Common Mode Errors Research Articles

Spatiotemporal Filtering and Noise Analysis for Regional GNSS Network in Antarctica Using Independent Component Analysis

The common mode error (CME) and optimal noise model are the two most important factors affecting the accuracy of time series in regional Global Navigation Satellite System (GNSS) networks. Removing the CME and selecting the optimal noise model can effectively improve the accuracy of GNSS coordinate time series. The CME, a major source of error, is related to the spatiotemporal distribution; hence, its detrimental effects on time series can be effectively reduced through spatial filtering. Independent component analysis (ICA) is used to filter the time series recorded by 79 GPS stations in Antarctica from 2010 to 2018. After removing stations exhibiting strong local effects using their spatial responses, the filtering results of residual time series derived from principal component analysis (PCA) and ICA are compared and analyzed. The Akaike information criterion (AIC) is then used to determine the optimal noise model of the GPS time series before and after ICA/PCA filtering. The results show that ICA is superior to PCA regarding both the filter results and the consistency of the optimal noise model. In terms of the filtering results, ICA can extract multisource error signals. After ICA filtering, the root mean square (RMS) values of the residual time series are reduced by 14.45%, 8.97%, and 13.27% in the east (E), north (N), and vertical (U) components, respectively, and the associated speed uncertainties are reduced by 13.50%, 8.06% and 11.82%, respectively. Furthermore, different GNSS time series in Antarctica have different optimal noise models with different noise characteristics in different components. The main noise models are the white noise plus flicker noise (WN+FN) and white noise plus power law noise (WN+PN) models. Additionally, the spectrum index of most PN is close to that of FN. Finally, there are more stations with consistent optimal noise models after ICA filtering than there are after PCA filtering.

室内空间测量定位系统共模误差分析与消除

室内空间测量定位系统共模误差分析与消除

Comprehensive Analysis of the Effects of Common Mode Error on the Position Time Series of a Regional GPS Network

This study uses the daily horizontal and vertical Global Positioning System (GPS) position time series of 41 regionally distributed GPS stations in Southern California covering the period of January 2011 to January 2017 to extract the common mode error (CME) in east-north-up (ENU) components with the principal component analysis (PCA) method. We assume the first component with common spatial responses is CME. Firstly, we focus on the effects of CME on the root mean square (RMS) of the GPS time series. The results indicate that after being filtered, CMEs can reduce the average RMS values by 42.9, 39.1 and 28.8% for ENU components, respectively. Secondly, we investigate the changes in noise type before and after spatio-temporal filtration. The outcome reveals that noise model of the GPS position time series can be mainly described by power law noise (PL) plus white noise (WH). After CME correction, 32, 12 and 13% of the stations’ noise types are altered for ENU components, respectively. Thirdly, we confirm that stations whose noise properties can be best described by PL + WH, PL + WH and FL + WH or RW (Random walk noise) + FL + WH show no obvious differences in velocity and velocity uncertainty. Stations whose noise properties are described by RW + FL + WH, PL + WH and RW + FL + WH show significant differences in velocity and velocity uncertainty. Therefore, for all GPS stations, excluding the ones whose noise properties are described by the RW + FL + WH model, we estimate the noise parameters and velocity before and after spatio-temporal filtration by fitting a PL + WH model. According to our findings, the PCA method does not appear to be efficient for horizontal components. The CME is superimposed on the stochastic process realization for the vertical components. The impact of CME on vertical velocity estimation cannot be ignored, and eliminating CME enhances the credibility of the determined velocity field. Finally, we discuss the correlation between CME and mass loadings. The results of the Pearson correlation analysis and wavelet coherence analysis indicate that CME cannot be interpreted by mass loadings in a regional GPS network and that it may be related to GPS technique errors.

High‐precision differential time integrator based on time adder

A high-precision time integrator is presented whose output is the accumulation of sequence of time inputs. A novel time adder with time-domain differential structure is proposed to avoid common-mode errors such as supply noise and leakage current. The performance under various process, voltage and temperature conditions is examined in detail. By using two time adders in parallel, a differential synchronous time integrator is proposed, which is easier to cascade with other time-mode arithmetic circuit. Implemented in 65 nm 1.2 V CMOS technology, the proposed time integrator achieves a gain of 27.97 dB with a 317 kHz 30 ps peak-to-peak sinusoidal input, and consumes 152 .7 μ W with 50 MHz sampling rate. The experimental results confirm the integration operation is realised properly and accurately.

