Amplitude estimation of rectangular narrow-band radio pulse with unknown duration and initial phase

This study investigates algorithms for the estimation of amplitude of the radio signal with rectangular envelope and unknown duration and initial phase. The synthesis and analysis of quasi-likelihood and quasi-coherent estimation algorithm have been performed. This algorithm implies that the unknown duration and initial phase are replaced with certain expected values of these parameters. The loss in accuracy of amplitude estimation owing to the a priori lack of knowledge of the duration and the initial phase is analyzed. The quasi-likelihood noncoherent algorithm for amplitude estimation with the initial phase adaptation is synthesized and its statistical characteristics such as the estimate bias and variance are determined. The relationships of the loss in estimation accuracy owing to the a priori lack of knowledge of signal duration are derived. The maximum likelihood algorithm for amplitude estimation was synthesized and analyzed. This algorithm implies that the unknown duration and the initial phase are replaced with their maximum likelihood estimates. The gain in accuracy of the maximum likelihood estimate as compared to the quasi-likelihood ones was investigated. It is shown that a priori lack of knowledge of the signal duration does not affect asymptotically the accuracy of maximum likelihood estimate of amplitude at large values of signal-to-noise ratio.     

Estimation of the optical pulse duration with rectangular intensity profile of unknown height

The quasi-likelihood and maximum likelihood algorithms of duration estimation have been synthesized and analyzed. The losses in accuracy of quasi-likelihood estimate caused by a priori lack of knowledge of pulse intensity were also found. The accuracy of the maximum likelihood estimate of duration was found to be asymptotically invariant to the presence of a priori information about the pulse intensity.     

Maximum Likelihood Estimate of the Arrival Time of Ultra-Wideband Quasi-Radio Signal with Unknown Amplitude and Phase

The maximum likelihood algorithm for estimating the arrival time of ultra-wideband quasi-radio signal with unknown amplitude and phase has been synthesized. The duration of the specified signal can amount to several periods or a fraction of harmonic oscillation period. The realization of maximum likelihood algorithm (ML) for estimating the arrival time of ultra-wideband quasi-radio signal is shown to be appreciably more complex than the realization of ML algorithm for estimating the arrival time of narrowband radio signal. The probability of reliable estimate, bias and scattering of ML estimate of the arrival time of ultra-wideband quasi-radio signal have been found with due regard for anomalous errors making it possible to investigate its threshold properties. The computer methods of statistical simulation were used to determine the performance efficiency of the synthesized algorithm of ML estimate and the limits of the application scope of obtained asymptotically exact (with the rise of signal-to-noise ratio) formulas for the characteristics of time arrival estimate of ultra-wideband quasi-radio signal with unknown amplitude and phase.     

Estimation of duration of the rectangular optical pulse with unknown background intensity

The quasi-likelihood and asymptotically maximum likelihood algorithms of duration estimation have been synthesized and analyzed. The losses in estimation accuracy caused by a priori lack of knowledge of background intensity were also found.     

Estimation of ultrawideband quasi-radio signal duration

Quasi-likelihood and maximum likelihood algorithms of duration estimation for ultra-wideband quasi-radio signal of arbitrary shape with unknown amplitude and initial phase, influenced by additive Gaussian white noise, are synthesized. It was considered that conditions of relatively narrow band of received signal are not satisfied and its duration can constitute only several periods or a fraction of period of harmonic oscillation. It is shown that the structure of the algorithm for duration estimation of ultra-wideband quasi-radio signal is significantly different from the structure of duration estimation algorithm for narrowband radio signal. Relative bias and variance are determined as the statistical characteristics of synthesized duration estimates. The influence of unknown amplitude and initial phase on the accuracy of duration estimation is investigated. Quantitative limits for relation of signal bandwidth to its center frequency are formulated, such that the classical solution of the problem of duration estimation for narrowband radio signal possesses the required accuracy.     

Characteristics of estimating the amplitude of ultrawideband quasi-radio signal

Thesynthesis and analysis of the maximum likelihood algorithm for estimating the amplitude of ultrawideband quasi-radio signal with unknown amplitude and phase have been performed. The duration of the specified signal can amount to several periods or a fraction of the period of harmonic oscillation. The characteristics of the classical maximum likelihood estimate of the amplitude of a narrow-band radio signal were found while receiving an ultrawideband quasi-radio signal. The conditions of applicability of the model of narrow-band radio signal were defined for solving the problem of amplitude estimation with the specified accuracy.     

