Frequency Estimation Algorithm Research Articles

Analysis of Ranging Precision in an FMCW Radar Measurement Using a Phase-Locked Loop

The standard deviation in a frequency modulated continuous wave radar distance measurement using a charge pump phase-locked loop (PLL) is calculated analytically. The phase noise of the PLL is modeled as an Ornstein-Uhlenbeck process resulting in a Lorentzian spectrum. We calculate the distance error as a function of the receiver noise bandwidth and the target distance. Depending on the frequency estimation algorithm and the target distance, the rms distance error due to PLL phase noise increases by about 6-9 dB with doubling the target distance. By contrast, the white noise in the radar receiver raises the distance error by about 12 dB in the far field with distance doubling, making this error contribution dominant for large target distances. These findings are verified by measurements on a scalable 61/122-GHz radar sensor platform.

A new grid frequency estimation algorithm based on the fractional FFT for IoT nodes time stamps

In the era of Internet of Things, so many wireless networked sensors and smart devices are embedded in infrastructures. For so many different wireless sensors, accurate times tamps are important to interpret data. In general, time stamps can be obtained by atomic clocks and GPS. The paper used the natural timestamping which is based on the grid frequency estimation. For grid frequency estimation, the paper proposed maximum merging model in fractional cepstrum domain for dealing with complicated power grid channel interference in China grids with data measured by the wireless sensor networks. The proposed method outperforms existing power grid frequency measurement algorithms, because the existing do not consider the facts that harmonic is time-varying and the pass band of some recording devices do not cover grid frequency. Through analyzing the results of analog frequency measurement, actual voice frequency measurement and recording audio tampering detection, this method is better than the one Bykhovsky proposed. It can be preferably applied to the grid frequency measurement, recording location recognition and audio tamper detection.

A Matlab/Simulink Development and Verification Platform for a Frequency Estimation System

The precise estimation of the frequency of the signal is of great significance in the Radar system, the electronic warfare system and many other systems. In this paper, we propose a development and verification platform for the frequency estimation system in the Matlab and Simulink environment. Its open-extensibility architecture enables the performance evaluation of different frequency estimation algorithms and its graphic interface can greatly promote the system design, simulation and verification efficiency.

Joint Two-Dimensional DOA and Frequency Estimation for L-Shaped Array via Compressed Sensing PARAFAC Method

In this paper, we combine the compressed sensing theory with the parallel factor (PARAFAC) model to present a 2-D direction of arrival (2D-DOA) and a frequency estimation algorithm for an L-shaped array. We first build the multi-delay outputs data as the PARAFAC model, then compress it with partitioning and perform the PARAFAC decomposition through a trilinear alternating least square algorithm. Finally, we reconstruct the received data with sparsity to obtain the automatically paired 2D-DOA and frequency. The proposed algorithm is effective for both uniform and non-uniform L-shaped array, and owing to the compression process, it holds the properties of lower computational complexity and smaller capacity for data storage, compared with a traditional PARAFAC algorithm. The angle and frequency estimation performance of the proposed algorithm is close to the traditional PARAFAC method, and outperforms the estimating signal parameters via a rotational invariance techniques algorithm and a propagator method. Simulation results verify the effectiveness and superiority of our approach.

Minimum frequency estimation of power system considering governor deadbands

The extensive existence of governor deadband has a significant influence on the minimum frequency of power system after a disturbance. However, the strong nonlinearity of deadband makes it difficult to quantify its impact on the frequency response. For this end, the backlash non-linearity is adopted to represent for the governor with deadband. The non-linear characteristics of governor with deadband are thus well approximated. The describing function method is applied to linearise the backlash non-linearity. Then a first-order model of governor system is derived to consider the deadband effect quantitatively. Minimum frequency estimation algorithm is proposed based on the first-order model. The proposed algorithm is effective to reflect the effects of various widths of deadbannd on the minimum value of frequency. Case study is conducted to prove its adequate performance in minimum frequency estimation with a practical power grid in China.

