Amplitude Estimation Error Research Articles

An Optimization of Least-Square Harmonic Phasor Estimators in Presence of Multi-Interference and Harmonic Frequency Variance

The wide application of power electronic devices brings an increasing amount of undesired harmonic and interharmonic tones, and accurate harmonic phasor estimation under a complex signal input is an important task for smart grid applications. In this paper, an optimization of least-square dynamic harmonic phasor estimators, considering multi-interference and harmonic frequency variance, is proposed. A comprehensive error index (CEI) composed of the fundamental-leakage-led harmonic amplitude estimation error, harmonic mutual interference, out-of-band interference, and harmonic frequency deviation is employed. The largest CEI part of least-square algorithms using three different signal decomposition models is analyzed for the first time, and variables to reduce this error component are then introduced using singular value decomposition. With the CEI and defined variables, a minimum-error estimation of harmonic phasors under various interference and harmonic frequency change is discussed. Numerical tests are performed, and the test results show that after the proposed optimization is applied to least-square algorithms, the harmonic phasor estimation errors are considerably reduced, especially for low-order harmonics. We also show the possibility of choosing desired optimal phasor filter design by balancing the measurement accuracy and data latency. For example, when the window length is set to three nominal cycles, the proposed optimization can yield both good accuracy and fast measurement speed for estimating harmonic phasors under multi-interference and harmonic frequency variance.

Sound Pressure Signal-Based Bone Cutting Depth Control in Robotic Vertebral Lamina Milling

This paper aims to improve the performance of the robot-assisted bone milling operation. Based on a standard spinal surgery procedure, we established a dynamic bone milling model, which indicates that the cutting depth can be monitored based on the amplitudes of some specific harmonics of the milling sound pressure signal. The nominal frequency of these harmonics is an integer multiple of the spindle rotation frequency of the surgical milling tool. Therefore, we accurately extracted the absolute amplitude and frequency of the harmonics with nominal frequencies. We used the total harmonic amplitude to monitor the cutting depth and decrease the harmonic amplitude estimation error according to the absolute frequency of the first harmonic. A spine surgical robot carried out the bone milling experiment on artificial bone materials to verify. The results show that we can monitor the bone cutting depth with an accuracy of ±0.1 mm within the depth [0.1–1.2 mm] based on the auditory sense of the robot. The proposed method can improve the accuracy when a spine surgical robot performs the bone milling operation and make robot-assisted milling operation more accessible to inexperienced doctors via feedbacking the bone cutting depth in real-time.

Evaluation of Site Errors in LLS Magnetic Direction Finding Caused by Large Hills Using the 3D‐FDTD Technique

AbstractAngle and amplitude estimation errors in magnetic direction finding, called site errors, are important sensor‐specific errors in lightning location systems (LLS). They are known to be caused by nearby cables and overhead lines due to induced currents. Due to the reflection and diffraction of electromagnetic waves, hills and mountains are also expected to generate these effects. In this paper, numerical computations applying the finite‐difference time‐domain (FDTD) method are performed to analyze the impact of hills or mountains on the angle and amplitude estimation of LLS sensors for typical first and subsequent return strokes (RS). The influence of hill size, the distance of sensors to the hill, ground parameters, and sensor bandwidth, are evaluated. The results show that on top of low ridges of only 125 m elevation, up to ±10° angle site error and +50% amplitude site error occur. A key finding is that due to field attenuation caused by lossy ground and sensor bandwidth limitations, there is practically no difference in the angle site errors for first and subsequent RS. For two sensors, the average site errors obtained from real sensor measurements are compared to results from 3D‐FDTD simulations, modeling the real terrain based on a digital elevation model. The simulation results are in good agreement with the observed, average angle site errors.

SDR Based Modulation Performance of RF Signal under Different Communication Channel

Hardware components are an integral part of Hardware Define Radio (HDR) for seamless operations and optimal performance. On the other hand, Software Define Radio (SDR) is a program that does not rely on any hardware components for its performance. Both of the latter radio programmers utilize modulation functions to make their core components from signal processing viewpoint. The following paper concentrates on SDR based modulation and their performance under different modulations. The bit error rate (BER) of modulations such as PSK, QAM, and PSAM were used as indicators to test channel quality estimation in planar Rayleigh fading. Though it is not commonly used for channel fading, the method of the adder determines the regionally segmented channel fading. Thus, the estimation error of the channel change substantially reduces the performance of the signal, hence, proving to be an effective option. Moreover, this paper also elaborates that BER is calculated as a function of the sample size (signal length) with an average of 20 decibels. Consequently, the size of the results for different modulation schemes has been explored. The analytical results through derivations have been verified through computer simulation. The results focused on parameters of amplitude estimation error for 1dB reduction in the average signal-to-noise ratio, while the combined amplitude deviation estimation error results are obtained for a 3.5 dB reduction.

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.

