High-resolution Frequency Estimation Research Articles

Parameter Estimation Algorithm of Frequency-Hopping Signal in Compressed Domain Based on Improved Atomic Dictionary.

This paper considers the problem of estimating the parameters of a frequency-hopping signal under non-cooperative conditions. To make the estimation of different parameters independently of each other, a compressed domain frequency-hopping signal parameter estimation algorithm based on the improved atomic dictionary is proposed. By segmenting and compressive sampling the received signal, the center frequency of each signal segment is estimated using the maximum dot product. The signal segments are processed with central frequency variation using the improved atomic dictionary to accurately estimate the hopping time. We highlight that one superiority of the proposed algorithm is that high-resolution center frequency estimation can be directly obtained without reconstructing the frequency-hopping signal. Additionally, another superiority of the proposed algorithm is that hopping time estimation has nothing to do with center frequency estimation. Numerical results show that the proposed algorithm can achieve superior performance compared with the competing method.

Low-Complexity High-Resolution Frequency Estimation of Multi-Sinusoidal Signals

High-resolution frequency estimation is crucial for some applications. Accordingly, the present study proposes three high-performance computationally-efficient methods for high-resolution frequency estimators, which are designed based on a modified likelihood function. Traditional maximum likelihood based approaches for high-resolution frequency estimation are inefficient since the associated optimization problem is non-convex. Accordingly, in the first estimator proposed in this study, the amplitudes and frequencies of the multi-sinusoidal signals are estimated iteratively based on a simple linear Taylor approximation and a low-dimensional closed-form solution in every iteration. In the second estimator, the frequencies are determined directly using a primal decomposition approach and a gradient descent search method. Finally, a novel low-complexity parallel interference cancellation (PIC)-based frequency estimation approach is developed. The simulation results show that the proposed designs not only meet the Cramér-Rao lower bound (CRLB) in most cases of the conducted examples, but also possess lower computational complexity than existing state-of-the-art approaches.

High-precision frequency estimation for FMCW radar applications based on parameterized de-alternating and modified ICCD

In this paper, aiming to achieve high-resolution frequency estimation for frequency-modulated continuous wave (FMCW) radar applications, a novel frequency estimation algorithm based on parameterized de-alternating (PDA) is proposed. According to the beat signal model, the proposed PDA method is performed with a matched kernel function to achieve the best de-alternating performance (i.e. the maximum conversion from an oscillating signal to a constant signal). The kernel parameter is estimated by solving an optimization problem which is simple and computationally efficient. Moreover, for a multiple target scenario, the intrinsic chirp component decomposition (ICCD) method is employed to isolate different components of the beat signal, which can eliminate the mutual interference between adjacent components when performing the PDA method. Compared with the commonly used FFT technique, our method can greatly improve the frequency estimation resolution and achieve superior ranging performance with a limited bandwidth. Both simulated and experimental validations are provided to show the effectiveness of the proposed methods.

Grouping FFT Based Two-Stage High Sensitivity Signal Acquisition With Sign Transitions

The acquisition performance of weak global navigation satellite system signals, especially those with secondary codes, is susceptible to sign transitions. To better understand and overcome the negative impact of sign transitions, this paper derived a new receiver auto-correlation function. The straightforward formula shows that sign transitions can reduce the accuracy of the Doppler estimate. To meet the initialization requirements of the tracking block, a two-stage high-sensitivity acquisition frame is proposed based on sign combinations search using matrix notation. The first stage adopts the conventional non-coherent combination (NC) algorithm to obtain the coarse code phase. And the second stage achieves high-resolution frequency estimation through fast Fourier transform (FFT). Besides, a novel grouping FFT algorithm is proposed to reduce the complexity of the second stage. The Beidou navigation satellite system (BDS) B1I signal is used as an example to verify the performances. Compared with conventional NC algorithm, the statistical performance of the new algorithm, in terms of the detection probabilities and frequency errors, can be greatly improved. To be specific, the proposed algorithm can actualize the 90% detection possibility of BDS B1I signal at a carrier-to-noise ratio (C/N0) of 23.9 dB-Hz within 200 ms with a Doppler accuracy of about 31 Hz. And the computing load of the second stage is reduced by about 11.6% compared with the conventional FFT approach. Actual data test further verifies the superiority of the new method. Inevitably, the total processing time increases by about 30%.

