Cross-correlation Estimator Research Articles

A robust correlation receiver for distance estimation

Many methods for distance estimation, such as the ultrasonic pulse-echo method, involve the estimation of a time-of-flight (TOF). In this paper, a signal model is developed that, apart from the TOF, accounts for an unknown, linear frequency dependent distortion as well as for additive noise. We derive a TOF estimator for this model based on the criteria of maximum likelihood. The resulting receiver can be seen as an extension or generalization of the well known cross-correlation, or matched filter, estimator described, e.g., by Nilsson. The novel receiver is found to be more robust against unknown pulse shape distortion than the cross-correlation estimator, giving less biased TOF estimates. Also, bias versus noise sensitivity can be controlled by proper model order selection. >

Implementation of ultrasound time-domain cross-correlation blood velocity estimators.

The implementation of real-time blood velocity estimators using time-domain cross-correlation is investigated. The basic algorithm is presented for doing stationary echo canceling, cross-correlation estimation and subsequent velocity estimation. Sampled data acquired at rates of approximately 20 MHz are used in the algorithm imposing a heavy burden on the signal processing hardware. The algorithm is analyzed with regard to the high sampling frequency, and a method for performing real-time high-speed data movement and cross-correlation is suggested. Implementation schemes based on using the sign of the data as well as the full precision are proposed. From an analysis of the process it is concluded that the sign data implementation can attain real-time processing. This can also be obtained for the full precision data, however, at the expense of using a number of dedicated signal processing chips. Both implementations suggested can handle the estimation of velocities for A-lines acquired from multiple directions.

Stationary echo canceling in velocity estimation by time-domain cross-correlation

The application of stationary echo canceling to ultrasonic estimation of blood velocities using time-domain cross-correlation is investigated. Expressions are derived that show the influence from the echo canceler on the signals that enter the cross-correlation estimator. It is demonstrated that the filtration results in a velocity-dependent degradation of the signal-to-noise ratio. An analytic expression is given for the degradation for a realistic pulse. The probability of correct detection at low signal-to-noise ratios is influenced by signal-to-noise ratio, transducer bandwidth, center frequency, number of samples in the range gate, and number of A-lines employed in the estimation. Quantitative results calculated by a simple simulation program are given for the variation in probability from these parameters. An index reflecting the reliability of the estimate at hand can be calculated from the actual cross-correlation estimate by a simple formula and used in rejecting poor estimates or in displaying the reliability of the velocity estimated.

The effect of frequency dependent scattering and attenuation on the estimation of blood velocity using ultrasound

A comprehensive theoretical performance comparison of the wideband maximum-likelihood (WMLE) and cross-correlation strategies, previously proposed and evaluated for the estimation of blood velocity using ultrasound is presented. It is based on evaluation of the bias, local and global accuracy, and signal-to-noise ratio (SNR) performance. The results show that the intervening medium does not bias either wideband estimation, due to the effect of tracking the scattering target. The presence of intervening tissue actually improves the global accuracy of both wideband estimators, without a significant change in the local accuracy of either wideband estimator. After the transmission of P pulses, a comparison of the performance of the two strategies shows that the cross-correlation estimator requires P(2 ) correlations to achieve performance similar to that of the WMLE with P operations. In addition, the WMLE can increase the effective SNR in comparison with cross correlation.

High-speed template matching algorithm using information of contour points

Template matching is a useful technique for matching images. This paper proposes a high-speed template matching technique which is effective for images that have sharp contours. The method uses only the image contour parts as one-dimensional templates. Although it can retain fine patterns, the data compression ratio and speed are very high. To improve reliability of matching, gray gradient information and intensity of contour points are used. Also, dilation of contours can reduce several errors due to disturbance of the contour or scaling. The algorithm herein can indicate differences between the template and the target image automatically after the alignment of images. The expanded algorithm applying the sequential similarity detection algorithm (SSDA) method also is discussed. Software simulation proved that the algorithm is 10 or 200 times faster than the conventional template matching technique which uses the cross-correlation estimation between two-dimensional (2-D) template and the target image. This algorithm was applied to special hardware. It can align two 512 × 512 pixels images in 40 ms when the size of the search area is 64 × 64.

Efficient multiframe Wiener restoration of blurred and noisy image sequences

Computationally efficient multiframe Wiener filtering algorithms that account for both intraframe (spatial) and interframe (temporal) correlations are proposed for restoring image sequences that are degraded by both blur and noise. One is a general computationally efficient multiframe filter, the cross-correlated multiframe (CCMF) Wiener filter, which directly utilizes the power and cross power spectra of only NxN matrices, where N is the number of frames used in the restoration. In certain special cases the CCMF lends itself to a closed-form solution that does not involve any matrix inversion. A special case is the motion-compensated multiframe (MCMF) filter, where each frame is assumed to be a globally shifted version of the previous frame. In this case, the interframe correlations can be implicitly accounted for using the estimated motion information. Thus the MCMF filter requires neither explicit estimation of cross correlations among the frames nor matrix inversion. Performance and robustness results are given.

