An adaptive and computationally efficient algorithm for parameters estimation of superimposed exponential signals with observations missing randomly

Compared with microwave synthetic aperture radar (SAR), terahertz SAR (THz-SAR) is easier to achieve ultrahigh-resolution image due to its higher frequency and shorter wavelength. However, higher carrier frequency makes THz-SAR image quality very sensitive to high-frequency vibration error of motion platform. Therefore, this paper proposes a novel high-frequency vibration error estimation and compensation algorithm for THz-SAR imaging based on local fractional Fourier transform (LFrFT). Firstly, the high-frequency vibration error of the motion platform is modeled as a simple harmonic motion and THz-SAR echo signal received in each range pixel can be considered as a sinusoidal frequency modulation (SFM) signal. A novel algorithm for the parameter estimation of the SFM signal based on LFrFT is proposed. The instantaneous chirp rate of the SFM signal is estimated by determining the matched order of LFrFT in a sliding small-time window and the vibration acceleration is obtained. Hence, the vibration frequency can be estimated by the spectrum analysis of estimated vibration acceleration. With the estimated vibration acceleration and vibration frequency, the SFM signal is reconstructed. Then, the corresponding THz-SAR imaging algorithm is proposed to estimate and compensate the phase error caused by the high-frequency vibration error of the motion platform and realize high-frequency vibration error estimation and compensation for THz-SAR imaging. Finally, the effectiveness of the novel algorithm proposed in this paper is demonstrated by simulation results.

Parameter estimation for a class of stochastic differential equations driven by small stable noises from discrete observations

A note on least-squares estimates from likelihood ratios

In this paper, we consider the superimposed exponential signals in zero-mean multiplicative and additive noise when all the noise are independently and identically distributed. We use a three-step iterative procedure to estimate the frequencies of the considered model. It is observed that the estimators are consistent and work quite well in terms of biases and mean square errors. Moreover, the convergence rate of the estimators attains O p (N −3/2), which is the best convergence rate in the case of only additive noise and constant amplitude.

Optimal detection of a known FSK-modulated binary signal in additive white Gaussian noise using a matched filter receiver requires knowledge of second-order noise statistics. The dependence on noise statistics causes the probability of detection to be sensitive to errors in the noise variance value. This makes the optimal scheme of limited use in situations where the noise statistics are unknown and cannot be estimated reliably. We propose an alternative approach, which has a more easily calculated test statistic than the optimal method and yields a constant false detection rate, regardless of noise statistics. While this approach has sub-optimal detection probability, it is significantly advantageous in applications where a primary interest is to limit false detections strictly. In addition, it allows one to determine easily the required detection length (in symbols) to achieve a desired performance level.

Audio based authentication has been proposed to be used as a second or third factor of authentication in Multi-Factor Authentication (MFA). Previous audio fingerprinting work has mostly used tonal frequencies which are not ideal in authentication as humans do not like sharp tonal frequencies as audio. This work investigates the usage of music as the audio for authentication instead of tonal frequencies. We also compare music with Dual Tone Multi Frequency (DTMF) audio. We present the results of our experimentation over source audio, feature extraction and performance under noise in this paper. The results of our experiments show that music in fact offers advantages such as better accuracy and better performance under noise in addition to sounding pleasant.KeywordsAuthenticationFingerprintingAudioMusicMobile devices

Convergence properties of empirical risk minimizers can be conveniently expressed in terms of the associated population risk. To derive bounds for the performance of the estimator under covariate shift, however, pointwise convergence rates are required. Under weak assumptions on the design distribution, it is shown that least squares estimators (LSE) over 1-Lipschitz functions are also minimax rate optimal with respect to a weighted uniform norm, where the weighting accounts in a natural way for the non-uniformity of the design distribution. This implies that although least squares is a global criterion, the LSE adapts locally to the size of the design density. We develop a new indirect proof technique that establishes the local convergence behavior based on a carefully chosen local perturbation of the LSE. The obtained local rates are then applied to analyze the LSE for transfer learning under covariate shift.

Two methods are considered for comparing the asymptotic efficiencies of robust detectors in the problem of detecting coherent signals in additive noise. The first of these methods considers the relative detector sample sizes for a fixed value of the detector power, while the second method considers the relative detector sample sizes for a fixed value of the local detector power, as measured by the local values of the slopes or curvatures of the detector power functions. These measures of efficiency are variations of the asymptotic relative efficiencies (AREs) of Pitman and Blomqvist, respectively, adapted to the robust detection problem. These two approaches are used to compare the performance of robust nonlinear correlators to that of robust M-detectors in both one-sided and two-sided detection problems, under an epsilon -contaminated mixture model for uncertainty in the noise statistics. Both measures of ARE, fixed-power and fixed-local-power, indicate that the robust nonlinear correlator outperforms the robust M-detector for this type of model. However, the fixed-local-power ARE is shown to be more useful in measuring the degree to which the robust nonlinear correlator is more efficient. >

This article presents a very efficient SLAM algorithm that works by hierarchically dividing a map into local regions and subregions. At each level of the hierarchy each region stores a matrix representing some of the landmarks contained in this region. To keep those matrices small, only those landmarks are represented that are observable from outside the region. A measurement is integrated into a local subregion using O(k2) computation time for k landmarks in a subregion. When the robot moves to a different subregion a full least-square estimate for that region is computed in only O(k3 log n) computation time for n landmarks. A global least square estimate needs O(kn) computation time with a very small constant (12.37 ms for n = 11300). The algorithm is evaluated for map quality, storage space and computation time using simulated and real experiments in an office environment.