Entanglement-Based dc Magnetometry with Separated Ions

We demonstrate sensing of inhomogeneous dc magnetic fields by employing entangled trapped ions, which are shuttled in a segmented Paul trap. As \textit{sensor states}, we use Bell states of the type $\left|\uparrow\downarrow\right>+\text{e}^{\text{i}\varphi}\left|\downarrow\uparrow\right>$ encoded in two $^{40}$Ca$^+$ ions stored at different locations. Due to the linear Zeeman effect, the relative phase $\varphi$ serves to measure the magnetic field difference between the constituent locations, while common-mode fluctuations are rejected. Consecutive measurements on sensor states encoded in the $\text{S}_{1/2}$ ground state and in the $\text{D}_{5/2}$ metastable state are used to separate an ac Zeeman shift from the linear dc Zeeman effect. We measure magnetic field differences over distances of up to $6.2~\text{mm}$, with accuracies of around 300~fT, sensitivities down to $12~\text{pT} / \sqrt{\text{Hz}}$, and spatial resolutions down to $10~\text{nm}$. For optimizing the information gain while maintaining a high dynamic range, we implement an algorithm for Bayesian frequency estimation.

A Novel Open-Loop Frequency Estimation Method for Single-Phase Grid Synchronization Under Distorted Conditions

In this paper, a new open-loop architecture with good dynamic performance and strong harmonic rejection capability is proposed for single-phase grid synchronization under distorted conditions. Different from previous single-phase grid synchronization algorithms based on the phase-locked loop technique, the proposed method is to estimate the frequency and phase angle of the grid voltage in an open-loop manner so that fast dynamic response and enhanced system stability can be achieved. First, an open-loop frequency estimation algorithm is introduced under ideal grid condition. Then, it is extended to distorted grid voltages through the combination of the developed frequency estimation unit and a prefiltering stage consisting of a second-order low-pass filter and a cascaded delayed signal cancellation (DSC) module. In addition, a transient process smoothing unit is designed to achieve smooth frequency transients in cases where the grid voltage experiences fast and large changes. The working principle of the new frequency estimation algorithm and the developed single-phase grid synchronization approach is given in detail, together with some simulation and experiment results for verifying their performance.

Resolution improvement of low frequency AC magnetic field detection for modulated MR sensors.

Magnetic modulation methods especially Micro-Electro-Mechanical System (MEMS) modulation can improve the sensitivity of magnetoresistive (MR) sensors dramatically, and pT level detection of Direct Current (DC) magnetic field can be realized. While in a Low Frequency Alternate Current (LFAC) magnetic field measurement situation, frequency measurement is limited by a serious spectrum aliasing problem caused by the remanence in sensors and geomagnetic field, leading to target information loss because frequency indicates the magnetic target characteristics. In this paper, a compensation field produced with integrated coils is applied to the MR sensor to remove DC magnetic field distortion, and a LFAC magnetic field frequency estimation algorithm is proposed based on a search of the database, which is derived from the numerical model revealing the relationship of the LFAC frequency and determination factor [defined by the ratio of Discrete Fourier Transform (DFT) coefficients]. In this algorithm, an inverse modulation of sensor signals is performed to detect jumping-off point of LFAC in the time domain; this step is exploited to determine sampling points to be processed. A determination factor is calculated and taken into database to figure out frequency with a binary search algorithm. Experimental results demonstrate that the frequency measurement resolution of the LFAC magnetic field is improved from 12.2 Hz to 0.8 Hz by the presented method, which, within the signal band of a magnetic anomaly (0.04-2 Hz), indicates that the proposed method may expand the applications of magnetoresistive (MR) sensors to human healthcare and magnetic anomaly detection (MAD).

Spinning frequency estimation algorithm of MEMS gyro’s output signal based on FFT coefficient

To obtain accurate demodulation of the spinning frequency of MEMS carrier-driven gyro output signal, a frequency estimation algorithm combining the real and imaginary parts on the basis of fast Fourier transformation (FFT) coefficient was proposed. Both signal simulation and real-time test were performed to verify the advantages of FFT coefficient frequency estimation algorithm. In the signal simulation, CCS software was used in the demodulation and error analysis of the spinning frequency of gyro signal simulated by signal generator. Results showed that the maximum relative error of spectrum detection algorithm is 2.53%, and the maximum relative error of FFT frequency estimation algorithm is 0.1%. In the real-time test, demodulation and error analysis of the spinning frequency of gyro signal were conducted under real-time test through three-axis precise turntable. The maximum relative error of spectrum detection algorithm is 2.33%, and the maximum relative error of FFT frequency estimation algorithm is 0.1%. Experimental results indicated that, compared with spectrum detection algorithm, FFT frequency estimation algorithm exhibits higher demodulation precision, reduced maximum relative error by 2.23---2.43%, and is convenient for hardware implementation.

