Parametric estimation of the orientation of textured planarsurfaces

This paper presents a parametric solution to the problem of estimating the orientation in space of a planar textured surface, from a single, noisy, observed image of it. The coordinate transformation from surface to image coordinates, due to the perspective projection, transforms each homogeneous sinusoidal component of the surface texture into a sinusoid whose frequency is a function of location. The functional dependence of the sinusoid phase in location is uniquely determined by the tilt and slant angles of the surface. Using the phase differencing algorithm we fit a polynomial phase model to a sinusoidal component of the observed texture. Assuming the estimated polynomial coefficients are the coefficients of a Taylor series expansion of the phase, we establish a linear recursive relation between the model parameters and the unknown slant and tilt. A linear least squares solution of the resulting system provides the slant and tilt estimates. To improve accuracy, an iterative refinement procedure is applied in a small neighborhood of these estimates. The performance of the proposed algorithms is evaluated by applying them to images of different planar surfaces, and by comparing their statistical performance with the Cramer-Rao bound. The combined two-stage algorithm is shown to produce estimates that are close to the bound.     

Parameter estimation of 2-D random amplitude polynomial-phasesignals

Phase information has fundamental importance in many two-dimensional (2-D) signal processing problems. In this paper, we consider 2-D signals with random amplitude and a continuous deterministic phase. The signal is represented by a random amplitude polynomial phase model. A computationally efficient estimation algorithm for the signal parameters is presented. The algorithm is based on the properties of the mean phase differencing operator, which is introduced and analyzed. Assuming that the signal is observed in additive white Gaussian noise and that the amplitude field is Gaussian as well, we derive the Cramer-Rao lower bound (CRB) on the error variance in jointly estimating the model parameters. The performance of the algorithm in the presence of additive white Gaussian noise is illustrated by numerical examples and compared with the CRB     

Two-Dimensional Polynomial Phase Signals: Parameter Estimation and Bounds

This paper considers the problem of parametric modeling and estimation of nonhomogeneous two-dimensional (2-D) signals. In particular, we focus our study on the class of constant modulus polynomial-phase 2-D nonhomogeneous signals. We present two different phase models and develop computationally efficient estimation algorithms for the parameters of these models. Both algorithms are based on phase differencing operators. The basic properties of the operators are analyzed and used to develop the estimation algorithms. The Cramer-Rao lower bound on the accuracy of jointly estimating the model parameters is derived, for both models. To get further insight on the problem we also derive the asymptotic Cramer-Rao bounds. The performance of the algorithms in the presence of additive white Gaussian noise is illustrated by numerical examples, and compared with the corresponding exact and asymptotic Cramer-Rao bounds. The algorithms are shown to be robust in the presence of noise, and their performance close to the CRB, even at moderate signal to noise ratios.     

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 simple estimator for frequency and decay rate

A simple, computationally inexpensive algorithm is developed for estimating the frequency and decay rate of a complex exponential. Two iterations of the algorithm attains the Cramer-Rao bound on the variance of the frequency and decay rate estimate for a complex exponential in white Gaussian noise. The algorithm uses an adaptive window that changes its shape with the estimate of the decay rate. Formulas are derived for the bias and variance of the estimator, and its performance is demonstrated in simulations     

Cisoid parameter estimation in the colored noise case: asymptoticCramer-Rao bound, maximum likelihood, and nonlinear least-squares

The problem of estimating the parameters of complex-valued sinusoidal signals (cisoids, for short) from data corrupted by colored noise occurs in many signal processing applications. We present a simple formula for the asymptotic (large-sample) Cramer-Rao bound (CRB) matrix associated with this problem. The maximum likelihood method (MLM), which estimates both the signal and noise parameters, attains the performance corresponding to the asymptotic CRB, as the sample length increases. More interestingly, we show that a computationally much simpler nonlinear least-squares method (NLSM), which estimates the signal parameters only, achieves the same performance in large samples     

Improved estimation of hyperbolic frequency modulated chirp signals

This article deals with parameter estimation of product signals consisting of hyperbolic FM and chirp factors. A computationally simple algorithm that decouples estimation of the chirp parameters from those of the hyperbolic FM part is presented. It relies on a simple data transformation that removes the hyperbolic FM component, leaving one with the simpler problem of estimating chirp parameters. For the latter, the high-order ambiguity function (HAF) is adopted. Schemes for estimating the hyperbolic FM parameter are also proposed. The method improves on existing approaches and is shown to provide performance close to the Cramer-Rao bound     