A method is proposed to improve the accuracy of the parameter estimates of highly damped sinusoidal signals in additive noise. The method first utilizes singular value decomposition (SVD) of the signal matrix to reduce the noise effect, then based on the noise-reduced signals the weighted sum of squared errors is minimized using an adaptive lattice filter algorithm to estimate the parameters in the backward linear prediction model. In the case of large damping factors, the experimental results show that the proposed method gives more accurate estimates than the eigenvector method. >

In the application of extreme value analysis it is usually assumed that the size of the samples from which the extreme values are obtained is sufficiently large for the asymptotic extreme value distribution to be used. The necessary sample size depends upon the population distribution and this is generally not known; but assuming a Weibull distribution, which is often fitted to wind speed and wave height data, it is shown that the rate of convergence is rapid and that the asymptotic distribution may be used for a sample size as small as ten. An ‘exponential approximation’ for the distribution of maxima is sometimes confused with the extreme value distribution. This approximate form is derived for the Weibull distribution and the essential difference between it and the asymptotic extreme value distribution is explained.

We show that the concept of correlation detection of deterministic signals in additive Gaussian noise can be extended in a natural manner to the detection of signals that are transmitted through a "Gaussian" random channel besides being corrupted by additive Gaussian noise. Such situations are typical in communication over scatter-multipath channels (with or without a specular component). In the deterministic case, the receiver essentially crosscorrelates the received signal with the signal before the additive noise was introduced. When a random channel is present, however, this latter signal, i.e., the output of the random channel, is not known at the receiver, However, knowing the statistics of the channel and the noise, the receiver can make an estimate of it from the received signal on the hypothesis that a particular signal was transmitted. The optimum receiver then crosscorrelates this estimate with the received signal.

Chemical shift based methods are often used to achieve uniform water-fat separation that is insensitive to Bo inhomogeneities. Many spin-echo (SE) or fast SE (FSE) approaches acquire three echoes shifted symmetrically about the SE, creating time-dependent phase shifts caused by water-fat chemical shift. This work demonstrates that symmetrically acquired echoes cause artifacts that degrade image quality. According to theory, the noise performance of any water-fat separation method is dependent on the proportion of water and fat within a voxel, and the position of echoes relative to the SE. To address this problem, we propose a method termed "iterative decomposition of water and fat with echo asymmetric and least-squares estimation" (IDEAL). This technique combines asymmetrically acquired echoes with an iterative least-squares decomposition algorithm to maximize noise performance. Theoretical calculations predict that the optimal echo combination occurs when the relative phase of the echoes is separated by 2pi/3, with the middle echo centered at pi/2+pik (k=any integer), i.e., (-pi/6+pik, pi/2+pik, 7pi/6+pik). Only with these echo combinations can noise performance reach the maximum possible and be independent of the proportion of water and fat. Close agreement between theoretical and experimental results obtained from an oil-water phantom was observed, demonstrating that the iterative least-squares decomposition method is an efficient estimator.

The concept of the modulation transfer function (MTF) can be successfully applied to evaluating the quality of speech transmission in room acoustics (noisy reverberant environments) as functions of reverberation (reverberation time) and additive noise (signal to noise ratio) (Houtgast and Steeneken, J. Acoust. Soc. Am., 77, 1069-1077, 1985). This paper proposes a method of restoring the power envelope from noisy reverberant speech based on the MTF concept. The proposed method does not need the impulse response and noise conditions in room acoustics to be measured to enhance speech. The proposed approach suppresses the effects of reverberation and noise on the power envelopes by restoring the smeared MTF. We carried out massive simulations of noise-suppression and dereverberation on noisy reverberant speech to objectively evaluate the proposed method. The results revealed that the proposed method could simultaneously work well with both the suppression of noise and dereverberation. We further tested the proposed method as a front-end processor for ASR systems in noisy reverberant environments, and compared it with other methods (MFCC, CMN, spectral subtraction, and RASTA filtering on a constant-bandwidth filterbank). The results demonstrated that the improvement in recognition with the proposed method was more effective than that in extremely noisy reverberant environments.

The errors-in-variables (EIV) model is a nonlinear model, the parameters of which can be solved by singular value decomposition (SVD) method or the general iterative algorithm. The existing formulae for covariance matrix of total least squares (TLS) parameter estimates don't fully consider the randomness of quantities in iterative algorithm and the biases of parameter estimates and residuals. In order to reflect more reasonable precision information for TLS adjustment, the derivative-free unscented transformation with scaled symmetric sampling strategy, i.e. scaled unscented transformation (SUT), is introduced and implemented. In this contribution, we firstly discuss the existing various solutions of TLS adjustment and covariance matrices of TLS parameter estimates and derive the general first-order approximate cofactor matrices of random quantities in TLS adjustment. Secondly, based on the combination of TLS iterative algorithm and calculation process of SUT, we design the two SUT algorithms to calculate the biases and the second-order approximate covariance matrices. Finally, the straight line fitting model and plane coordinate transformation model are used to demonstrate that applying SUT for precision estimation of TLS adjustment is feasible and effective.