Error Estimation Method Research Articles

A Joint Estimation Method of the Channel Phase Error and Motion Error for Distributed SAR on a Single Airborne Platform Based on a Time-Domain Correlation Method

Distributed synthetic aperture radar (SAR) is a system in which transmitting or receiving arrays are distributed on multiple platforms or at different locations on one platform. Distributed SAR can be used for high-resolution wide-swath (HRWS) imaging. The typical platform used for distributed SAR is a satellite constellation, which has long baselines and an ideal trajectory. Instead of satellite constellations, this paper focuses on distributed SAR on a single airborne platform, for which the channel error and motion error are coupled. Furthermore, the traditional channel error estimation methods are invalid. Thus, based on the time-domain correlation method (TDCM), this article proposes a joint estimation method of the channel phase error and motion error for the distributed SAR on a single airborne platform. Firstly, a channel error and motion error coupled phase error model of the distributed SAR is constructed. A joint estimation method of the channel phase error and motion error is then proposed. Finally, a simulation and real data processing are provided to demonstrate the effectiveness of the proposed method.

Research on Angle Random Walk Suppression and Error Estimation and Compensation Method Based on Online Weight Distribution of Multi-RINSs

Rotary inertial navigation system(RINS) can suppress constant and slowly varying errors of inertial sensors through rotary modulation technology. However, the angle random walk(ARW) error of gyro can not be modulated, which has become the key factor of restricting the long-term navigation accuracy of RINS. In this paper, the influence of ARW on long-term navigation accuracy of RINS is analyzed. In view of the situation that GPS and other external auxiliary information are not available, an ARW suppression and error estimation and compensation method based on online weight distribution of multi-RINSs is proposed. Considering the disturbance of deflection to attitude and the disturbance of lever arm effect to velocity, the dynamic weighted average of position information of multi-RINSs are selected as the measurement, the equivalent error parameters of each RINS are estimated and compensated by KF filter is proposed. The simulation results show that the navigation errors caused by ARW can be reduced several times by using the proposed suppression method, and the weighted average position information to estimate and compensate the equivalent error of each RINS, which can further improve the navigation accuracy of each RINS by about 3 times, and proved that the proposed method of restraining ARW and error estimation and compensation is effective. It makes the relationship among the RINSs of from backup to auxiliary, which has significant value for further improving the autonomous long-term navigation accuracy.

Measurement Error Estimation for Distributed Smart Meters Through a Modified BP Neural Network

Smart meters generally suffer degradation of metering accuracy and performance due to aging, faults, and other factors, which, however, are difficult to detect. This study proposes a measurement error estimation method for distributed smart meters based on a modified BP neural network. First, the relationship model between the metering correction coefficient, network loss, and energy consumption measurement value for the distributed system is established. Then, a modified BP neural network for the parameter estimation method is proposed, in which the internal activation function, iterative step size, and other parameters are comprehensively designed. Finally, the parameters of the distributed smart meter measurement error are solved through training and learning. The case study verifies the effectiveness of the proposed method, and this study lays a theoretical foundation for accurate prediction of the measurement error for distributed smart meters.

An improved coastline inflection method for geolocation correction of Microwave Radiation Imager data

ABSTRACT Geolocation accuracy is an important factor affecting the application of microwave remote sensing data. For effective application of microwave radiation data in quantitative remote sensing, geolocation errors should be corrected. The coastline inflection method (CIM) is widely used for geolocation correction of microwave radiometer data, which consists of the inflection point identification process and the error estimation process. The detected coastline that is composed of the brightness temperature inflection points can be identified in the first process, and the error between the detected coastline and the true coastline can be estimated in the second process. However, both processes will be affected when the coastline is complex or disturbed by some clouds, rain, etc. Therefore, we improve the CIM in its two processes. Firstly, a method based on the dynamic threshold is used to identify inflection points. Secondly, a new geolocation error estimation method combining the Iterative Closest Point (ICP) algorithm and the Kernel Correlation (KC) algorithm is proposed to estimate geolocation errors. By applying the proposed method, the FengYun-3C (FY-3C) Microwave Radiation Imager (MWRI) dataset selected in the specified regions from 1 April 2019 to 1 October 2019 is processed. For the data with complex coastline structure or some interference factors, compared with the CIM based on a surface fitting interpolation model and ICP algorithm, the number of inflection points is increased by about 70%, and the mean geolocation errors in cross- and along-track directions are reduced by about 24.12% and 21.61%, respectively. For the data with simple coastline structure and less interference, the two methods have similar effects. For all selected data, the mean geolocation errors in cross- and along-track directions is reduced from [0.5376, 0.5528] pixels to [0.1581, 0.1110] pixels. Mean geolocation accuracy is improved by approximately 75%.

