Bias Estimation Method Research Articles

A new method for GLONASS inter-frequency bias estimation based on long baselines

Frequency division multiplexing of GLONASS signals causes inter-frequency bias (IFB) in receiving equipment. IFB significantly increases the difficulties of fixing GLONASS ambiguities and limits the accuracy and reliability of GLONASS positioning and orbit determination. Accurately estimating and calibrating IFB can effectively solve such a problem. However, at present, most methods of IFB estimation are based on zero and short baselines, in which case it is not only difficult to realize fast and efficient IFB estimation but also one cannot fully utilize publicly available IGS and CORS data. Therefore, we present a new method for GLONASS IFB estimation based on long baselines. First, to weaken the influence of inter-frequency code bias, the wide-lane ambiguities are calculated directly based on the wide-lane combinations of observations. Then, according to the range of inter-frequency phase bias (IFPB) rates, a IFPB defined as the difference in IFPBs between adjacent frequencies, a step-by-step search schedule is designed to remove the impacts of IFPB on wide-lane and narrow-lane ambiguity resolution. Finally, after fixing integer wide-lane and narrow-lane ambiguities, the IFPB rate can be estimated. An experimental network is set up to verify the validity of this method; the experiment includes the data observed for 31 days at 542 stations in Europe and North America. The IFPB rates of 38 receiver types from nine manufacturers are successfully determined. Experimental results show that the estimated IFPB rates for the same receiver type stabilize within a month with a standard deviation of less than 1.4 mm/∆f (millimeters per frequency number increment, ∆f denotes the frequency difference of adjacent GLONASS frequencies with frequency number increment of 1). Generally, the difference in IFPB rates of receiver types from the same manufacturer does not exceed 2.5 mm/∆f. However, the estimated IFPB rates of Septentrio’s newly produced receivers, as compared with that of the old receiver types, show a rate difference of up to 50 mm/∆f. This significant difference should be considered for practical applications.

Ridge Estimates of Regression Coefficients for SoilMoisture Retention of IraqiSoils

Statistical literature has several methods for coping with multicollinearity problem.Ridge regression “RR” is compared with multiple linear regression for studying “Suction Characteristics of Subgrade Soils from North Iraq- SCSSNI”. Multiple linear regression “MLR” of “SCSSNI” data usually encounters a collinearly problem, which adversely affects long term prediction performance. The collinearly problem can be eliminated or greatly improved by using ridge regression, which is a biased estimation method with potentially smaller mean square error “MSE” as an alternative to ordinary least square “OLS”. In this study, ridge regression (a biased estimation method has been evaluated with a constant bias ) and the prediction performance was compared with that of ordinary least square“OLS” based multiple linear regression “MLR”. The bias constant of was selected bu examining the ridge trace. At this point, the estimated coefficients are stable and their variance inflation factors “VIFs” become smaller. To evaluate the robustness of each model the standard error of prediction” SEPs” has been compared, the prediction of original values using MLR model shows slightly better results comparing to that of ridge regression model, which is due to an intentional bias is associated in the ridge model. To compare RR and MLR, the coefficient of determination, “VIFs”, and standard error “SE” of parameters has been studied. If the variance of the ridge estimator could be tremendously reduced, the mean square error tends to be smaller than the OLS. The prediction results of a ridge model showed more stable prediction performance as compared to that of MLR, by removing or decreasing the collinearly problem.

