Frequency Estimation Precision Research Articles

Frequency Estimation Enhancement for Industrial Free Induction Decay Signals Under Low SNR via Hankelization and Modified Covariance

The frequency of a free induction decay (FID) signal from an industrial proton precession magnetometer (PPM) is proportional to the magnetic field strength. To achieve high-precision frequency estimation for an FID signal with a low signal-to-noise ratio (SNR), a long estimation period is always required which limits the application scenarios of the PPMs, such as aeromagnetic detection. To break through the contradiction between frequency estimation precision and time, this paper proposes an enhanced frequency estimation method via Han-kelization and modified covariance, dubbed EFE-HMC. First, the collected one-dimensional FID signal is constructed as a third-order tensor through Hankelization, and then the noise tensors are removed by multi-linear singular value decomposition to improve the SNR; second, the pre-processed third-order tensor is inverted into a one-dimensional signal, and the modified covariance is employed to estimate the corresponding signal frequency; and third, an experimental test platform is constructed to compare the proposed EFE-HMC with three state-of-the-art methods including Carry Chain, equal precision, and Dn-ResUnet. The results demonstrate that when the SNR is lower than -10 dB and the estimation time varies from 50 ms to 200 ms, the frequency estimation precision is improved by 60% on average. Moreover, the frequency estimation time is reduced by about 150 ms when the frequency estimation precision is better than 0.03 Hz.

Noisy Quantum Metrology Enhanced by Continuous Nondemolition Measurement.

We show that continuous quantum nondemolition (QND) measurement of an atomic ensemble is able to improve the precision of frequency estimation even in the presence of independent dephasing acting on each atom. We numerically simulate the dynamics of an ensemble with up to N=150 atoms initially prepared in a (classical) spin coherent state, and we show that, thanks to the spin squeezing dynamically generated by the measurement, the information obtainable from the continuous photocurrent scales superclassically with respect to the number of atoms N. We provide evidence that such superclassical scaling holds for different values of dephasing and monitoring efficiency. We moreover calculate the extra information obtainable via a final strong measurement on the conditional states generated during the dynamics and show that the corresponding ultimate limit is nearly achieved via a projective measurement of the spin-squeezed collective spin operator. We also briefly discuss the difference between our protocol and standard estimation schemes, where the state preparation time is neglected.

Improving the precision of frequency estimation via long-time coherences

In recent years, several estimation strategies have been formulated to determine the value of an unknown parameter in the most precise way, taking into account the presence of noise. These strategies typically rely on the use of quantum entanglement between the sensing probes and they have been shown to be optimal in the asymptotic limit in the number of probes, as long as one performs measurements on shorter and shorter time scales. Here, we present a different approach to frequency estimation, which exploits quantum coherence in the state of each sensing particle in the long time limit and is obtained by properly engineering the environment. By means of a commonly used master equation, we show that our strategy can overcome the precision achievable with entanglement-based strategies for a finite number of probes. We discuss a possible implementation of the scheme in a realistic setup that uses trapped ions as quantum sensors.

Generalized demodulation with tunable E-Factor for rolling bearing diagnosis under time-varying rotational speed

Generalized demodulation (GD) is one of the most effective approaches to demodulating the time-varying frequency component. However, it is sensitive to the initial frequency value. Theoretically, the slower the rotational speed is, the lower frequency estimation precision based on the time-frequency representation (TFR) will be. Therefore, for the vibration signal whose phase function is estimated by the instantaneous frequency extracted from the TFR under lower initial speed, the demodulation error is significant. As such, the concept of energy factor (E-Factor) is defined. E-Factor represents the frequency coordinate value of the target instantaneous frequency on the demodulated time-frequency plane, i.e., the energy of the instantaneous frequency can be converted to a changeable parameter E-Factor, rather than the fixed initial value. Based on it, we propose the generalized demodulation with tunable E-Factor (GDTEF), which can map the trajectory of time-varying frequency to a line parallel to time axis with the frequency coordinate E-Factor in the time-frequency domain, and further exploit its merit to bearing fault detection. First, extract the instantaneous fault characteristic frequency (IFCF) from the TFR of the envelope obtained by the joint application of Hilbert transform and short-time Fourier transform (STFT). Second, configure E-Factor adaptively according to the IFCF fitting function, and then reconstruct the original signal according to the E-Factor. Then, finalize the phase function of the reconstructed signal based on the fitting function. Finally, identify the fault pattern via the demodulation spectrum. It is validated that the novel method can enhance the demodulation precision by processing the simulated and measured signals. What's more, the proposed method possesses stronger noise immunity in processing the time-varying frequency vibration signal.