Bias compensation in the instantaneous frequency estimators based on the time–frequency representations and ICI algorithm

In this study, the author has proposed a technique for a bias compensation in the intersection-of-the-confidenceintervals (ICI) algorithm for the instantaneous frequency (IF) estimation. Algorithms from the ICI class are based on selection of the signal adaptive window length in the time-frequency representation-based IF estimators giving a trade-off between a bias and variance. The main difficulty in these estimators is sensitivity to a high noise influence that is producing outliers in estimates used for the ICI algorithm initialisation. Several ICI algorithm modifications are proposed in order to achieve robustness to the high noise influence. However, these techniques can suffer from the emphatic bias. The proposed bias compensation algorithm is based on the estimation of high-order IF derivative. It gives improvement in the mean squared error for more than 5 dB with respect to the state-of-the-art variants of the ICI algorithm.

Improved Frequency Estimation in Unbalanced Three-Phase Power System Using Coupled Orthogonal Constant Modulus Algorithm

A new iterative method for frequency estimation in the unbalanced three-phase power system is proposed. The proposed solution is based on the transformation of unbalanced three-phase voltage signal into a complex exponential by using the orthogonal constant modulus algorithm. In addition, based on the transformed signal, a simple adaptive algorithm for frequency estimation is proposed. Beside the proposed approach, any frequency estimator designed for a single-tone complex exponential can be used here, which is also the advantage of the proposed method. Simulation results confirm that the proposed algorithm exhibits better performance compared to the considered algorithms.

Normalized Autocorrelation Function Based Doppler Signal Frequency Estimation Algorithm

Normalized Autocorrelation Function Based Doppler Signal Frequency Estimation Algorithm

A Complex Least Squares Enhanced Smart DFT Technique for Power System Frequency Estimation

A complex-valued least-squares (CLS) framework is proposed in order to enhance the accuracy of the smart discrete Fourier transform (SDFT) algorithms for power system frequency estimation in the presence of noise and harmonic pollution. It is first established that the underlying time-series relationship among the consecutive DFT fundamental components employed by the original SDFT algorithms does not hold when noises or unexpected higher order harmonics are present, resulting in suboptimal estimation performances. To eliminate these adverse effects on the frequency estimation, the degree of the relationship breakdown is next quantified via a model mismatch error vector. The CLS technique is then employed to minimize the mean-square model deviation when the SDFT voltage modelling is suboptimal. The proposed CLS-enhanced SDFT (CLS-SDFT) methods are shown to be more accurate than the original ones in heavily noisy and harmonic-distorted environments, typical scenarios in online frequency estimation. The benefits of the SDFT framework are verified by simulations for various power system conditions, as well as for real-world measurements.

Joint DOA and Frequency Estimation for Linear Array with Compressed Sensing PARAFAC Framework

In this paper, a joint direction of arrival (DOA) and frequency estimation algorithm of narrow-band signals is proposed via compressed sensing (CS) parallel factor (PARAFAC) framework. The proposed algorithm constructs the data model into a PARAFAC model, and compresses it to a smaller one. Then trilinear alternating least-squares (TALS) algorithm is exploited to estimate the compressed parameter matrices, and finally the joint DOA and frequency estimation is obtained via the spatial sparsity and the frequency sparsity. Due to compression, the proposed algorithm has lower computational complexity than the conventional PARAFAC algorithm, and saves more memory capacity for practical application. The DOA and frequency estimation performance of the proposed algorithm is very close to that of the conventional PARAFAC algorithm, and better than those of the estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm and the propagator method (PM). Furthermore, the proposed algorithm can achieve automatically paired DOA and frequency estimation. Besides, it is applicable for nonuniform linear arrays. Effectiveness of the proposed algorithm is assessed by simulations.

Fixed-point algorithms for frequency estimation and structured low rank approximation

We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, i.e., frequency estimation. For the basic formulation of the fixed-point algorithm we show that it converges to the solution of a related minimization problem, namely the one obtained by replacing the original objective function with its convex envelope and keeping the structured matrix constraint unchanged. It often happens that this solution agrees with the solution to the original minimization problem, and we provide a simple criterion for when this is true. We also provide more general fixed-point algorithms that can be used to treat the problems of making weighted approximations by sums of exponentials given equally or unequally spaced sampling. We apply the method to the case of missing data, although the above mentioned convergence results do not hold in this case. However, it turns out that the method often gives perfect reconstruction (up to machine precision) in such cases. We also discuss multidimensional extensions, and illustrate how the proposed algorithms can be used to recover sums of exponentials in several variables, but when samples are available only along a curve.