Spatially varying surface seasonal oscillations and 3-D crustal deformation of the Tibetan Plateau derived from GPS and GRACE data

Measurements of 189 continuous and 933 campaign-mode Global Positioning System (GPS) stations with 3–16 yr data spans over the Tibetan Plateau reveal contemporary three-dimensional (3-D) crustal deformation during 1999–2016. The Empirical Orthogonal Function method was used to characterize the spatial variations in the surface deformation with distinct seasonal oscillations at the GPS sites in five regions of the Tibetan Plateau. We find that these surface variations are highly correlated with the corresponding mass load signals observed by the Gravity Recovery and Climate Experiment (GRACE) mission. The improved GPS processing strategy used to determine the 3-D velocity field includes maximum likelihood estimation, removal of common mode errors from GPS time series using Principal Component Analysis (PCA), and power law plus white noise stochastic error modeling. We determined the rates of vertical crustal movement by removing GRACE-observed non-tectonic origin load deformation, 2002–2016. The corrected vertical crustal deformation shows that the Himalaya region is uplifting at an average rate of ∼1.7 mm yr−1, and that the northeastern Tibetan Plateau is uplifting at an average rate of ∼1.3 mm yr−1. In addition, the horizontal velocity relative to the stable Eurasian plate and its corresponding dilatation throughout the Tibetan Plateau suggest that tectonic shortening and crustal thickening is occurring at −90 to −80 nanostrain yr−1 in the southern Tibetan Plateau and −30 to −20 nanostrain yr−1 in the northeastern Tibetan Plateau, which could be related to the geologic shortening and elastic strain accumulation. The interior Tibetan Plateau exhibits crustal thinning and block movement along strike-slip faults. Eastward motion of the crust north of the Xianshuihe-Xiaojiang Fault system relative to crust to its south results in shear strain and reflects eastward escape of plastic crustal material in the southeastern Tibetan Plateau.

Accuracy enhancement of high-rate GNSS positions using a complete ensemble empirical mode decomposition-based multiscale multiway PCA

In order to improve the possibility of correct interpretation of some geophysical phenomena such seismology, it is important to reduce systematic errors such as common mode error (CME) and multipath errors, and to improve the accuracy of high-rate (1–5 Hz) displacements. This paper focuses on accuracy enhancement and noise assessment of high-rate Global Navigation Satellite System (GNSS) position time series of regional network of GNSS stations. Complete ensemble empirical mode decomposition-based multiscale multiway principal component analysis (C-MSMPCA) denoising method is introduced to denoise the high-rate (1–5 Hz) GNSS position time series, whose performance was compared with those of modified sidereal filtering (MSF), stacking filtering, PCA and the recently developed multiscale multiway PCA (MSMPCA). It turns out that C-MSMPCA can significantly eliminate the high-frequency random noise and remove the low-frequency CME, and other systematic errors such as multipath errors. Furthermore, for denoising high-rate GNSS time series, C-MSMPCA is more precise than the other denoising methods. Irrespective of sampling rates and data processing strategies, C-MSMPCA can respectively reach the accuracy of submillimeter- and millimeter-levels on the horizontal and vertical components of high-rate GNSS displacements. Spectral analysis on the 1 Hz coordinate time series from the Sichuan GNSS Continuous Observing Network of China suggests that Gauss-Markov process is an adequate noise model for the noise characteristics of the filtered GNSS data using MSMPCA and C-MSMPCA. The CME magnitudes of MSMPCA are 2.61, 2.55, and 6.72 mm (east, north, and vertical), and those of C-MSMPCA are 2.69, 2.80, and 7.80 mm, respectively.

Reliability Importance of Components in a Real-Time Computing System with Standby Redundancy Schemes

Component importance analysis is to measure the effect on system reliability of component reliabilities, and is used to the system design from the reliability point of view. On the other hand, to guarantee high reliability of real-time computing systems, redundancy has been widely applied, which plays an important role in enhancing system reliability. One of commonly used type of redundancy is the standby redundancy. However, redundancy increases not only the complexity of a system but also the complexity of associated problems such as common-mode error. In this paper, we consider the component importance analysis of a real-time computing system with warm standby redundancy in the presence of Common-Cause Failures (CCFs). Although the CCFs are known as a risk factor of degradation of system reliability, it is difficult to evaluate the component importance measures in the presence of CCFs analytically. This paper introduces a Continuous-Time Markov Chain (CTMC) model for real-time computing system, and applies the CTMC-based component-wise sensitivity analysis which can evaluate the component importance measures without any structure function of system. In numerical experiments, we evaluate the effect of CCFs by the comparison of system performance measure and component importance in the case of system without CCF with those in the case of system with CCFs. Also, we compare the effect of CCFs on the system in warm and hot standby configurations.