Phase estimation characteristics of ultra-wideband quasi-radio signal

Synthesis and analysis of the maximum likelihood algorithm for estimating the phase of ultra-wideband quasi-radio signal with unknown amplitude and phase are performed. Duration of the specified signal may amount to several periods or a fraction of the period of harmonic oscillation. Characteristics of the classical maximum likelihood phase estimate of a narrow-band radio signal are found when receiving an ultra-wideband quasi-radio signal. Applicability conditions of narrow-band radio signal model are defined for solving the problem of phase estimation with the specified accuracy.     

Efficiency of estimating duration of a signal with unknown amplitude

Quasi-likelihood and maximum likelihood algorithm for estimating duration of a signal with arbitrary share and unknown amplitude are synthesized. Operation efficiency characteristics for the synthesized algorithms are determined. Operation of the synthesized algorithms is verified and applicability limits for asymptotic expressions are obtained using computer emulation     

Estimation of the radio pulse duration with unknown phase

Quasi-likelihood and maximum likelihood algorithms for estimating the duration of a radio signal having arbitrary waveform and unknown phase were synthesized. Asymptotically exact characteristics of the estimates were also found.     

Maximum likelihood analysis of cardiac late potentials

This study presents a new time-domain method for the detection of late potentials in individual leads. Basic statistical properties of the ECG samples are modeled in order to estimate the amplitude and duration of late potentials. The signal model accounts for correlation in both time and across the ensemble of beats. Late potentials are modeled as a colored process with unknown amplitude which is disturbed by white, Gaussian noise. Maximum likelihood estimation is applied to the model for estimating the amplitude of the late potentials. The resulting estimator consists of an eigenvector-based filter followed by a nonlinear operation. The performance of the maximum likelihood procedure was compared to that obtained by traditional time-domain analysis based on the vector magnitude. It was found that the new technique yielded a substantial improvement of the signal-to-noise ratio in the function used for endpoint determination. This improvement leads to a prolongation of the filtered QRS duration in cases with late potentials     

Array signal Processing in the known waveform and steering vector case

The amplitude estimation of a signal that is known only up to an unknown scaling factor, with interference and noise present, is of interest in several applications, including using the emerging quadrupole resonance (QR) technology for explosive detection. In such applications, a sensor array is often deployed for interference suppression. This paper considers the complex amplitude estimation of a known waveform signal whose array response is also known a priori. Two approaches, viz., the Capon and the maximum likelihood (ML) methods, are considered for the signal amplitude estimation in the presence of temporally white but spatially colored interference and noise. We derive closed-form expressions for the expected values and mean-squared errors (MSEs) of the two estimators. A comparative study shows that the ML estimate is unbiased, whereas the Capon estimate is biased downwards for finite data sample lengths. We show that both methods are asymptotically statistically efficient when the number of data samples is large but not when the signal-to-noise ratio (SNR) is high. Furthermore, we consider a more general scenario where the interference and noise are both spatially and temporally correlated. We model the interference and noise vector as a multichannel autoregressive (AR) random process. An alternating least squares (ALS) method for parameter estimation is presented. We show that in most cases, the ALS method is superior to the model-mismatched ML (M/sup 3/L) method, which ignores the temporal correlation of the interference and noise.     

Amplitude estimation of signal with unknown duration

Quasilikelihood and maximum likelihood algorithms for estimating the amplitude of arbitrary waveform signal with unknown duration have been synthesized. Characteristics of the synthesized algorithms have been also found.     

Coordinate estimation of the image with unknown intensity and area

The synthesis and analysis of the quasi-likelihood and maximum likelihood algorithms have been made for estimating image coordinates. The loss in accuracy of the quasi-plausible estimate as compared with the accuracy of the maximum likelihood estimate has been found.     

Estimating the Instants of Appearance and Disappearance of an Optical Pulse with the Rectangular Intensity Profile of an Unknown Height

The quasi-likelihood, maximum-likelihood, and quasi-optimal algorithms for estimating the instants of appearance and disappearance of an optical pulse with the rectangular intensity profile of an unknown height are synthesized and analyzed. The losses in estimation accuracy due to the a priori unknown intensity of the optical pulse are found.     

Quasiprobable estimation of arrival instant of finite signal

An algorithm, synthesized for some predictable signal’s form, is used to estimate the arrival instant of a signal having a priori unknown form. Asymptotically exact expressions against a background of Gaussian white influence, when signal-to-noise ratio is growing, were determined. Computer-aided simulation of the synthesized algorithm is carried out.     