Methodology for Flicker Estimation and Its Correlation to Environmental Factors in Photovoltaic Generation

Flicker is a very common power quality disturbance due to the inclusion of photovoltaic (PV) generation on the electric grid. This paper presents a methodology for flicker estimation in a PV generation that fuses multiple signal classification and discrete wavelet transform to provide high-resolution frequency estimation with an accurate amplitude measurement. This tool considers that flicker is not stationary over time and that more than one frequency component can exist on a voltage signal. In Addition, this paper finds that sun irradiance, temperature, and the action of the solar inverter are the sources of flicker in PV generation. The methodology is applied to real signals from three days with different weather conditions. In Addition, two different solar inverters are evaluated to see their influence on the parameters of flicker. Results show that flicker can contain more than one frequency component that can change over time. Finally, this paper shows that around 70% to 80% of flicker is linked to irradiance and cell temperature whereas the 20% to 30% can be attributed to the operation of solar inverters.

Advances in Automotive Radar: A framework on computationally efficient high-resolution frequency estimation

Radar technology is used for many applications of advanced driver assistance systems (ADASs) and is considered as one of the key technologies for highly automated driving (HAD). An overview of conventional automotive radar processing is presented and critical use cases are pointed out in which conventional processing is bound to fail due to limited frequency resolution. Consequently, a flexible framework for computationally efficient high-resolution frequency estimation is presented. This framework is based on decoupled frequency estimation in the Fourier domain, where high-resolution processing can be applied to either the range, relative velocity, or angular dimension. Real data obtained from series-production automotive radar sensor are presented to show the effectiveness of the presented approach.

Multiple signal classification based on automatic order selection method for broken rotor bar detection in induction motors

Multiple signal classification (MUSIC) algorithm has been widely used to obtain high-resolution frequency estimation for an accurate identification of frequency components in low signal-to-noise ratios. One of the main drawbacks associated with the use of the MUSIC algorithm is that its performance is fully deteriorated when a wrong frequency signal dimension order is chosen, producing that some spurious frequencies could appear or some signal frequencies could be missing. In this paper, it is proposed a multi-objective optimization method to address the frequency signal dimension order problem. The proposed approach is based on a novel feature extraction of frequency components, which allows determining an adequate frequency signal dimension order. The methodology has been integrated as part of the MUSIC algorithm, and it can find the optimal order within a predefined frequency bandwidth, where the user is interested to find a frequency component. To evaluate the effectiveness of the proposed methodology, experimental results from several current signals obtained in the detection of broken rotor bar fault in induction motors have been tested.

고해상도 주파수 추정 기법을 통한 차량용 레이더 시스템의 간섭 완화에 관한 연구

With the increased demand for automotive radar systems, mutual interference between vehicles has become a crucial issue that must be resolved to ensure better automotive safety. Mutual interference between frequency modulated continuous waveform (FMCW) radar system appears in the form of increased noise levels in the frequency domain and results in a failure to separate the target object from interferers. The traditional fast fourier transform (FFT) algorithm, which is used to estimate the beat frequency, is vulnerable in interference-limited automotive radar environments. In order to overcome this drawback, we propose a high-resolution frequency estimation technique for use in interference environments. To verify the performance of the proposed algorithms, a 77GHz FMCW radar system is considered. The proposed method employs a high-resolution algorithm, specially the multiple signal classification and estimation of signal parameters via rotational invariance techniques, which are able to estimate beat frequency accurately.

Matrix pencil based phase derivative estimation in digital holographic interferometry

A novel technique is proposed for the direct two-dimensional phase derivatives estimation based on the matrix pencil approach in digital holographic interferometry. The interference field is represented as a two-dimensional complex sinusoidal signal in an analysis window around each pixel. The method provides high resolution frequency estimates and does not require the two-dimensional search in the spectral domain. A simple denoising procedure is proposed based on singular value decomposition of the interference field. The uncertainty in the frequency estimate is utilized as a parameter to identify the regions containing high fringe concentration on the object surface. Simulation and experimental results are provided to show the noise robustness and the practical applicability of the proposed method.