Common mode error in Antarctic GPS coordinate time-series on its effect on bedrock-uplift estimates

Spatially correlated common mode error (CME) always exists in regional, or-larger, global positioning system (GPS) networks. We applied independent component analysis (ICA) to GPS vertical coordinate time-series in Antarctica from 2010 to 2014 and made a comparison with the principal component analysis (PCA). Using PCA/ICA, the time-series can be decomposed into a set of temporal components and their spatial responses. We assume the components with common spatial responses are CME. An average reduction of ∼40 per cent about the root-mean-square (RMS) values was achieved in both PCA and ICA filtering. However, the common mode components obtained from the two approaches have different spatial and temporal features. ICA time-series present interesting correlations with modelled atmospheric and non-tidal ocean loading displacements. A white noise plus power law (PL) noise model was adopted in the GPS velocity estimation using maximum likelihood estimation analysis, with ∼55 per cent reduction of the velocity uncertainties after filtering using ICA. Meanwhile, spatiotemporal filtering reduces the amplitude of PL and periodic terms in the GPS time-series. Finally, we compare the GPS uplift velocities, after correction for elastic effects, with recent models of glacial isostatic adjustment (GIA). The agreements of the GPS observed velocities and four GIA models are generally improved after the spatiotemporal filtering, with a mean reduction of ∼0.9 mm yr−1 of the weighted RMS values, possibly allowing for more confident separation of various GIA model predictions.

A Filtering of Incomplete GNSS Position Time Series with Probabilistic Principal Component Analysis

For the first time, we introduced the probabilistic principal component analysis (pPCA) regarding the spatio-temporal filtering of Global Navigation Satellite System (GNSS) position time series to estimate and remove Common Mode Error (CME) without the interpolation of missing values. We used data from the International GNSS Service (IGS) stations which contributed to the latest International Terrestrial Reference Frame (ITRF2014). The efficiency of the proposed algorithm was tested on the simulated incomplete time series, then CME was estimated for a set of 25 stations located in Central Europe. The newly applied pPCA was compared with previously used algorithms, which showed that this method is capable of resolving the problem of proper spatio-temporal filtering of GNSS time series characterized by different observation time span. We showed, that filtering can be carried out with pPCA method when there exist two time series in the dataset having less than 100 common epoch of observations. The 1st Principal Component (PC) explained more than 36% of the total variance represented by time series residuals’ (series with deterministic model removed), what compared to the other PCs variances (less than 8%) means that common signals are significant in GNSS residuals. A clear improvement in the spectral indices of the power-law noise was noticed for the Up component, which is reflected by an average shift towards white noise from − 0.98 to − 0.67 (30%). We observed a significant average reduction in the accuracy of stations’ velocity estimated for filtered residuals by 35, 28 and 69% for the North, East, and Up components, respectively. CME series were also subjected to analysis in the context of environmental mass loading influences of the filtering results. Subtraction of the environmental loading models from GNSS residuals provides to reduction of the estimated CME variance by 20 and 65% for horizontal and vertical components, respectively.

The Consideration of Formal Errors in Spatiotemporal Filtering Using Principal Component Analysis for Regional GNSS Position Time Series

