppler frequency estimation schemes that are based on open-loop structures and that are designed to achieve different ranges of Doppler frequencies that can be estimated are introduced. These estimators show different degrees of complexity and (at least for high signal-to-noise ratios) significantly different estimation errors. Their performance is compared by using a simulation approach     

EM-based recursive estimation of channel parameters

Recursive (online) expectation-maximization (EM) algorithm along with stochastic approximation is employed in this paper to estimate unknown time-invariant/variant parameters. The impulse response of a linear system (channel) is modeled as an unknown deterministic vector/process and as a Gaussian vector/process with unknown stochastic characteristics. Using these models which are embedded in white or colored Gaussian noise, different types of recursive least squares (RLS), Kalman filtering and smoothing and combined RLS and Kalman-type algorithms are derived directly from the recursive EM algorithm. The estimation of unknown parameters also generates new recursive algorithms for situations, such as additive colored noise modeled by an autoregressive process. The recursive EM algorithm is shown as a powerful tool which unifies the derivations of many adaptive estimation methods     

Maximum-likelihood estimation of Rician distribution parameters

The problem of parameter estimation from Rician distributed data (e.g., magnitude magnetic resonance images) is addressed. The properties of conventional estimation methods are discussed and compared to maximum-likelihood (ML) estimation which is known to yield optimal results asymptotically. In contrast to previously proposed methods, ML estimation is demonstrated to be unbiased for high signal-to-noise ratio (SNR) and to yield physical relevant results for low SNR     

相机自运动参数的鲁棒性估计

相机自运动估计是视觉导航中的关键技术之一,主要是通过分析相机在不同位置拍摄到的场景图像来获取相机的运动信息.从数学上讲,相机自运动估计已经形成了完备的理论基础,但是由于图像中包含大量的噪声,会使算法的性能大幅度降低,因此,如何提高自运动估计的鲁棒性是当前面临的主要问题.主要研究了基于匹配点对的自运动估计的鲁棒性问题,其核心思想是:同时利用多种算法进行自运动参数估计,从中选择最优的估计结果以提高算法性能.首先利用SIFT特征提出两幅图像中的匹配点对,然后采用一种匹配点对选取策略减小匹配点对的错误率.利用多种方法对基本矩阵进行估计,依据成像约束关系从中选择最优估计,以获得最佳估计结果.最后利用仿真数据和实验图像对算法进行验证,实验结果表明了算法的有效性.     

Splitting and shift of hot magnetophonon resonance peaks in a two-dimensional electron gas

The splitting of the magnetophonon resonance peaks in a two-dimensional electron system is investigated as function of the electric field (or average electron velocity) for different values of the broadening of the Landau levels. We found that for small broadening the maxima in the magnetophonon oscillations are split into two peaks. A new physical interpretation is presented for this splitting which is based on the separate contributions of LO-phonon absorption and emission processes. A shift of the resonance maxima is found when the broadening of the Landau levels is large. A new explanation is given for the apparent temperature and electron density dependence of the optical phonon frequency in heterostructures as determined from magnetophonon resonance experiments. A mechanism is proposed which is able to produce the observed shift in the resonant position and which is consistent with an interaction with the optical phonon mode of the bulk material.