A Novel Adaptive Frequency Estimation Algorithm Based on Interpolation FFT and Improved Adaptive Notch Filter

Abstract The convergence rate and the continuous tracking precision are two main problems of the existing adaptive notch filter (ANF) for frequency tracking. To solve the problems, the frequency is detected by interpolation FFT at first, which aims to overcome the convergence rate of the ANF. Then, referring to the idea of negative feedback, an evaluation factor is designed to monitor the ANF parameters and realize continuously high frequency tracking accuracy. According to the principle, a novel adaptive frequency estimation algorithm based on interpolation FFT and improved ANF is put forward. Its basic idea, specific measures and implementation steps are described in detail. The proposed algorithm obtains a fast estimation of the signal frequency, higher accuracy and better universality qualities. Simulation results verified the superiority and validity of the proposed algorithm when compared with original algorithms.

An approved frequency tracking method in connected element interferometry

Carrier tracking loop is a basic method of frequency tracking in CEI (connected element interferometry), but the tracking error is very large or even worse at high dynamic. To solve this problem, a frequency tracking method assisted by open loop frequency estimation is proposed in this paper. First, an open-loop frequency estimation algorithm is used to estimate the frequency of signals at different moments, then, the least squares fitting method is used to estimate the corresponding dynamic parameters of different orders. Next, a local signal is generated to compensate the received signal. After eliminating most of the dynamic characteristics, the signal is fed into PLL (Frequency locked loop) and high-precision frequency tracking results can be obtained. Simulation results show that, in the condition of low SNR, the new method has higher accuracy than the method assisted by FLL (Frequency locked loop), and the processing time is shorter. When there is a two order Doppler frequency change, the open-loop assisted method can overcome the steady phase error of the PLL, and is of great significance in the applications of connected elements interferometry.

A novel frequency estimation algorithm based on DFT and second derivative

AbstractIn this paper, a novel frequency estimation algorithm based on discrete Fourier transform (DFT) and second derivative is proposed. The proposed algorithm consists of three stages, namely, DFT, second derivative, and frequency estimation. First, the input signal is decomposed using DFT into two orthogonal components, the real and imaginary parts. In other words, the signal is filtered with cosine and sine filters. Secondly, the second derivatives of the two orthogonal components are obtained by numerical approximation. Because this step can cause an error, the central difference approximation for five-point second derivative is used for error reduction. Finally, the two orthogonal components and their second derivatives are combined to estimate the power frequency considering a zero-crossing problem and the gains of finite impulse response (FIR) filters. The performance of the proposed algorithm is evaluated considering frequency changes when generating the test signals. Besides, a dynamic conditio...

Resonant frequency estimation for adaptive notch filters in industrial servo systems

This paper proposes a new algorithm for estimating the resonant frequency of adaptive notch filters used in servo systems. Notch filters and adaptive notch filters are widely used in commercial servo systems for suppressing a resonance which is a major obstacle in improving their performance. However, the conventional frequency estimation algorithm gives a dynamic behavior that is proportional to the difference between the square of the estimated frequency and the square of the actual frequency. This can cause the estimation dynamics to be too slow for low-frequency resonances, if both low- and high-frequency resonances are present and if the estimator gain is designed for a high frequency. This paper develops a new algorithm to give a dynamic behavior that is proportional to the difference in the estimated frequency and actual frequency. This allows selecting the estimation parameters independent from the value of resonant frequencies. The developed algorithm is implemented to a production servo controller and applied to a production printed-circuit-board inspection system. The experimental results show that the developed algorithm is much more effective in suppressing the resonances of both low- and high-frequencies, compared to the pervious algorithm. Furthermore, the ability to suppress vibration allows increasing the feedback gain, which in turn allows improving the tack time performance from 190ms to 100ms. All experiments reported in this paper were performed in an actual industrial environment using a production system, and the developed algorithms are applied to the production system.

Evaluation of Frequency Estimation Algorithms Applied in System with Distributed Generation in Island Operation

Evaluation of Frequency Estimation Algorithms Applied in System with Distributed Generation in Island Operation