In the daily operation of regional GNSS (Global Navigation Satellite System) networks, the formal errors of all stations’ coordinate components are calculated. However, spatiotemporal filtering based on traditional Principal Component Analysis (PCA) for regional GNSS position time series does not take these formal errors into account. This paper developed a PCA-based approach to extract Common Mode Error (CME) from the position time series of a regional GNSS station network, where formal errors were applied to construct a weight factor. Because coordinate components with larger errors have smaller weight factors in extracting CME, the performance of our proposed approach was anticipated to be better than the traditional PCA approach. The position time series of 25 stations in the Yunnan Province, China, were analyzed using our approach, as well as the traditional PCA approach. The average errors of the residual time series after removing the CMEs with our approach were 1.30 mm, 1.72 mm, and 4.62 mm for North, East and Up components, and the reductions with respect to those of the original time series were 18.23%, 15.42%, and 18.25%, respectively. If CMEs were removed from the traditional PCA approach, the corresponding average errors were 1.34 mm, 1.81 mm, and 4.84 mm, with reductions of 15.84%, 10.86%, and 14.32%, respectively. Compared to the traditional PCA approach, the average errors of our approach were reduced by about 2.39%, 4.56%, and 3.93% in the North, East and Up components, respectively. Analysis of CME indicated that it mainly contained white and flicker noise. In the synthetic position time series with 500 repeated simulations, the CME extracted by our approach was closer to the true simulated values than those extracted by the traditional PCA approach, regardless of whether local effects were considered or not. Specifically, the mean root mean square (RMS) reduction of our approach, relative to PCA, ranged from 1.35% to 3.93%. Our simulations illustrated that the RMS reductions depended not only on the magnitude, but also the variation of the formal error series, which further highlights the necessity of considering formal errors in spatiotemporal filtering.

Multichannel Singular Spectrum Analysis in the Estimates of Common Environmental Effects Affecting GPS Observations

We described a spatio-temporal analysis of environmental loading models: atmospheric, continental hydrology, and non-tidal ocean changes, based on multichannel singular spectrum analysis (MSSA). We extracted the common annual signal for 16 different sections related to climate zones: equatorial, arid, warm, snow, polar and continents. We used the loading models estimated for a set of 229 ITRF2014 (International Terrestrial Reference Frame) International GNSS Service (IGS) stations and discussed the amount of variance explained by individual modes, proving that the common annual signal accounts for 16, 24 and 68% of the total variance of non-tidal ocean, atmospheric and hydrological loading models, respectively. Having removed the common environmental MSSA seasonal curve from the corresponding GPS position time series, we found that the residual station-specific annual curve modelled with the least-squares estimation has the amplitude of maximum 2 mm. This means that the environmental loading models underestimate the seasonalities observed by the GPS system. The remaining signal present in the seasonal frequency band arises from the systematic errors which are not of common environmental or geophysical origin. Using common mode error (CME) estimates, we showed that the direct removal of environmental loading models from the GPS series causes an artificial loss in the CME power spectra between 10 and 80 cycles per year. When environmental effect is removed from GPS series with MSSA curves, no influence on the character of spectra of CME estimates was noticed.

Effect of removing the common mode errors on linear regression analysis of noise amplitudes in position time series of a regional GPS network & a case study of GPS stations in Southern California

The analysis of the correlations between the noise in different components of GPS stations has positive significance to those trying to obtain more accurate uncertainty of velocity with respect to station motion. Previous research into noise in GPS position time series focused mainly on single component evaluation, which affects the acquisition of precise station positions, the velocity field, and its uncertainty. In this study, before and after removing the common-mode error (CME), we performed one-dimensional linear regression analysis of the noise amplitude vectors in different components of 126 GPS stations with a combination of white noise, flicker noise, and random walking noise in Southern California. The results show that, on the one hand, there are above-moderate degrees of correlation between the white noise amplitude vectors in all components of the stations before and after removal of the CME, while the correlations between flicker noise amplitude vectors in horizontal and vertical components are enhanced from un-correlated to moderately correlated by removing the CME. On the other hand, the significance tests show that, all of the obtained linear regression equations, which represent a unique function of the noise amplitude in any two components, are of practical value after removing the CME. According to the noise amplitude estimates in two components and the linear regression equations, more accurate noise amplitudes can be acquired in the two components.