Moving target imaging of a dual-channel ISAL with binary phase shift keying signals and large squint angles.

A dual-channel inverse synthetic aperture ladar imaging experimental system based on wide-pulse binary phase coded signals and its moving target imaging are introduced. The analysis, simulation, and experimental data processing results of binary phase coded signal Doppler compensation and pulse compression are included. The method of motion phase error estimation based on interferometric processing and the imaging method with small computation in the case of large squint angles are proposed, and the simulation results are presented. The effectiveness of the imaging method is verified by experimental data processing. Doppler frequency curves are estimated based on time-frequency analysis of echo signals, and the coarse compensation of motion phase error is realized. According to the interferometric phase and coherence coefficient of dual-channel echo signals' time-frequency analysis, the coherence of the dual-channel echo signals is checked, and along-track interferometry can be applied to the precise compensation. The stable interferometric phase and increased coherence coefficient of actual dual-channel data imaging results indicate the effectiveness of the motion phase error compensation method proposed. Considering characteristics of inverse synthetic aperture ladar (ISAL) imaging, after dividing echo signals into multiple sub-apertures, range-Doppler algorithm and sub-aperture stitching are adopted, the stitched image is corrected geometrically through Stolt transformation, and the computation is reduced.

Numerical solutions of the Bagley–Torvik equation by using generalized functions with fractional powers of Laguerre polynomials

Abstract In this study, a collocation approach is presented to solve Bagley–Torvik equation, which is a class of fractional differential equations. As most fractional differential equations do not have exact analytical solutions, it is needed numerical methods. This study is important because it presents a numerical method for fractional differential equations. The main purpose of this method is to obtain the approximate solution based on Laguerre polynomials of the Bagley–Torvik equation. To date, a collocation method based on the Laguerre polynomials has not been studied for the solutions of the Bagley–Torvik equation. This reveals the novelty of the study. The approximate solution is sought in form of the fractional powers of the Laguerre polynomials. By using the Caputo derivative, the matrix relation is created for term with fractional derivative in the equation. Similarly, the matrix relation of second derivative is computed in equation. Then, by using these matrix relations and the collocation points, the Bagley–Torvik problem is converted into a system of the linear algebraic equations. The solution of this system gives the coefficients of the assumed solution. Secondly, an error estimation method is given with the help of the residual function and also the Laguerre polynomial solution is improved by using the estimated error function. Then, the method is applied to four examples and the obtained numerical results are shown in tables and graphs. Also, the comparisons are made with other methods in the literature and so the presented method gives better results than other methods.

A Model-Based Iterative Learning Approach for Diffuse Optical Tomography.

Diffuse optical tomography (DOT) utilises near-infrared light for imaging spatially distributed optical parameters, typically the absorption and scattering coefficients. The image reconstruction problem of DOT is an ill-posed inverse problem, due to the non-linear light propagation in tissues and limited boundary measurements. The ill-posedness means that the image reconstruction is sensitive to measurement and modelling errors. The Bayesian approach for the inverse problem of DOT offers the possibility of incorporating prior information about the unknowns, rendering the problem less ill-posed. It also allows marginalisation of modelling errors utilising the so-called Bayesian approximation error method. A more recent trend in image reconstruction techniques is the use of deep learning, which has shown promising results in various applications from image processing to tomographic reconstructions. In this work, we study the non-linear DOT inverse problem of estimating the (absolute) absorption and scattering coefficients utilising a 'model-based' learning approach, essentially intertwining learned components with the model equations of DOT. The proposed approach was validated with 2D simulations and 3D experimental data. We demonstrated improved absorption and scattering estimates for targets with a mix of smooth and sharp image features, implying that the proposed approach could learn image features that are difficult to model using standard Gaussian priors. Furthermore, it was shown that the approach can be utilised in compensating for modelling errors due to coarse discretisation enabling computationally efficient solutions. Overall, the approach provided improved computation times compared to a standard Gauss-Newton iteration.

Making the most of data: Quantum Monte Carlo postanalysis revisited.