Robust Frequency-Hopping Spectrum Estimation Based on Sparse Bayesian Method

This paper considers the problem of estimating multiple frequency hopping signals with unknown hopping pattern. By segmenting the received signals into overlapped measurements and leveraging the property that frequency content at each time instant is intrinsically parsimonious, a sparsity-inspired high-resolution time-frequency representation (TFR) is developed to achieve robust estimation. Inspired by the sparse Bayesian learning algorithm, the problem is formulated hierarchically to induce sparsity. In addition to the sparsity, the hopping pattern is exploited via temporal-aware clustering by exerting a dependent Dirichlet process prior over the latent parametric space. The estimation accuracy of the parameters can be greatly improved by this particular information-sharing scheme and sharp boundary of the hopping time estimation is manifested. Moreover, the proposed algorithm is further extended to multi-channel cases, where task-relation is utilized to obtain robust clustering of the latent parameters for better estimation performance. Since the problem is formulated in a full Bayesian framework, labor-intensive parameter tuning process can be avoided. Another superiority of the approach is that high-resolution instantaneous frequency estimation can be directly obtained without further refinement of the TFR. Results of numerical experiments show that the proposed algorithm can achieve superior performance particularly in low signal-to-noise ratio scenarios compared with other recently reported ones.

Iterative Algorithm for High Resolution Frequency Estimation

Iterative Algorithm for High Resolution Frequency Estimation

Optimization of piano tunings by minimizing perceived beat loudness.

In order to create an ideal piano tuning that best matches the inharmonicities and spectra of each instrument, tuning frequencies are optimized using a new beat loudness perceptual model that considers the time dependence of the frequency and amplitude of individual partials. These optimized tunings are compared to prior inharmonicity‐based methods of tuning calculation. First, several pianos are prepared to an initial tuning using traditional methods. The resulting tones are recorded and analyzed in MATLAB. Each partial's frequency and amplitude are estimated at discrete time intervals over the duration of the tones. Beat rates are derived for the consonant musical intervals by employing phase‐based high resolution frequency estimation techniques on coincident partials. A beat loudness model is developed based on established perceptual theories of consonance and equal loudness contours. The total perceived beat loudness is then minimized by applying optimization and global search methods that alter the t...

A Study on High Resolution Ranging Algorithm for The UWB Indoor Channel

In this paper, we present a novel and numerically efficient algorithm for high resolution TOA(Time Of Arrival) estimation under indoor radio propagation channels. The proposed algorithm is not dependent on the structure of receivers, i.e, it can be used with either coherent or non-coherent receivers. The TOA estimation algorithm is based on a high resolution frequency estimation algorithm of Minimum-norm The efficiency of the proposed algorithm relies on numerical analysis techniques in computing signal or noise subspaces. The algorithm is based on the two step procedures, one for transforming input data to frequency domain data and the other for estimating the unknown TOA using the proposed efficient algorithm. The efficiency in number of operations over other algorithms is presented. The performance of the proposed algorithm is investigated by means of computer simulations. Throughout the analytic and computer simulation results, we show that the proposed algorithm exhibits superior performance in estimating TOA estimation with limited computational cost.

Application of frequency estimation algorithm based on a single vector sensor in underwater acoustic communication

A method of high resolution frequency estimation based on a single vector sensor using ESPRIT (Estimating Signal Parameters via Rotational Invariance Techniques) algorithm is proposed and applied to the underwater acoustic (UWA) communication system of frequency modulation. Higher resolution frequency estimation can be obtained by this algorithm using fewer snapshots comparing with the sound intensity frequency estimation. Results of simulation and lake experiment show that the proposed algorithm can improve the communication data rate and reduce the bandwidth of the system. Because higher signal-to-noise ratio (SNR) is demanded, this algorithm can be used in high speed short range UWA communication at present.

Resolution-enhanced Fourier transform method for the estimation of multiple phases in interferometry

A phase shifting method based on high-resolution frequency estimation and Fourier transform technique is introduced. This method, also referred to as the eigenvector method, draws on the complementary strengths of both these methods. The salient feature of the method lies in its ability to handle nonsinusoidal wave-forms, multiple piezoelectric transducers, and arbitrary phase steps in an optical configuration. The method does not need the addition of carrier fringes to separate the spectral contents in the intensity fringes. The proposed concept thus overcomes the limitations of methods based on Fourier transform techniques. The robustness of the proposed method is studied in the presence of noise.