A data-driven approach for denoising GNSS position time series

Global navigation satellite system (GNSS) datasets suffer from common mode error (CME) and other unmodeled errors. To decrease the noise level in GNSS positioning, we propose a new data-driven adaptive multiscale denoising method in this paper. Both synthetic and real-world long-term GNSS datasets were employed to assess the performance of the proposed method, and its results were compared with those of stacking filtering, principal component analysis (PCA) and the recently developed multiscale multiway PCA. It is found that the proposed method can significantly eliminate the high-frequency white noise and remove the low-frequency CME. Furthermore, the proposed method is more precise for denoising GNSS signals than the other denoising methods. For example, in the real-world example, our method reduces the mean standard deviation of the north, east and vertical components from 1.54 to 0.26, 1.64 to 0.21 and 4.80 to 0.72 mm, respectively. Noise analysis indicates that for the original signals, a combination of power-law plus white noise model can be identified as the best noise model. For the filtered time series using our method, the generalized Gauss–Markov model is the best noise model with the spectral indices close to − 3, indicating that flicker walk noise can be identified. Moreover, the common mode error in the unfiltered time series is significantly reduced by the proposed method. After filtering with our method, a combination of power-law plus white noise model is the best noise model for the CMEs in the study region.

Objective detection of long-term slow slip events along the Nankai Trough using GNSS data (1996\u20132016)

This paper presents a method for objective detection of long-term slow slip events with durations on the order of years, on the plate boundary along the Nankai Trough, relying on global navigation satellite system daily coordinate data. The Chugoku region of Japan was held fixed to remove common mode errors, and a displacement component was calculated relative to the direction of plate subduction. Correlations were then calculated between this displacement component and a 3-year ramp function with a 1-year slope. Nearly all periods of strong correlation coincide with periods of previously reported long-term slow slip events. A period of strong correlation around the Kii Channel in 2000–2002 is attributed to a previously undocumented long-term slow slip event beneath the Kii Channel and the eastern part of Shikoku Island with an equivalent moment magnitude of 6.6. This detection method reveals variation among long-term slow slip events along the Nankai Trough.

Study of seasonal and long-term vertical deformation in Nepal based on GPS and GRACE observations

Lithospheric deformation signal can be detected by combining data from continuous global positioning system (CGPS) and satellite observations from the Gravity Recovery and Climate Experiment (GRACE). In this paper, we use 2.5- to 19-year-long time series from 35 CGPS stations to estimate vertical deformation rates in Nepal, which is located in the southern side of the Himalaya. GPS results were compared with GRACE observations. Principal component analysis was conducted to decompose the time series into three-dimensional principal components (PCs) and spatial eigenvectors. The top three high-order PCs were calculated to correct common mode errors. Both GPS and GRACE observations showed significant seasonal variations. The observed seasonal GPS vertical variations are in good agreement with those from the GRACE-derived results, particularly for changes in surface pressure, non-tidal oceanic mass loading, and hydrologic loading. The GPS-observed rates of vertical deformation obtained for the region suggest both tectonic impact and mass decrease. The rates of vertical crustal deformation were estimated by removing the GRACE-derived hydrological vertical rates from the GPS measurements. Most of the sites located in the southern part of the Main Himalayan Thrust subsided, whereas the northern part mostly showed an uplift. These results may contribute to the understanding of secular vertical crustal deformation in Nepal.

Overpressure and Fluid Diffusion Causing Non-hydrological Transient GNSS Displacements

In this work, global navigation satellite system (GNSS) observations from the northern tip of the Adria microplate are analysed to differentiate non-periodic (transient) tectonic signals from other deviations from the linear trends primarily due to hydrological loading effects. We tested a recently proposed hypothesis that a porosity wave generated by fault-valve mechanisms in a seismogenic fault in the Bovec basin (western Slovenia) propagated throughout the surrounding region. After excluding potential spatially correlated common-mode errors in the considered time series, we investigated the relationship between the GNSS observations and periodic hydrological loading variations. The tests demonstrated that subtracting the hydrological term was effective at the global scale and that the frequency band of the transient signal (1.5 < T < 3.5 years) was not correlated with hydrological effects at the local scale (within a few kilometres of the station). Next, the results of previous works are used to calculate the permeability values and pore-pressure state at the source of the transient signal. The permeability values for the four main rock formations in the region are consistent with independent observations for similar lithotypes. The ratio between the effective stress and lithostatic load for different vertical profiles in the Bovec area indicated a state of overpressure, with pore-pressure close to the value of the lithostatic load. Thus, our results help define a scenario in which the porosity wave could have originated. Indeed, the formation of the domains of interconnected fractures, such as during the formation of a porosity wave, increases the permeability values, thereby relieving overpressure and restoring a state of equilibrium.