In quantum Monte Carlo (QMC) methods, energy estimators are calculated as (functions of) statistical averages of quantities sampled during a calculation. Associated statistical errors of these averages are often estimated. This error estimation is not straightforward and there are several choices of the error estimation methods. We evaluate the performance of three methods (the Straatsma method, an autoregressive model, and a blocking analysis based on von Neumann's ratio test for randomness) for the energy time series given by three QMC methods [diffusion Monte Carlo, full configuration interaction Quantum Monte Carlo (FCIQMC), and coupled cluster Monte Carlo (CCMC)]. From these analyses, we describe a hybrid analysis method which provides reliable error estimates for a series of various lengths of FCIQMC and CCMC's time series. Equally important is the estimation of the appropriate start point of the equilibrated phase. We establish that a simple mean squared error rule method as described by White [K. P. White, Jr., Simulation 69(6), 323 (1997)10.1177/003754979706900601] can provide reasonable estimations.

Adaptive location correction and path re-planning based on error estimation method in underwater sensor networks

Due to the accuracy limitation of the underwater positioning system and the interference of the external environment, the actual trajectory of the autonomous underwater vehicle (AUV) will deviate from the predetermined path during the underwater mission, which cannot guarantee the mission completion and safety. To reduce navigation errors, this paper introduces forward-looking sonar (FLS) and proposes a path correction scheme based on error estimation of underwater sensor networks: Derive the position and attitude of the AUV by processing FLS images to obtain the relative orientation between the robot and the target; combine the node information in the time-varying navigation map to calculate the error with the planned path; then fused with the a priori error of the underwater sensor network to build the error system model; completion of path re-planning based on the improved Bionic Neural Wave Network (BNWN) algorithm and time-varying navigation map; adjust the weight parameters during the iteration to make the drift error converge and finally complete the correction of the path. Simulation experiments prove that the path planned in this scheme can neutralize the drift errors from the algorithm level, and the AUV can complete the capture of dynamic and static targets with a small error when tracking this path.

A robust real-time flood forecasting method based on error estimation for reservoirs

Abstract The observed discharge, an important input for flood forecasting systems, can significantly affect the accuracy of forecasting results. Since the reservoir inflow is not measured directly but calculated based on the observed reservoir stage and the reservoir outflow, it always contains gross errors causing some inflow to be outliers. In this study, a robust error estimation method for real-time flood forecasting has been developed for reservoirs’ data processing. The method differs from the conventional flood forecasting method, in that it represses the gross errors by a robust loss function based on the real error distribution of measurements. Furthermore, a fluctuation coefficient has been proposed to quantify the degree of fluctuation of a jagged reservoir inflow. The performance of the method is evaluated by both synthetic data and real cases. By using floods generated synthetically by an ideal model in which the true values and errors are known, the method is shown to be efficient as theoretically expected. The results show that the method is efficient and universally applicable in different cases. And the degree of forecast improvement is positively related to the fluctuation coefficient of the floods. The more severe the fluctuation of the flood hydrograph, the more robust the method.

Joint Error Estimation and Calibration Method of Memory Nonlinear Mismatch for a Four-Channel 16-Bit TIADC System.

Memory nonlinear error greatly reduces the performance of analog-to-digital converters (ADCs), and this effect is more serious in a time-interleaved analog-to-digital converter (TIADC) system. In this study, the sinusoidal wave fitting method was adopted and a joint error estimation method was proposed to address the memory nonlinear mismatch problem of the current TIADC system. This method divides the nonlinear error estimation method into two steps: the nonlinear mismatch error is coarsely estimated offline using the least squares (LS) method, and then accurately estimated online using the recursive least squares (RLS) method. After the estimation, digital post-compensation method is adopted. The obtained error parameters are used to reconstruct the error and then the reconstructed error is reduced at the output. This study used a four-channel 16-bit TIADC system with an effective number of bits (ENOB) value of 10.06 bits after the introduction of a memory nonlinearity error, which was increased to 15.42 bits after calibration by the joint error estimation method. As a result, the spurious-free dynamic range (SFDR) increased by 36.22 dB. This error estimation method can improve the error estimation accuracy and reduce the hardware complexity of implementing the error estimation system using a field programmable gate array (FPGA).

Impact of financial development and internet use on export growth: New evidence from machine learning models

The current study empirically examines the impact of financial sector development and Internet use on exports value for thirty Chinese provinces from 2000 to 2018 using the Panel-Corrected Standard Error (PCSE) estimation method and Gaussian Process Regression (GPR) machine-learning model. The PCSE method shows that (i) the Internet use increases China's exports; (ii) the impact of the Internet on export growth is larger in high-middle developed provinces; (iii) Internet use increases exports in high-middle developed provinces; however, it has less contribution to exports in low-developing China's provinces; (iv) financial development does not influence export value in the three panels. We also find that the GPR machine-learning model is more robust in predicting the exports growth in China based on the financial development and Internet use, which shows that population, Internet use, GDP, and financial development are the most important factors to predict exports growth in China.

