Amplitude Estimation Of Signal Research Articles

Quantum Spectral Analysis by Continuous Measurement of Landau-Zener Transitions.

We demonstrate the simultaneous estimation of signal frequency and amplitude by a single quantum sensor in a single experimental shot. Sweeping the qubit splitting linearly across a span of frequencies induces a nonadiabatic Landau-Zener transition as the qubit crosses resonance. The signal frequency determines the time of the transition, and the amplitude its extent. Continuous weak measurement of this unitary evolution informs a parameter estimator retrieving precision measurements of frequency and amplitude. Implemented on radio-frequency-dressed ultracold atoms read out by a Faraday spin-light interface, we sense a magnetic signal with estimated sensitivities to amplitude of 11 pT/sqrt[Hz], frequency 0.026 Hz/Hz^{3/2}, and phase 0.084 rad/sqrt[Hz], in a single 300ms sweep from 7 to 13kHz. The protocol realizes a swept-sine quantum spectrum analyzer, potentially sensing hundreds or thousands of channels with a single quantum sensor.

A Novel Curve Clustering Method in Modal Decomposition for Amplitude Estimation of Period-Decreasing Signals in Brake Rotors

A Novel Curve Clustering Method in Modal Decomposition for Amplitude Estimation of Period-Decreasing Signals in Brake Rotors

Parametric Bayesian model for rotating blade frequency tracking with single probe blade tip timing

Blade tip timing (BTT) has become the most promising online monitoring method for turbine blade health. Most existing BTT data analysis methods have a narrow application scope for different types of BTT data and slow calculation speed, which adversely affects the practical industrial application of BTT. In this study, we propose a parametric Bayesian model for rotating blade frequency tracking with a single probe. Compared with existing methods, this method has a wider application range and fast computation speed; moreover, it minimizes the number of probes used. Numerical simulation and experimental results show that the method is highly feasible and robust. In addition, the advantages of this method in signal amplitude estimation are demonstrated. The results are significant for online blade health monitoring of turbines.

Joint Parameter Estimation From Binary Observations Over Decentralized Channels

In wireless sensor networks, due to the bandwidth constraint, the distributed nodes (DNs) might only provide binary representatives of the source signal, and then transmit them to the central node (CN). In this paper, we consider the joint estimation of signal amplitude and background noise variance from binary observations over decentralized channels. We first analyze the Cramér–Rao lower bounds (CRLBs) of the parameters of interest and develop a quasilinear estimator (QLE), in which the desirable estimates can be obtained from several intermediate parameters linearly. Next, we consider a more realistic situation where the decentralized channel is noisy during the data transmission. Based on the error propagation model, the asymptotic analysis shows that the performance of the proposed QLE is mainly dominated by the thresholds of the quantizers, which encourages us to adopt a correlated quantization (CQ) scheme by exploiting the spatial correlation among background noises/channel noises. To ease the implementation of QLE in practice, an adaptive quantization (AQ) scheme is also proposed so as to obtain reasonable selections of the required thresholds. Finally, numerical simulations are provided to validate our theoretical findings.

Real-time phase and amplitude estimation of neurophysiological signals exploiting a non-resonant oscillator

A recent advancement in the field of neuromodulation is to adapt stimulation parameters according to pre-specified biomarkers tracked in real-time. These markers comprise short and transient signal features, such as bursts of elevated band power. To capture these features, instantaneous measures of phase and/or amplitude are employed, which inform stimulation adjustment with high temporal specificity. For adaptive neuromodulation it is therefore necessary to precisely estimate a signal's phase and amplitude with minimum delay and in a causal way, i.e. without depending on future parts of the signal. Here we demonstrate a method that utilizes oscillation theory to estimate phase and amplitude in real-time and compare it to a recently proposed causal modification of the Hilbert transform. By simulating real-time processing of human LFP data, we show that our approach almost perfectly tracks offline phase and amplitude with minimum delay and is computationally highly efficient.