A micro-array bio detection system based on a GMR sensor with 50-ppm sensitivity

Bio detection is widely utilized in hospitals and laboratories. However, conventional bio detection methods suffer from long detection time, complex operation, and low sensitivity, and these issues prevent their use in point of care testing (POCT) applications. Microelectronic bio detection methods are proposed to overcome these issues. Bio detection based on a micro-electronic technique allows easy integration of a system, leading to a fast detection speed and simple operation. In this work, a fully microelectronic bio detection system including a sensor design, a read-out strategy, and data processing is proposed based on a GMR biosensor. A GMR sensor chip is designed and different passivation layer thicknesses are tested to improve sensitivity. A 40 nm thickness passivation is realized to produce the largest response without oxidization and breakdown. In order to integrate the read-out circuit and simplify operations, a 4-channel read-out biochip is designed and fabricated, and this exhibits a super-low output noise corresponding to $-116.84$ dBm/Hz at the operation frequency. This means that the noise only approximately corresponds to the signal level of five magnetic nanoparticles with a diameter of 200 nm. A reference sensor is also utilized to cancel the unwanted signal and reduce common-mode noise and error to improve sensitivity. Measurements indicate that 90% suppression is achieved. The measurements also reveal that a sensitivity of 50 ppm is achieved with the proposed GMR bio detection system.

Spatiotemporal filtering for regional GPS network in China using independent component analysis

Removal of the common mode error (CME) is a routine procedure in postprocessing regional GPS network observations, which is commonly performed using principal component analysis (PCA). PCA decomposes a network time series into a group of modes, where each mode comprises a common temporal function and corresponding spatial response based on second-order statistics (variance and covariance). However, the probability distribution function of a GPS time series is non-Gaussian; therefore, the largest variances do not correspond to the meaningful axes, and the PCA-derived components may not have an obvious physical meaning. In this study, the CME was assumed statistically independent of other errors, and it was extracted using independent component analysis (ICA), which involves higher-order statistics. First, the ICA performance was tested using a simulated example and compared with PCA and stacking methods. The existence of strong local effects on some stations causes significant large spatial responses and, therefore, a strategy based on median and interquartile range statistics was proposed to identify abnormal sites. After discarding abnormal sites, two indices based on the analysis of the spatial responses of all sites in each independent component (east, north, and vertical) were used to define the CME quantitatively. Continuous GPS coordinate time series spanning $$\sim $$ 4.5 years obtained from 259 stations of the Tectonic and Environmental Observation Network of Mainland China (CMONOC II) were analyzed using both PCA and ICA methods and their results compared. The results suggest that PCA is susceptible to deriving an artificial spatial structure, whereas ICA separates the CME from other errors reliably. Our results demonstrate that the spatial characteristics of the CME for CMONOC II are not uniform for the east, north, and vertical components, but have an obvious north–south or east–west distribution. After discarding 84 abnormal sites and performing spatiotemporal filtering using ICA, an average reduction in scatter of 6.3% was achieved for all three components.

Orthogonal transformation in extracting of common mode error from continuos GPS network

Orthogonal transformation in extracting of common mode error from continuos GPS network

Design and Verification of a Digital Controller for a 2-Piece Hemispherical Resonator Gyroscope.

A Hemispherical Resonator Gyro (HRG) is the Coriolis Vibratory Gyro (CVG) that measures rotation angle or angular velocity using Coriolis force acting the vibrating mass. A HRG can be used as a rate gyro or integrating gyro without structural modification by simply changing the control scheme. In this paper, differential control algorithms are designed for a 2-piece HRG. To design a precision controller, the electromechanical modelling and signal processing must be pre-performed accurately. Therefore, the equations of motion for the HRG resonator with switched harmonic excitations are derived with the Duhamel Integral method. Electromechanical modeling of the resonator, electric module and charge amplifier is performed by considering the mode shape of a thin hemispherical shell. Further, signal processing and control algorithms are designed. The multi-flexing scheme of sensing, driving cycles and x, y-axis switching cycles is appropriate for high precision and low maneuverability systems. The differential control scheme is easily capable of rejecting the common mode errors of x, y-axis signals and changing the rate integrating mode on basis of these studies. In the rate gyro mode the controller is composed of Phase-Locked Loop (PLL), amplitude, quadrature and rate control loop. All controllers are designed on basis of a digital PI controller. The signal processing and control algorithms are verified through Matlab/Simulink simulations. Finally, a FPGA and DSP board with these algorithms is verified through experiments.