A 2-D robust high-resolution frequency estimation approach

This paper deals with a 2-D high-resolution frequency estimation method dedicated to images corrupted by outliers. Outliers are considered here as particular data points that do not fit an assumed model. We propose an efficient subspace estimation algorithm for 2-D complex sinusoids. In this framework the well-known model using the sum of complex exponentials fails for a small fraction of the data set causing the classical estimators to produce inaccurate results. To alleviate this drawback, we propose a new robust iterative Levenberg–Marquardt (LM) approach based method. The proposed approach operates in three main steps. First, we define a weight function based on the influence function which allows the “wrong” data to be detected and corrected. The influence function, which is inspired from the so-called M-estimator, measures the influence of a datum on the value of the estimated parameter. Second, a 2-D extension of the large sample approximation of the maximum likelihood (ML) estimator is developed in order to estimate image parameters. Third, the Levenberg–Marquardt (LM) technique is used to ensure the convergence of the ML estimator by detecting “wrong” data for each iteration. The effectiveness of the proposed method is illustrated by numerical simulations.

High-resolution frequency estimation technique for recovering phase distribution in interferometers

An integral approach to phase measurement is presented. First, the use of a high-resolution technique for the pixelwise detection of phase steps is proposed. Next, the robustness of the algorithm that is developed is improved by incorporation of a denoising procedure during spectral estimation. The pixelwise knowledge of phase steps is then applied to the Vandermonde system of equations for retrieval of phase values at each pixel point. Conceptually, our proposal involves the design of an annihilating filter that has zeros at the frequencies associated with the polynomial that describes the fringe intensity. The parametric estimation of this annihilating filter yields the desired spectral information embedded in the signal, which in our case represents the phase steps. The proposed method offers the advantage of extracting the interference phase of nonsinusoidal waveforms in the presence of miscalibration error of the piezoelectric transducer. In addition, in contrast to previously reported methods, this method does not require the application of selective phase steps between data frames for nonsinusoidal waveforms.

Estimation of damped and undamped sinusoids with application to analysis of electromagnetic FDTD simulation data

Computational electromagnetics deals with the problem of finding efficient and reliable solutions of Maxwell's equations. This is important in a variety of practical applications, such as antenna design and automatic target recognition, and time-domain computations are attractive for a large class of these problems. However, one is more often interested in the frequency characteristics of the solution. Using the Fourier transform to determine the resonance frequencies and damping factors requires long time series. implying severe computational complexity. An attractive alternative is to apply high-resolution frequency estimation, developed in the signal processing society over the past few decades. This is a challenging problem. though. as the number of interesting frequency components can be as large as several hundreds. To overcome the difficulties. we propose a frequency-domain subspace method that yields accurate frequency and damping estimates in a selected frequency band. The required electromagnetic simulation time can thereby be reduced by several orders of magnitude.

Separation of multiple time delays using new spectral estimation schemes

The problem of estimating multiple time delays in presence of colored noise is considered. This problem is first converted to a high-resolution frequency estimation problem. Then, the sample lagged covariance matrices of the resulting signal are computed and studied in terms of their eigenstructure. These matrices are shown to be as effective in extracting bases for the signal and noise subspaces as the standard autocorrelation matrix, which is normally used in MUSIC and the pencil-based methods. Frequency estimators are then derived using these subspaces. The effectiveness of the method is demonstrated on two examples: a standard frequency estimation problem in presence of colored noise and a real-world problem that involves separation of multiple specular components from the acoustic backscattered from an underwater target.

Simultaneous Schur decomposition of several nonsymmetric matrices to achieve automatic pairing in multidimensional harmonic retrieval problems

This paper presents a new Jacobi-type method to calculate a simultaneous Schur decomposition (SSD) of several real-valued, nonsymmetric matrices by minimizing an appropriate cost function. Thereby, the SSD reveals the average eigenstructure of these nonsymmetric matrices. This enables an R-dimensional extension of Unitary ESPRIT to estimate several undamped R-dimensional modes or frequencies along with their correct pairing in multidimensional harmonic retrieval problems. Unitary ESPRIT is an ESPRIT-type high-resolution frequency estimation technique that is formulated in terms of real-valued computations throughout. For each of the R dimensions, the corresponding frequency estimates are obtained from the real eigenvalues of a real-valued matrix. The SSD jointly estimates the eigenvalues of all R matrices and, thereby, achieves automatic pairing of the estimated R-dimensional modes via a closed-form procedure that neither requires any search nor any other heuristic pairing strategy. Moreover, we describe how R-dimensional harmonic retrieval problems (with R/spl ges/3) occur in array signal processing and model-based object recognition applications.