The five main influencing factors for lidar errors in complex terrain

Abstract. Lidars have become a valuable technology to assess the wind resource at hub height of modern wind turbines. However, because of the assumption of homogeneous flow in their wind vector reconstruction algorithms, common wind profile Doppler lidars suffer from errors at complex terrain sites. This study analyses the impact of the five main influencing factors for lidar measurement errors in complex terrain, i.e. orographic complexity, measurement height, surface roughness and forest, atmospheric stability, and half-cone opening angle, in a non-dimensional, model-based parameter study. In a novel approach, the lidar error ε is split up into a part εc, caused by flow curvature at the measurement points of the lidar, and a part εs, caused by the local speed-up effects between the measurement points. This approach allows for a systematic and complete interpretation of the influence of the half-cone opening angle φ of the lidar on the total lidar error ε. It also provides information about the uncertainty in simple lidar error estimations that are based on inflow and outflow angles at the measurement points. The model-based parameter study is limited to two-dimensional Gaussian hills with hill height H and hill half-width L. H/L and z/L, with z being the measurement height, are identified as the main scaling factors for the lidar error. Three flow models of different complexity are used to estimate the lidar errors. The outcome of the study provides various findings that enable an assessment of the applicability of these flow models. The study clearly shows that orographic complexity, roughness and forest characteristics, and atmospheric stability have a significant influence on lidar error estimation. Based on the error separation approach it furthermore allows for an in-depth analysis of the influence of reduced half-cone opening angles, explaining contradiction in the previously available literature. The choice and parameterization of flow models and the design of methods for lidar error estimation are found to be essential to achieve accurate results. The use of a Reynolds-averaged Navier–Stokes (RANS) computational fluid dynamics (CFD) model in conjunction with an appropriate forest model is highly recommended for lidar error estimations in complex terrain since forest (and roughness) tends to reduce the lidar error. If atmospheric stability variation at a measurement site plays a vital role, it should also be considered in the modelling. When planning a measurement campaign, an accurate estimation of the predicted lidar error should be carried out in advance to choose a reasonable measurement location. This will decrease measurement uncertainties and maximize the value of the measurement data.

Remote error estimation of smart meter based on clustering and adaptive gradient descent method

At present, the main way for electric power companies to check the accuracy of electric meters is that professionals regularly bring standard electric meters to the site for verification. With the widespread application of smart meters and the development of data processing technology, remote error estimation based on the operating data of smart meters becomes possible. In this paper, an error estimation method of smart meter based on clustering and adaptive gradient descent method is proposed. Firstly, the fuzzy c-means clustering method is used to preprocess the data to classify the operating conditions of each measurement, and then the adaptive gradient descent method is used to establish the error estimation model. The simulation results show that this method has high error estimation accuracy. This method has a small amount of calculation and high reliability and is suitable for large-scale power grids.

Experimental performance of deep learning channel estimation for an X-ray communication-based OFDM-PWM system.

A deep learning channel estimation scheme in orthogonal frequency division multiplexing for X-ray communication (XCOM) is studied. The scheme uses simulated and detected data obtained with different working parameters and numbers of pilots as training and testing data, respectively, for the deep neural network (DNN) model. The bit-error-rate performance of the DNN model under various system operating parameters, numbers of pilot sequences, and channel obstructions is investigated separately. Experiment results showed that the deep-learning-based approach can address the distortion of the air-scintillator channel for XCOM, giving a performance comparable to those of least-squares and minimum-mean-square error estimation methods.

Determining Errors in Directional Buoy-Derived Swell Heights via the Joint Analysis of Space-Borne Radars and WaveWatch III Simulations

Characterizing the uncertainties in buoy ocean wave records is critical not only for understanding the limitations of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> wave measurements, but also for interpreting the implied accuracies of the remotely sensed products in which these buoy data are used as validation references. This letter preliminarily assesses the error of long-period swell heights ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Hss</i> ) representing specific directional wave partition energy observed from deep-water buoys moored in the northeast Pacific. We propose a buoy <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Hss</i> error estimation method by combining dual and triple collocation using data derived from buoys, two kinds of space-borne radars and numerical simulations. Compared to traditional methods, the proposed approach can reveal “absolute” errors (with respect to the underlying truth) from buoy <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Hss</i> , accepting and then confirming that swell heights from buoy, satellite and model are all uncertain. This study simultaneously employs ocean swell products derived from synthetic/real aperture radars (Sentinel-1A/B and CFOSAT/SWIM) and WaveWatch III® ocean wave model hindcasts to diagnose the accuracy of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Hss</i> values observed by buoys of National Data Buoy Center (NDBC) and Coastal Data Information Program (CDIP) during the period from July 2019 to October 2021. We quantify that the NDBC’s 3-m heave-pitch-roll buoy (CDIP’s Waverider buoy) recorded <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Hss</i> have root-mean-square error of 0.17 m (0.12 m), or have about 10.65% (7.06%) uncertainty relative to the mean <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Hss</i> value (approximately 1.6 m). Our findings imply that the reference value uncertainties should be taken into account when understanding direct satellite <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Hss</i> validation against buoy <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> .