Constrained Phase Noise Estimation in OFDM Using Scattered Pilots Without Decision Feedback

In this paper, we consider an OFDM radio link corrupted by oscillator phase noise in the receiver, namely the problem of estimating and compensating for the impairment. To lessen the computational burden and delay incurred onto the receiver, we estimate phase noise using only scattered pilot subcarriers, i.e., no tentative symbol decisions are used in obtaining and improving the phase noise estimate. In particular, the phase noise estimation problem is posed as an unconstrained optimization problem whose minimizer suffers from the so-called amplitude and phase estimation error. These errors arise due to receiver noise, estimation from limited scattered pilot subcarriers and estimation using a dimensionality reduction model. It is empirically shown that, at high signal-to-noise-ratios, the phase estimation error is small. To reduce the amplitude estimation error, we restrict the minimizer to be drawn from the so-called phase noise geometry set when minimizing the cost function. The resulting optimization problem is a non-convex program. However, using the S-procedure for quadratic equalities, we show that the optimal solution can be obtained by solving the convex dual problem. We also consider a less complex heuristic scheme that achieves the same objective of restricting the minimizer to the phase noise geometry set. Through simulations, we demonstrate improved coded bit-error-rate and phase noise estimation error performance when enforcing the phase noise geometry. For example, at high signal-to-noise-ratios, the probability density function of the phase noise estimation error exhibits thinner tails which results in lower bit-error-rate.

Nonparametric Signal Processing Validation in T-Wave Alternans Detection and Estimation

Although a number of methods have been proposed for T-Wave Alternans (TWA) detection and estimation, their performance strongly depends on their signal processing stages and on their free parameters tuning. The dependence of the system quality with respect to the main signal processing stages in TWA algorithms has not yet been studied. This study seeks to optimize the final performance of the system by successive comparisons of pairs of TWA analysis systems, with one single processing difference between them. For this purpose, a set of decision statistics are proposed to evaluate the performance, and a nonparametric hypothesis test (from Bootstrap resampling) is used to make systematic decisions. Both the temporal method (TM) and the spectral method (SM) are analyzed in this study. The experiments were carried out in two datasets: first, in semisynthetic signals with artificial alternant waves and added noise; second, in two public Holter databases with different documented risk of sudden cardiac death. For semisynthetic signals (SNR = 15dB), after the optimization procedure, a reduction of 34.0% (TM) and 5.2% (SM) of the power of TWA amplitude estimation errors was achieved, and the power of error probability was reduced by 74.7% (SM). For Holter databases, appropriate tuning of several processing blocks, led to a larger intergroup separation between the two populations for TWA amplitude estimation. Our proposal can be used as a systematic procedure for signal processing block optimization in TWA algorithmic implementations.

Accuracy analysis of the amplitude estimation of a sine-wave by the energy-based method using the direct and indirect procedures

The energy-based method (EBM) can be used to estimate the amplitude of a sine-wave either directly from Discrete Fourier Transform (DFT) samples or indirectly. In this paper the accuracies achieved with both these approaches are compared when some of the most commonly used cosine class windows are adopted. The effect on the estimation accuracy of the algorithm error, the spectral interference from the image component, and wideband noise superimposed to the sine-wave signal are separately evaluated and compared. The statistical efficiencies of both procedures with respect to the unbiased single-tone Cramér-Rao lower bound are determined and compared. Moreover, the overall root mean square of the amplitude estimation error achieved when taking into account all the three contributions above is derived for both direct and indirect estimation procedures. The accuracy of the obtained expressions is verified by means of computer simulations. Besides, experimental data validate the theoretical results.

Analytical formula for three points sinusoidal signals amplitude estimation errors

In this note, we show that the amplitude estimation of sinusoidal signals proposed in Wu and Hong [Wu, S.T., and Hong, J.L. (2010), ‘Five-point Amplitude Estimation of Sinusoidal Signals: With Application to LVDT Signal Conditioning’, IEEE Transactions on Instrumentation and Measurement, 59, 623–630] is a particular case of Vizireanu and Halunga [Vizireanu, D.N, and Halunga, S.V. (2011), ‘Single Sine Wave Parameters Estimation Method Based on Four Equally Spaced Samples’, International Journal of Electronics, 98(7), pp. 941–948]. An analytical formula for amplitude estimation errors as effects of sampling period deviation is obtained.

Fractional baud-length coding

Abstract. We present a novel approach for modulating radar transmissions in order to improve target range and Doppler estimation accuracy. This is achieved by using non-uniform baud lengths. With this method it is possible to increase sub-baud range-resolution of phase coded radar measurements while maintaining a narrow transmission bandwidth. We first derive target backscatter amplitude estimation error covariance matrix for arbitrary targets when estimating backscatter in amplitude domain. We define target optimality and discuss different search strategies that can be used to find well performing transmission envelopes. We give several simulated examples of the method showing that fractional baud-length coding results in smaller estimation errors than conventional uniform baud length transmission codes when estimating the target backscatter amplitude at sub-baud range resolution. We also demonstrate the method in practice by analyzing the range resolved power of a low-altitude meteor trail echo that was measured using a fractional baud-length experiment with the EISCAT UHF system.