Cramér-Rao Bounds for spectral parametric estimation with compressive multiband architectures

This article tackles the topic of performance analysis for Spectrum Sensing based on Compressive Sampling (CS). More precisely, the lower bound on the variance of any unbiased estimator, the Cramér-Rao Bound (CRB), is investigated in the context of spectral parametric estimation. Compressed samples are obtained from a multiband architecture like the Modulated Wideband Converter, the Quadrature-Analog-to-Information Converter or the Periodic Non Uniform Sampler. An expression of the Fisher information matrix, which allows to compute the CRB, is established for a compressive multiband architecture assuming a disjoint spectral subband model. The relationships between Fisher matrices in a generic framework are exposed: first between compressive multiband and subsampling architectures, then between subsampling and Nyquist sampling architectures. Based on these new considerations, the issue of interferer detection, a canonical case and also a huge thorn in the side of wideband radiofrequency receivers is tackled. A benchmark between Nyquist, Subsampling and Compressive Multiband Sampling approaches is provided for frequency and amplitude estimation of dual-tone signals. This analysis illustrates the way in which interferences between parameters occur in estimation with Compressive Sampling. It is then shown how properties of the sensing matrix for popular compressive architectures enable to control the precision of spectral parametric estimation in specific subbands. This control opportunity opens the door to adaptive methods.

Accurate and Fast Amplitude Estimation of Signal Distorted by Noise and Harmonics for Control of VSI

Arriving at an accurate and fast amplitude estimation of the sine-wave distorted by harmonics and noise is important for the control of voltage source inverters in grid-connected photovoltaic system. In this article, the three-point interpolation discrete Fourier transform method based on the maximum sidelobe decay windows is proposed for accurate amplitude estimation. The proposed amplitude estimator is speeded-up by using the guaranteed stable recursive method. The influence of noise on the proposed amplitude estimator is investigated, and the amplitude estimation error caused by the spectral interference is also analyzed. The accuracy and effectiveness of the proposed method are verified through simulation and experiments, where the state-of-art amplitude estimation methods and the boundaries specified in the Standard IEEE C37.118.1-2011 are considered.

FFT-Based Amplitude Estimation of Power Distribution Systems Signal Distorted by Harmonics and Noise

This paper estimates amplitude of a power distribution systems signal corrupted with white noise and harmonics by using the windowed symmetrical interpolation fast Fourier transform. The polynomial coefficients of amplitude estimation are derived. The influence of harmonic and the spectral interference (leakage) from image parts is analyzed. The analytical expression of the amplitude estimation variance is derived and compared with the unbiased Cramer–Rao lower bound. The proposed methods are validated through computer simulations and experiments.

Signal Amplitude Estimation and Detection From Unlabeled Binary Quantized Samples

Signal amplitude estimation and detection from unlabeled quantized binary samples are studied, assuming that the order of the time indexes is completely unknown. First, maximum likelihood (ML) estimators are utilized to estimate both the permutation matrix and unknown signal amplitude under arbitrary, but known signal shape and quantizer thresholds. Sufficient conditions are provided under which an ML estimator can be found in polynomial time and an alternating maximization algorithm is proposed to solve the general problem via good initial estimates. In addition, the statistical identifiability of the model is studied. Furthermore, the generalized likelihood ratio test (GLRT) detector is adopted to detect the presence of signal. In addition, an accurate approximation to the probability of successful permutation matrix recovery is derived, and explicit expressions are provided to reveal the relationship between the number of signal samples and the number of quantizers. Finally, numerical simulations are performed to verify the theoretical results.

Statistical simulation of signal-to-noise ratio estimation

The research addresses an urgent issue of operational control of the signal-to-noise ratio in radio-electronic systems. The proposed signal-to-noise ratio estimation technique is based on the maximum likehood estimation of the signal amplitude when observed against the white Gaussian noise. The paper presents block diagrams of sumilation in Simulink, which implement the proposed technique, in particular, a module for calculating the maximum likehood estimation of the signal amplitude, which involves quadrature heterodyning of the input signal, accumulation of the readings of the obtained components in the observation interval, and calculation of the square root of the sum of squares of in-phase and quadrature correlations. The statistical simulation (1,000 tests) was performed to verify the accuracy of the proposed technique. It was established that the mean-squared deviation of the signal-tonoise ratio estimation error is approximately 0.1 dB in the case of unlimited (by width) input and reference signals. With requirements to signal width reduced, or with sign approximation of input and reference signals, the mean-squared deviation of the signal-to-noise ratio estimation error does not exceed 0.2 dB. The results obtained confirm high accuracy and feasibility of the proposed estimator. The materials of this paper can be of use in the operative quality control of space communication channels. Keywords: signal-to-noise ratio, signal amplitude estimation, white Gaussian noise, simulation model, statistical simulation

Performance of an Algorithm for Estimation of Flux, Background, and Location on One-dimensional Signals

Optimal estimation of signal amplitude, background level, and photocenter location is crucial to the combined extraction of astrometric and photometric information from focal plane images, in particular from the one-dimensional measurements performed by Gaia on intermediate to faint magnitude stars. Our goal is to define a convenient maximum likelihood framework that is suited to the efficient iterative implementation and assessment of noise level, bias, and correlation among variables. The analytical model is investigated numerically and verified by simulation over a range of magnitude and background values. The estimates are unbiased, with a well-understood correlation between amplitude and background, and with a much lower correlation of either of them with location, further alleviated in case of signal symmetry. Two versions of the algorithm are implemented and tested against each other, respectively, for independent and combined parameter estimation. Both are effective and provide consistent results, but the latter is more efficient because it takes into account the flux-background estimate correlation.