Phase correction autocorrelation-based frequency estimation method for sinusoidal signal

To improve the precision of frequency estimation, a phase correction autocorrelation-based frequency estimation method for sinusoidal signal is proposed. Firstly, a phase correction autocorrelation is developed to reduce the effect of non-half period sampling signal on autocorrelation. Secondly, reference signal is generated according to phase correction autocorrelation signal. Finally, an error function between phase correction autocorrelation signal and reference signal is constructed and frequency estimation is obtained by calculating the minimum of error function. To demonstrate the superiority of the proposed method, computational complexity is analyzed, simulations and experiments are performed. Theoretical analysis and simulations demonstrate that the proposed method reduces the influence of non- half period sampling signal and has better frequency estimation performance than the interpolated DFT method, the modified covariance method for correlation, the two-stage autocorrelation method and the expanded autocorrelation method. The measurement experiments of LFMCW radars validate the effectiveness and superiority of the proposed method in practice.

Signal Frequency Estimation Based on Kalman Filtering Method

In order to further improve the frequency estimation precision under high dynamic, the frequency estimation method based on Kalman filter is studied. Two methods of Kalman filter directly using for frequency estimation are studied, taking the phase of echo signal and the echo signal for measurements, which adopt nonlinear and linear Kalman filtering algorithm to estimate the Doppler frequency. Based on the study of performance of these two methods, the Doppler adaptability of the two methods is studied. The simulation results show that the speed precision is improved. But, the two methods of this research are limited by the fixed frequency conversion, and when Doppler changed a large range, the filtering is easy to diverge.

A phase match based frequency estimation method for sinusoidal signals.

Accurate frequency estimation affects the ranging precision of linear frequency modulated continuous wave (LFMCW) radars significantly. To improve the ranging precision of LFMCW radars, a phase match based frequency estimation method is proposed. To obtain frequency estimation, linear prediction property, autocorrelation, and cross correlation of sinusoidal signals are utilized. The analysis of computational complex shows that the computational load of the proposed method is smaller than those of two-stage autocorrelation (TSA) and maximum likelihood. Simulations and field experiments are performed to validate the proposed method, and the results demonstrate the proposed method has better performance in terms of frequency estimation precision than methods of Pisarenko harmonic decomposition, modified covariance, and TSA, which contribute to improving the precision of LFMCW radars effectively.

Noise-assisted Ramsey interferometry

I analyze a metrological strategy for improving the precision of frequency estimation via Ramsey interferometry with strings of atoms in the presence of correlated dephasing. This strategy does not employ entangled states, but rather a product state which evolves into a stationary state under the influence of correlated dephasing. It is shown that by using this state an improvement in precision compared to standard Ramsey interferometry can be gained. This improvement is not an improvement in scaling, i.e. the estimation precision has the same scaling with the number of atoms as the standard quantum limit, but an improvement proportional to the free evolution time in the Ramsey interferometer. Since a stationary state is used, this evolution time can be substantially larger than in standard Ramsey interferometry which is limited by the coherence time of the atoms.

FEATURES OF THE INSTANTANEOUS FREQUENCY ESTIMATION ALGORITHM WITH PRE-FILTERING

Instantaneous frequency is one of the basic signal parameters which provides important information about the time-varying spectral changes in non-stationary signals. Features of the harmonic signal frequency estimation algorithm in different signal and interference situations are researched. Research methodology is a statistical modeling. Appearance of an additional harmonic considerably worsen precision of estimation because the algorithm does not have any filtering properties. For linear frequency deviation estimation approximately equals middle between initial and final frequencies in the window. Frequency estimation of a noise process, that is formed by 2nd order filters, is almost proportional to central or cut-off frequency. There is optimal formative filter frequency for different filter parameters and estimation conditions. Reasonability of using pre-filtering in order to improve estimation precision is proved. Identified positive effect of mixture pre-filtering is also useful for estimation of frequency of periodic non-harmonic signals with higher harmonics. A great feature of the algorithm is a accurate estimation at intervals equal to a period of the signal, which brings us to the actual instantaneous frequency and provides the opportunity to observe its trend over time. Distorted factors cause significant worsening of frequency estimation precision. It can be improved by pre-filtering. The 2nd order filter using is reasonable only in case of weak a priori ambiguity, in other cases the 1st order filter is more preferable.