The optical mouse for vibratory motion sensing

The optical mouse has been previously shown to be able to provide highly accurate measurements of slow displacements with a commercial unit with 0.0635 mm resolution. Here, its efficiency for vibratory displacements is investigated. It was found that frequency and amplitude thresholds existed beyond which the position–time distributions obtained would not permit analysis. From the analyzable distributions derived, frequency estimation errors below 15% in magnitude could only be comfortably achieved if the frequency was limited to 35 Hz and the amplitude limited to 0.4 mm, while amplitude estimation errors below 20% in magnitude could only be safely attained if the frequency was limited to 5 Hz and the amplitude limited to 0.2 mm. This work concludes that the optical mouse technology currently available is workable, but has a confined scope of low frequency and low amplitude application in vibration motion sensing. Nevertheless, this range still makes it useful as a dynamic sensor in a reasonable number of applications where low cost is particularly required.

The optical mouse for vibratory motion sensing

The optical mouse has been previously shown to be able to provide highly accurate measurements of slow displacements with a commercial unit with 0.0635 mm resolution. Here, its efficiency for vibratory displacements is investigated. It was found that frequency and amplitude thresholds existed beyond which the position–time distributions obtained would not permit analysis. From the analyzable distributions derived, frequency estimation errors below 15% in magnitude could only be comfortably achieved if the frequency was limited to 35 Hz and the amplitude limited to 0.4 mm, while amplitude estimation errors below 20% in magnitude could only be safely attained if the frequency was limited to 5 Hz and the amplitude limited to 0.2 mm. This work concludes that the optical mouse technology currently available is workable, but has a confined scope of low frequency and low amplitude application in vibration motion sensing. Nevertheless, this range still makes it useful as a dynamic sensor in a reasonable number of applications where low cost is particularly required.

Effect of channel estimation error on M-QAM BER performance in Rayleigh fading

We determine the bit-error rate (BER) of multilevel quadrature amplitude modulation (M-QAM) in flat Rayleigh fading with imperfect channel estimates, Despite its high spectral efficiency, M-QAM is not commonly used over fading channels because of the channel amplitude and phase variation. Since the decision regions of the demodulator depend on the channel fading, estimation error of the channel variation can severely degrade the demodulator performance. Among the various fading estimation techniques, pilot symbol assisted modulation (PSAM) proves to be an effective choice. We first characterize the distribution of the amplitude and phase estimates using PSAM. We then use this distribution to obtain the BER of M-QAM as a function of the PSAM and channel parameters. By using a change of variables, our exact BER expression has a particularly simple form that involves just a few finite-range integrals. This approach can be used to compute the BER for any value of M. We compute the BER for 16-QAM and 64-QAM numerically and verify our analytical results by computer simulation. We show that for these modulations, amplitude estimation error leads to a 1-dB degradation in average signal-to-noise ratio and combined amplitude-phase estimation error leads to 2.5-dB degradation for the parameters we consider.

Flat-top smoothing of periodograms and frequency averagings to increase the accuracy in estimating power spectral density

During the last years, many algorithms have been performed which are suitable both to increase the accuracy of estimating techniques in the frequency domain, and the precision and dynamic performance of digital instrumentation affected by a white quantization noise source. However, in the estimation of the power spectral density (PSD) function of a stationary random process through digital techniques, there is still one major drawback due to the trade-off between bias and variance, which the user should control. The performance of the periodogram estimator can be improved by averaging or smoothing the estimates, in the frequency domain, of nonoverlapping sections of the data sample but, for a finite sample size, we cannot completely control both bias and variance; when we attempt to reduce one, the other one increases. The main aim of this paper is to show how the estimation accuracy of a smoothed periodogram can be improved by adopting flat-top tapering in conjunction with averaging of 75% overlapped time slices of the data sample, based on Welch's method. The expressions for both components—those due to variance and bias—of the global (rms) amplitude estimation error have been derived and a lot of comparisons with the accuracy level given by classical cosine windows are proposed in order to confirm the better behaviour of the preoposed measurement technique. It has been developed and optimized to be very useful for control, diagnostics (ATE) and monitoring of electrical and electronic systems, under noisy non-sinusoidal conditions.

Leakage error in Fast Fourier analysis

Leakage, a common phenomenon in digital Fast Fourier Analysis, is discussed. An analytical explanation of leakage is presented with examples used to illustrate the detrimental effects to accurate signal analysis. Through this development, it is shown that signal amplitude errors of more than 36% are possible as a result of leakage. Also, an analytical method to resolve the error introduced by leakage, and hence to obtain accurate signal information, is presented. In conjunction with this methodology examples are provided to demonstrate the improvement in signal amplitude and frequency estimation possible. Amplitude estimation errors of 14·4% are reduced to 1·5% in one example. Finally, charts for quick estimation of signal amplitude and frequency based on this analytical method are presented. For further illustration, examples of use of this method are also given.