Sparse phase imaging based on complex domain nonlocal BM3D techniques

The paper is addressed to 2D phase and amplitude estimation of complex-valued signals – that is, in particular, to estimation of modulo-2π interferometric phase images from periodic and noisy observations. These degradation mechanisms make phase image estimation a challenging problem. A sparse nonlocal data-adaptive imaging formalized in complex domain is used for phase and amplitude image reconstruction. Following the procedure of patch-based technique, the image is partitioned into small overlapping square patches. Block Matching Three Dimensional (BM3D) technique is developed for forming complex domain sparse spectral representations of complex-valued data. High Order Singular Value Decomposition (HOSVD) applied to BM3D groups enables the design of the orthonormal complex domain 3D transforms which are data adaptive and different for each BM3Ds group. An iterative version of the complex domain BM3D is designed from variational formulation of the problem. The convergence of this algorithm is shown. The effectiveness of the new sparse coding based algorithms is illustrated in simulation experiments where they demonstrate the state-of-the-art performance.

FM jamming cancellation suppression based on noise floor estimation with dynamic threshold

Technique of FM jamming time domain cancellation suppression based on noise floor estimation with dynamic threshold is researched, by using the colored noise NLR filter estimation algorithm instead of the narrowband filtering algorithm, the problem that the target echo signal is lost in the process of jamming amplitude estimation is solved. Through the phase analysis of the jamming signal, the problem of jamming signal amplitude estimation in the background of echo signal is transformed into the problem of useful signals spectral estimation in colored noise background. Combined with the characteristics of the low frequency components of the useful signal, the traditional NLR filtering algorithm is improved by adding the dynamic threshold, so as to achieve the purpose of colored noise’s non-invasive estimation, and then to obtain more accurate jamming signal amplitude estimation. The simulation results show that compared with the traditional jamming cancellation algorithm, this algorithm can improve the SJR of the echo signal better and the anti - jamming ability is stronger.

Single Snapshot Detection and Estimation of Reflections From Room Impulse Responses in the Spherical Harmonic Domain

We study the detection and estimation of the parameters related to the deterministic model of the reflections of room impulse responses measured with a spherical microphone array. More specifically, we investigate the problem of detecting and estimating several reflections of a single snapshot of data in the spherical harmonic (SH) domain with four detection and four estimation methods, presented previously in the array processing research. Three of the estimation methods are based on Bayesian Maximum a Posteriori (MAP) estimation, and they employ a prior normal distribution on the signals. The estimation methods are compared with the deterministic maximum likelihood (DML) method [Tervo & Politis 2015]. In the detection task, two information criteria-based methods, minimum description length (MDL) and Akaike information criteria (AIC), a normalized likelihood (NL) based method, and a Bayesian detection scheme (BDS) are explored. The experiments study the performance of the methods with simulated and real data experiments. The simulation results show that the MAP estimation methods have a lower root mean squared error (RMSE) than DML in the reflection signal amplitude estimation, but all three have similar performance in the direction of arrival (DOA) and noise variance estimation, although in general RMSE of DOA estimation of MAP methods is slightly lower that that of DML. In addition, in the detection task, the BDS and AIC are the most robust against additive noise, and NL and AIC have the best detection rate when more than two reflections are simulated. The results of the real data experiments show that all the estimation methods have similar performance for DOA and noise variance estimation, while the Bayesian MAP methods have a clearly lower RMSE for reflection signal amplitude estimation than DML. In total, NL has the highest detection rate in the real data experiments.