Estimating the frequencies of two sinusoids using only the phaseangles of complex-valued data

The problem of estimating the frequencies of two complex sinusoids using only the phase data is addressed. Under the assumption that the amplitudes of the two signals are not equal, a computationally efficient approximate maximum likelihood estimation (AMLE) is obtained. This AMLE uses only the phase angles of the complex-valued data to estimate frequencies and uses the envelope data to resolve an inherent algebraic sign ambiguity in the difference frequency. At moderately high SNRs, satisfactory results are obtained from computer simulations. The mean-square errors of the estimates are compared with the corresponding values of the Cramer-Rao lower bounds (CRLBs)     

Performance analysis of spatial smoothing with interpolated arrays

The interpolated spatial smoothing algorithm is a computationally efficient method for estimating the directions of arrival (DOAs) of signals, some of which may be perfectly correlated. It extends the spatial smoothing method to arbitrary array geometries. A statistical performance analysis of the algorithm is presented. Closed-form expressions for the covariance matrix of the DOA estimation errors are derived using a perturbation analysis. Evaluating these expressions for specific cases and comparing them to the Cramer-Rao lower bound for the DOA estimates provides insight into the statistical efficiency of this algorithm. The formulas for the error covariance are quite general and can be specialized to provide results for other DOA estimation algorithms as well     

PERFORMANCE ANALYSIS OF THE MUSIC ALGORITHM IN THE PRESENCE OF AMPLITUDE AND PHASE ERROR

This paper presents the performance analysis of the MUSIC algorithm in the presence of channel amplitude and phase Error. Theoretical expression for the error of DOA estimating with MUSIC algorithm and Cramer-Rao bound are derived. It is compared with simulations performed for some representative cases. The results of theoretical expression and simulation show that existence of these errors will increase the error of DOA estimating and degrade its performance.     

Computationally efficient maximum likelihood estimation ofstructured covariance matrices

By invoking the extended invariance principle (EXIP), we present herein a computationally efficient method that provides asymptotic (for large samples) maximum likelihood (AML) estimation for structured covariance matrices and is referred to as the AML algorithm. A closed-form formula for estimating the Hermitian Toeplitz covariance matrices that makes AML computationally simpler than most existing Hermitian Toeplitz matrix estimation algorithms is derived. Although the AML covariance matrix estimator can be used in a variety of applications, we focus on array processing. Our simulation study shows that AML enhances the performance of angle estimation algorithms, such as MUSIC, by making them very close to the corresponding Cramer-Rao bound (CRB) for uncorrelated signals. Numerical comparisons with several structured and unstructured covariance matrix estimators are also presented     

高密度全场主动离焦三维测量的精度分析

向物体投射正交正弦光栅或正弦光栅,都能实现我们提出的高密度全场离焦三维测量,实验发现测量精度依赖于投射模式和物体毒面纹理。计算机模拟显示物体深度测量精度与物体纹理的调制度、频率和投射光栅方向有关。对各种纹理,正交正弦光栅投射的测量精度都高于正弦光栅投射的测量精度。在相同实验条件下,正交正弦光栅和正弦光栅投射的弱纹理表面的深度测量均方误差分别为0．18mm和0．25mm,较强纹理表面的均方误差为0．35ram和0．54mm。     

The effects of phase on high-resolution frequency estimators

Several different ways in which the initial phase differences between two closely spaced sinusoids manifests itself, e.g., in the singular values of the data matrix, the angles between signal vectors, and the Cramer-Rao bound, are described. A closed-form expression for the singular values of the data matrices used in subspace-based algorithms and an expression for the angle between the signal components are presented. Based on these expressions, conjectures are made regarding the effect of the relative phase difference between signal components on the resolving ability of subspace-based techniques. The behavior of the Cramer-Rao bound for the two-complex-sinusoid case is examined as a function of phase difference. Predictions are made as to the effect of this behavior on expected algorithm performance as a function of the phase difference. Empirical results that validate the prediction are provided     