Markov-based eigenanalysis method for frequency estimation

This paper proposes an eigenanalysis-based method for estimating the frequencies of complex-valued sine waves. The basic idea behind this method consists of using a set of linearly independent vectors that are orthogonal to the signal subspace spanned by the principal eigenvectors of the data covariance matrix. Exploiting that orthogonality condition gives an overdetermined system of linear equations, the unknown parameters of which are uniquely related to the frequencies. Analytical expressions are derived for the covariances of the equation errors in the sample version of the aforementioned linear system of equations. Based on these expressions a Markov-like estimate of the unknown parameters is introduced, which asymptotically (with respect to either the number of data samples or the signal-to-noise ratio) provides the minimum variance frequency estimates in a fairly large class of consistent estimators. The paper includes Monte-Carlo simulations that support the theoretical analysis results and show that those results may apply to scenarios with rather low values of the number of data samples and the signal-to-noise ratio     

Threshold parameter estimation in nonadditive non-Gaussian noise

Threshold or weak-signal locally optimum Bayes estimators (LOBEs) of signal parameters, where the observations are an arbitrary mixture of signal and noise, the latter being independent, are first derived for “simple” as well as quadratic cost functions under the assumption that the signal is present a priori. It is shown that the desired LOBEs are either a linear (simple cost function) or a nonlinear (quadratic cost function) functional of an associated locally optimum and asymptotically optimum Bayes detector. Second, explicit classes of (threshold) optimum estimators are obtained for both cost functions in the coherent as well as in the incoherent reception modes. Third, the general results are applied to amplitude estimation, where two examples are considered: (1) coherent amplitude estimation in multiplicative noise with simple cost function (SCF) and (2) incoherent amplitude estimation with quadratic cost function (QFC) of a narrowband signal arbitrarily mixed with noise. Moreover, explicit estimator structures are given together with desired properties (i.e. efficiency of the unconditional maximum likelihood (ML) estimator) and Bayes' risks. These properties are obtained by employing contiguity-a powerful concept in modern statistics-implied by the locally asymptotically normal character of the detection algorithms     

Cramer-Rao bounds and maximum likelihood estimation for randomamplitude phase-modulated signals

The problem of estimating the phase parameters of a phase-modulated signal in the presence of colored multiplicative noise (random amplitude modulation) and additive white noise (both Gaussian) is addressed. Closed-form expressions for the exact and large-sample Cramer-Rao Bounds (CRBs) are derived. It is shown that the CRB is significantly affected by the color of the modulating process when the signal-to-noise ratio (SNR) or the intrinsic SNR is small. Maximum likelihood type estimators that ignore the noise color and optimize a criterion with respect to only the phase parameters are proposed. These estimators are shown to be equivalent to the nonlinear least squares estimators, which consist of matching the squared observations with a constant amplitude phase-modulated signal when the mean of the multiplicative noise is forced to zero. Closed-form expressions are derived for the efficiency of these estimators and are verified via simulations     

相参短脉冲辐射源双站TDOA/FDOA直接定位算法

当目标辐射源脉冲信号持续时间较短时, FDOA引起的信号脉内相位变化很小,几乎可以忽略,无法实现TDOA和FDOA联合定位。针对上述问题,通过对相参辐射源信号脉冲间相位补偿,提出了一种利用信号的TDOA和FDOA信息的最大似然直接定位算法。考虑采用运动双站对固定目标辐射源定位情况,以确定性未知信号为模型,推导了高斯白噪声背景下相参脉冲信号联合定位的最大似然估计算法,仿真分析验证了该算法可以利用双站实现对短脉冲相参辐射源的TDOA/FDOA定位。此外,还推导了相参脉冲联合定位的CRLB,表明所提算法在常规信噪比下定位精度可以达到CRLB。      

A diagonal growth curve model and some signal-processing applications

We consider a variation of the growth-curve (GC) model, referred to as the diagonal growth-curve (DGC) model, where the steering vectors and waveforms are both known and the complex amplitude matrix is constrained to be diagonal. A closed-form approximate maximum likelihood (AML) estimator for this model is derived based on the maximum likelihood principle. We analyze the statistical properties of this method theoretically and show that the AML estimate is unbiased and asymptotically statistically efficient for a large snapshot number. Via several numerical examples in array signal processing and spectral analysis, we also show that the proposed AML estimator can achieve better estimation accuracy and exhibit greater robustness than the best existing methods.