Three-point estimator of sinusoidal signal amplitude

ABSTRACTThe paper presents an estimator that makes it possible to estimate the amplitude on the basis of three initial sinusoidal signal samples. Such an estimator is called a three-point amplitude estimator. Simulations consisting in generating and acquiring quantised samples of a signal affected by Gaussian noise have been run. To generate and acquire the samples, a MathCAD computer program has been used. An experiment has been conducted consisting in generating and acquiring sine-wave voltage signal samples. To generate the signal, an Agilent 33220A function generator has been applied. To acquire the samples, an Agilent 3458A voltmeter has been applied. Based on the collected samples, the values of a three-point estimator and a four-point estimator proposed by Vizireanu and Halunga have been computed. Maximum errors have been determined on the basis of the errors of the results of signal amplitude estimation. It has been shown that, in comparison with a four-point estimator, a three-point estimator can estimate the signal amplitude with higher accuracy.

A Method of m-Point Sinusoidal Signal Amplitude Estimation

Abstract The paper presents a new and original method of m-point estimation of sinusoidal signal amplitude. In this method, an m-point estimator is calculated on the basis of m initial signal samples. The way the estimator is constructed is explained. It is shown that the starting point for constructing the estimator is two initial signal samples. Next, in order to determine the estimator general form, three and m subsequent initial signal samples appearing in a signal period are used. Some special cases of an estimator are considered. Such an estimator is compared with a four-point estimator proposed by Vizireanu and Halunga. It is shown that the m-point estimator makes it possible to estimate the signal amplitude more accurately.

An improved correlation method for amplitude estimation of gravitational background signal with time-varying frequency.

In the measurement of the gravitational constant G with angular acceleration method, the accurate estimation of the amplitude of the useful angular acceleration generated by source masses depends on the effective subtraction of the spurious gravitational signal caused by room fixed background masses. The gravitational background signal is of time-varying frequency, and mainly consists of the prominent fundamental frequency and second harmonic components. We propose an improved correlation method to estimate the amplitudes of the prominent components of the gravitational background signal with high precision. The improved correlation method converts a sinusoidal signal with time-varying frequency into a standard sinusoidal signal by means of the stretch processing of time. Based on Gaussian white noise model, the theoretical result shows the uncertainty of the estimated amplitude is proportional to σNT, where σ and N are the standard deviation of noise and the number of the useful signal period T, respectively.

Federated ultra‐tightly coupled GPS/INS integrated navigation system based on vector tracking for severe jamming environment

Considering all integration methods currently available for global positioning system (GPS) and inertial navigation system (INS) integrated navigation system, ultra-tightly coupled (UTC) GPS/INS system is the best choice for accurate and robust navigation. However the performance of UTC GPS/INS system based on scalar tracking (ST) degrades in severe jamming environments. To solve this problem an innovative federated UTC GPS/INS system based on vector tracking (VT) is proposed. On the basis of UTC integration, three Kalman filters are developed to accomplish the goals of signal amplitude estimation, VT and integration navigation. By replacing the traditional ST loops with VT filter, the tracking ability is remarkably reinforced. More importantly, a new mathematical model of VT is proposed and the key innovation of this model is that it can provide adaptation ability to integration Kalman filter, so that the navigation performance can be improved under various jamming conditions. A simulation platform covering all procedures of GPS/INS integrated navigation is employed to verify the effectiveness of the proposed architecture. Tracking and navigation results show that the federated UTC GPS/INS integrated system based on VT improves both the tracking and navigation performance significantly under severe jamming environments compared with that of ST system.

Modified Cramér-Rao Bounds for Continuous-Phase Modulated Signals

We consider the estimation of signal amplitude, time offset, and the parameters of a polynomial-phase signal from a continuous-phase modulated (CPM) signal that contains both unknown data symbols and known pilot symbols. Transformation of the polynomial-phase signal into an orthogonal basis allows us to derive the modified Cramér-Rao bounds (MCRB) for the problem of vector-parameter estimation in closed form. Numerical results demonstrate that the achievable estimation accuracy significantly depends on the burst structure and highlight the need for properly designed pilot sequences. Since our bounds are easy to evaluate, they can aid the design of pilot and burst configuration for CPM systems.

Modified integration method for amplitude estimation of fundamental frequency measuring signal for power system protection

The integration method for amplitude estimation of fundamental frequency signal, using appropriate integration interval, can be used when measuring signal is composed of fundamental and high harmonics of order 2n or fundamental and high harmonics of order 3n, n=1,2,3.... It is not possible to find the integration interval to get the integration method which is simultaneous immune to high harmonics of order 2n, 3n, 5n etc.. In this paper, the integration method is modified to get the method which is simultaneous immune to high harmonics of order 2n, 3n and 5n, n=1,2,3.... The obtained method is tested at miscellaneous form of measuring signals using Matlab.