On periodic pulse interval analysis with outliers and missingobservations

Analysis of periodic pulse trains based on time of arrival is considered, with perhaps very many missing observations and contaminated data. A period estimator is developed based on a modified Euclidean algorithm. This algorithm is a computationally simple, robust method for estimating the greatest common divisor of a noisy contaminated data set. The resulting estimate, although it is not maximum likelihood, is used as initialization in a three-step algorithm that achieves the Cramer-Rao bound (CRB) for moderate noise levels, as shown by comparing Monte Carlo results with the CRBs. This approach solves linear regression problems with missing observations and outliers. Comparisons with a periodogram approach based on a point process model are shown. An extension using multiple independent data records is also developed that overcomes high levels of contamination     

DS-CDMA synchronization in time-varying fading channels

The problem of estimating propagation delays of the transmitted signals in a direct-sequence code-division multiple-access (DS-CDMA) system operating over fading channels is considered. Even though this study is limited to the case when the propagation delays are fixed during the observation interval, the channel gain and phase are allowed to vary in time. Special attention is given to the near-far problem which is catastrophic for the standard acquisition algorithm. An estimator based on subspace identification techniques is proposed, and the Cramer-Rao bound, which serves as an optimality criterion, is derived. The Cramer-Rao bound is shown to be independent of the near-far problem, which implies that there is no fundamental reason for propagation delay estimators to be near-far limited. Furthermore, the proposed algorithm is experimentally shown to be robust against the near-far problem     

Estimation of Intracellular Potentials from Evoked Neural Pulse Trains

An algorithm is presented for estimating the time course of intracellular generator potentials on the basis of the times of occurrence of evoked neural impulses, under conditions of external sinusoidal stimulation, and assuming SS-IPFM encoding. Recorded neural pulses are applied to the output of a theoretical SS-IPFM encoder (``in reverse') and a least-squares criterion is adopted for estimating the input sinusoid and its harmonics which would have given rise to the same train of pulses. Illustrative simulation examples of the algorithm are given, and its practical applications are discussed.     

Maximum likelihood estimation and Cramer-Rao bounds for directionof arrival parameters of a large sensor array

A maximum likelihood (ML) method is developed for estimation of direction of arrival (DOA) and associated parameters of narrowband signals based on the Taylor's series expansion of the inverse of the data covariance matrix R for large M, M specifying number of sensors in the array. The stochastic ML criterion function can thus be simplified resulting in a computationally efficient algorithm for DOA estimation. The more important result is the derivation of asymptotic (large M) expressions for the Cramer-Rao lower bound (CRB) on the covariance matrix of all unknown DOA angles for the general D source case. The derived bound is expressed explicitly as a function of snapshots, signal-to-noise ratio (SNR), sensors, separation, and correlation between signal sources. Using the condition of positive definiteness of the Fisher information matrix a resolution criterion is proposed which gives a tight lower limit on the minimum resolvable angle     

Estimation of amplitude and phase parameters of multicomponentsignals

This paper considers the problem of estimating signals consisting of one or more components of the form a(t)e/sup jφ(t/), where the amplitude and phase functions are represented by a linear parametric model. The Cramer-Rao bound (CRB) on the accuracy of estimating the phase and amplitude parameters is derived. By analyzing the CRB for the single-component case, if is shown that the estimation of the amplitude and the phase are decoupled. Numerical evaluation of the CRB provides further insight into the dependence of estimation accuracy on signal-to-noise ratio (SNR) and the frequency separation of the signal components. A maximum likelihood algorithm for estimating the phase and amplitude parameters is also presented. Its performance is illustrated by Monte-Carlo simulations, and its statistical efficiency is verified     

Range-velocity estimation of multiple targets in randomised stepped-frequency radar

A novel algorithm for estimating the ranges and velocities of multiple moving targets in randomised stepped-frequency pulse-train radar is presented. By using the iterative alternating projection technique, this algorithm can achieve high range-velocity resolution and estimation accuracy close to the Cramer-Rao bounds. The sidelobe pedestal problem of randomised stepped-frequency waveforms can also be mitigated. The effectiveness of the algorithm is illustrated with simulation results.     

一种基于相关系数的频率估计算法

针对单点频信号,基于相关系数,在现有频率估计方法的基础上,提出了一种新的频率估计算法,称之为相关测频算法。该方法在FFT的基础上,结合相关系数进行估计。理论研究和仿真分析表明:当被估计信号的信噪比较大时,相关测频算法的估计误差接近Cramer-Rao下界。与迭代插值FFT估计算法和改进Rife算法相比,相关测频算法的估计精度略低,但计算量较低,适合工程应用。