STABILITY OF THE ESTIMITATION OF FREQUENCY OF THE HARMONIOUS SIGNAL WITH THE CONSTANT COMPONENT TO PULSE HINDRANCES

The impulse interference impact on robustness of quazioptimal frequency estimation of harmonic signal with additive constant component and Gaussian noise are researched. The critical conditions for instability are defined. The dependencies of frequency estimation precision on parameters chaotic impulse interferences are obtained by statistic modeling.

Noise reduction in Doppler ultrasound signals using an adaptive decomposition algorithm

A novel de-noising method for improving the signal-to-noise ratio (SNR) of Doppler ultrasound blood flow signals, called the matching pursuit method, has been proposed. Using this method, the Doppler ultrasound signal was first decomposed into a linear expansion of waveforms, called time–frequency atoms, which were selected from a redundant dictionary named Gabor functions. Subsequently, a decay parameter-based algorithm was employed to determine the decomposition times. Finally, the de-noised Doppler signal was reconstructed using the selected components. The SNR improvements, the amount of the lost component in the original signal and the maximum frequency estimation precision with simulated Doppler blood flow signals, have been used to evaluate a performance comparison, based on the wavelet, the wavelet packets and the matching pursuit de-noising algorithms. From the simulation and clinical experiment results, it was concluded that the performance of the matching pursuit approach was better than those of the DWT and the WPs methods for the Doppler ultrasound signal de-noising.

Frequency estimation precision in Doppler optical coherence tomography using the Cramer-Rao lower bound

Doppler optical coherence tomography (DOCT) is a technique for simultaneous cross-sectional imaging of tissue structure and blood flow. We derive the fundamental uncertainty limits on frequency estimation precision in DOCT using the Cramer-Rao lower bound in the case of additive (e.g., thermal, shot) noise. Experimental results from a mirror and a scattering phantom are used to verify the theoretical limits. Our results demonstrate that the stochastic nature of frequency noise influences the precision of flow imaging, and that the noise model must be selected judiciously in order to estimate the frequency precision.

Doppler ultrasound signal denoising based on wavelet frames.

A novel approach was proposed to denoise the Doppler ultrasound signal. Using this method, wavelet coefficients of the Doppler signal at multiple scales were first obtained using the discrete wavelet frame analysis. Then, a soft thresholding-based denoising algorithm was employed to deal with these coefficients to get the denoised signal. In the simulation experiments, the SNR improvements and the maximum frequency estimation precision were studied for the denoised signal. From the simulation and clinical studies, it was concluded that the performance of this discrete wavelet frame (DWF) approach is higher than that of the standard (critically sampled) wavelet transform (DWT) for the Doppler ultrasound signal denoising.

An Evaluation of Random and Systematic Plot Placement for Estimating Frequency

A computer simulation study was conducted to evaluate the effects of pattern on the precision of frequency estimates as determined from random and systematic plot placement. Computer graphics were used to generate artificial population maps containing 40 or 80 clumps of differing spatial intensity with known frequencies of 20, 35, and 50%0. The maps were repeatedly sampled both randomly and systematically using a 200-plot sample size to obtain frequency estimates. Three systematic plot spacings (4, 8, and 12) along randomly located transects were evaluated. Analysis indicated that frequency means from systematic plot placement were signiflcantly affected by clumping, pattern intensity, and plot spacing. Random sampling resulted in frequency means that were unaffected by clumping or pattern intensity, and more consistently estimated population frequencies. An evaluation of probabilities of occurrence of Type I errors when statistically comparing frequency estimates from systematic plot placement Indicated higher Type I error rates as compared to random sampling.