Time delay estimation at high signal-to-noise ratio

The estimation of the delay between two signals is examined in the limit of high signal-to-noise ratio (SNR). It is shown that for the case of white noise, cross correlation with no prefiltering approaches the optimal maximum-likelihood (ML) estimator as the SNR grows to infinity. In simulation experiments with SNRs greater than 1, it outperforms the approximate ML estimator, which is based on estimated spectra. Other algorithms, such as generalized cross correlation or parameter estimation algorithms, are shown to be suboptimal at high SNRs.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The accuracy of cross-correlation estimates of quasar emission-line region sizes

The use of cross-correlation analyses of emission-line and optical continuum fluxes to determine broad-line region (BLR) sizes in low-luminosity quasars is examined in detail. Uncertainties associated with this method are discussed, and analytic formulas for estimating errors and determining confidence levels are presented. It is pointed out that systematic correlated errors between continuum and line fluxes are particularly dangerous and can lead to BLR sizes that may be too small. The results of some Monte Carlo simulations which are matched as closely as possible to real situations are presented. They indicate that the very small BLR size estimated by the cross-correlation method is not highly reliable. 15 references.

Experimental evaluation of the performance of pulsed two-color laser-ranging systems

Two-color laser-ranging systems can be used to estimate the atmospheric delay by measuring the difference in propagation times between two optical pulses transmitted at different wavelengths. This paper describes horizontal-path ranging experiments that were conducted using flat diffuse targets and cube-corner reflector arrays. Measurements of the timing accuracy of the cross-correlation estimator, atmospheric delay, received pulse shapes, and signal power spectra are presented. The results are in general agreement with theory and indicate that target speckle can be the dominant noise source when the target is small and is located far from the ranging system or when the target consists of a small number of cube-corner reflectors.

On time delay estimation involving received signals

The estimation of time delay between two received signals is reexamined for the three basic approaches to this problem: 1) phase data, 2) generalized cross correlation, and 3) parameter estimation. For a simple delay problem with short data lengths, arguments are presented to refute the claim that the parameter estimation approach is superior to the usual cross-correlation method. Special consideration is given to the more complex problem of estimating the time delay when signals are received through transmitting media with unknown transfer functions. Although the phase data and cross-correlation methods would generally yield biased estimates in this case, it is verified that positivity and monotonicity of the media impulse response functions are sufficient conditions to assure an unbiased cross-correlation estimate when the source signal is a white process. The problem is then reformulated as a parameter estimation problem, and comparison is made with the simpler generalized cross-correlation method using time limited data.

The automated analysis of data from single ionic channels.

The development of single channel recording has brought with it the need to analyse enormous amounts of data. The data analysis is time consuming and subject to observer biases since the events are random in time and are contaminated with uncorrelated noise. We have developed a heuristic pattern recognition program which identifies with high precision single channel currents and rejects contaminating noise. The program interactively provides for a variety of amplitude and duration measures. Analysis is flexible and rapid: a file containing over 10,000 events can be analysed in under 2 h. Specific detection features include variable lowpass filtering, automatic baseline restoration, and adaptive amplitude thresholds. A record is analysed through duration histograms, binomial estimates of the number of active channels present, cross-correlation estimates between parameters, spectral analysis of events and background noise, and stationarity of mean channel current. The graphic output facilities can plot raw data (after filtering and baseline restoration) with the idealized signal superimposed or with detected events underlined. A batch processing facility has been included to allow processing of data during periods of low computer demand.

Simultaneous estimation of residual static and crossdip corrections

Seismic surveys on land are frequently conducted along nonlinear survey lines. Familiar examples include crooked lines controlled by existing road networks or by surface typography, lines that are otherwise linear but along which shotpoints occasionally must be offset laterally, and intentionally designed three‐dimensional (3-D) or broad‐line surveys. Departures from linear profiles introduce an element of complexity—crossdip—into the problem of estimating residual near‐surface reflection static time corrections (statics). Crossdip is the component of dip normal to the local profile direction. We have incorporated the effect of crossdip into the system of simultaneous equations that model residual static anomalies. The observed traveltimes of all reflections selected for analysis are represented as linear combinations of source and receiver static anomalies, structural shapes, residual normal moveouts, and crossdip terms. The static time components are taken to be surface‐consistent and independent of reflecting horizon, whereas the other solution parameters are subsurface‐consistent and pertain to specific horizons. Unfortunately, the inclusion of crossdip in the equations increases the degree of nonuniqueness of residual statics solutions. Its inclusion, however, is a necessity wherever horizons having differing crossdips are analyzed simultaneously. Such simultaneous analysis often is the best means for upgrading the reliability of the crosscorrelation estimates (i.e., the traveltime observations) upon which all statics are based. Synthetic‐data examples demonstrate the degree to which crossdip estimates and statics estimates can be separated from one another. Although estimates of crossdips are a useful by‐product, the accuracy of the static corrections is considered of prime importance. When critical crossdip terms are ignored in a statics solution, the quality of the common‐depthpoint (CDP) stacks suffer, as shown in comparison processings of field sections. Moreover, crossdip estimates from 3-D or broad‐line surveys are questionable if crossdip and static corrections are not considered in a unified solution.

Effect of Record Length on Noise-Induced Error in the Cross Correlation Estimate

There is a continuing increase in the use of correlation in engineering. In these applications some or all of the signals to be analyzed may be obscured by noise. Since determination of the autocorrelation or cross correlation requires knowledge of the signals for all time, one must use the observed signals to obtain an estimate of the desired correlation function. These estimates, autocorrelograms or crosscorrelograms, are affected when the signal is obscured by noise. A theoretical investigation of the noise-induced error in correlograms is presented. It is shown that the rms error is inversely proportional to the square root of the record length for virtually any noise which might be encountered. This provides a guide for the reduction of the noise error to any desired level. In addition, bounds on the error are determined for some more common types of noise. Experimental results are described which verify the theoretical developments. The theoretical results are applied to a study of the transmission of action potentials through the cockroach ganglion.