Evaluating Remote Sensing Precipitation Products Using Double Instrumental Variable Method

Error estimation of precipitation products is an important procedure in the data quality evaluation. It is a challenging task due to the lack of the in-situ ground observations and the variations of the geophysical characteristics in regions with complex terrain. Compared with the traditional methods, the double instrumental variable (DIV) method has the merits of being able to estimate the errors between two products. In this study, the double instrumental variable method for data error estimation is applied and validated on precipitation products in regions with complex terrain. The DIV-based Errors for two state-of-the-art precipitation products IMERG and SM2RAIN are being further verified by using another high-accuracy ground-based precipitation products CMPA. The results indicate that the DIV-based Errors of IMERG and SM2RAIN range from 0 to 25 mm per day and 0 to 15 mm per day, respectively. The RMSEs of IMERG and SM2RAIN compared with CMPA, which are defined as CMPA-based Errors, are ranging from 0 to 23 mm and 0 to 22 mm, respectively. It is concluded that the spatial distribution of the DIV-based Errors shows the consistency with the CMPA-based Errors, which further demonstrates the potential of using double instrumental variable method for precipitation products fusion.

PARAFAC-Direct: A Joint Parameters Estimation Method for Slow-Time MIMO

Aiming at solving the problem that the unambiguous Doppler range of slow-time MIMO is narrower than that of conventional MIMO signals, a new signal processing method based on tensor decomposition is proposed. In the proposed method, a novel tensor model is designed to describe the echo signals of slow-time MIMO radar and retains more useful information which is lost in conventional methods based on Doppler spectrum separation. The proposed algorithm applies PARAFAC to separate target parameters into three matrices, then minimum mean squared error estimation and least squares method are used to estimate the target parameters respectively. Simulation experiments have demonstrated that the proposed method can exploit unambiguous Doppler range, and simultaneously estimate target’s direction of departure, direction of arrival and Doppler frequency without further parameter pairing.

A method for evaluating the accuracy of curved surface flattening

Based on the analysis of the existing methods for estimating the surface flattening error, they can be roughly classified into two types of estimation methods: the relative area error analysis method and the relative length error analysis method. The advantages and disadvantages of these methods are summarized in the paper. Combining the general surface flattening methods and sheet metal stamping forming process, a more reasonable, scientific and comprehensive evaluation system for the accuracy of surface flattening is proposed. In line with the unfolding characteristics of the grid surface, the relative average area error of triangles is used instead of the traditional area error estimation method. The accumulated length error is replaced by the relative length error of each triangle in the estimation method, and the value of the change in the orientation (direction, position) relationship between the triangles is increased to assess the deformation error of the surface flattening method. The mass attributes of the patch are introduced. The minimum displacement energy method is used to supplement the evaluation of surface flattening accuracy. Finally, a comprehensive evaluation system is established and proposed, which takes into account the accuracy of local and global surface flattening.

A Novel Channel Errors Calibration Algorithm for Multichannel High-Resolution and Wide-Swath SAR Imaging

For a spaceborne high-resolution and wide-swath synthetic aperture radar (HRWS-SAR) system, it usually uses the digital beamforming technology. However, in practice, because of the influences of temperature, antenna pattern, receiving antenna, and other error factors, there may exist the range synchronization time errors, amplitude errors, and phase errors among different spatial channels. These nonideal factors will significantly degrade the multichannel data reconstruction performance, resulting in a smeared SAR image. To address this issue, in this article we propose a novel channel error correction algorithm based on the orthogonal projection theory. First, the optimal weight of each Doppler ambiguity component is calculated by the orthogonal projection. Then, the cost function is constructed based on the power maximization criterion, from which the channel phase errors can be obtained. Finally, the HRWS-SAR imaging can be finely realized after performing the channel balancing. Compared with the conventional phase error estimation method, the proposed algorithm does not require to perform the matrix eigenvalue decomposition, avoiding the signal leakage phenomenon under low SNR case. The effectiveness of the proposed algorithm is validated by both airborne and space-borne real SAR data.