Ambiguity resolved precise point positioning with GPS and BeiDou

This paper focuses on the contribution of the global positioning system (GPS) and BeiDou navigation satellite system (BDS) observations to precise point positioning (PPP) ambiguity resolution (AR). A GPS + BDS fractional cycle bias (FCB) estimation method and a PPP AR model were developed using integrated GPS and BDS observations. For FCB estimation, the GPS + BDS combined PPP float solutions of the globally distributed IGS MGEX were first performed. When integrating GPS observations, the BDS ambiguities can be precisely estimated with less than four tracked BDS satellites. The FCBs of both GPS and BDS satellites can then be estimated from these precise ambiguities. For the GPS + BDS combined AR, one GPS and one BDS IGSO or MEO satellite were first chosen as the reference satellite for GPS and BDS, respectively, to form inner-system single-differenced ambiguities. The single-differenced GPS and BDS ambiguities were then fused by partial ambiguity resolution to increase the possibility of fixing a subset of decorrelated ambiguities with high confidence. To verify the correctness of the FCB estimation and the effectiveness of the GPS + BDS PPP AR, data recorded from about 75 IGS MGEX stations during the period of DOY 123-151 (May 3 to May 31) in 2015 were used for validation. Data were processed with three strategies: BDS-only AR, GPS-only AR and GPS + BDS AR. Numerous experimental results show that the time to first fix (TTFF) is longer than 6 h for the BDS AR in general and that the fixing rate is usually less than 35 % for both static and kinematic PPP. An average TTFF of 21.7 min and 33.6 min together with a fixing rate of 98.6 and 97.0 % in static and kinematic PPP, respectively, can be achieved for GPS-only ambiguity fixing. For the combined GPS + BDS AR, the average TTFF can be shortened to 16.9 min and 24.6 min and the fixing rate can be increased to 99.5 and 99.0 % in static and kinematic PPP, respectively. Results also show that GPS + BDS PPP AR outperforms single-system PPP AR in terms of convergence time and position accuracy.

Data assimilation in integrated hydrological modelling in the presence of observation bias

Abstract. The use of bias-aware Kalman filters for estimating and correcting observation bias in groundwater head observations is evaluated using both synthetic and real observations. In the synthetic test, groundwater head observations with a constant bias and unbiased stream discharge observations are assimilated in a catchment-scale integrated hydrological model with the aim of updating stream discharge and groundwater head, as well as several model parameters relating to both streamflow and groundwater modelling. The coloured noise Kalman filter (ColKF) and the separate-bias Kalman filter (SepKF) are tested and evaluated for correcting the observation biases. The study found that both methods were able to estimate most of the biases and that using any of the two bias estimation methods resulted in significant improvements over using a bias-unaware Kalman filter. While the convergence of the ColKF was significantly faster than the convergence of the SepKF, a much larger ensemble size was required as the estimation of biases would otherwise fail. Real observations of groundwater head and stream discharge were also assimilated, resulting in improved streamflow modelling in terms of an increased Nash–Sutcliffe coefficient while no clear improvement in groundwater head modelling was observed. Both the ColKF and the SepKF tended to underestimate the biases, which resulted in drifting model behaviour and sub-optimal parameter estimation, but both methods provided better state updating and parameter estimation than using a bias-unaware filter.

Iterative algorithms of biased estimation methods in binary logistic regression

Logistic regression is a widely used method to model categorical response data, and maximum likelihood (ML) estimation has widespread use in logistic regression. Although ML method is the most used method to estimate the regression coefficients in logistic regression model, multicollinearity seriously affects the ML estimator. To remedy the undesirable effects of multicollinearity, estimators alternative to ML are proposed. Drawing on the similarities between the multiple linear and logistic regressions, ridge, Liu and two parameter estimators are proposed which are based on the ML estimator. On the other hand, first-order approximated ridge estimator is proposed for use in logistic regression. This study will present further solutions to the problem in the form of alternative estimators which reduce the effect of collinearity. Owing to this, first-order approximated Liu, iterative Liu and iterative two parameter estimators are proposed. A simulation study as well as real life application are carried out to ascertain the effect of sample size and degree of multicollinearity, in which the ML based, first-order approximated and iterative biased estimators are compared. Graphical representations are presented which support the effect of the shrinkage parameter on the mean square error and prediction mean square error of the biased estimators.

A Hybrid Method for Interpolating Missing Data in Heterogeneous Spatio-Temporal Datasets

Space-time interpolation is widely used to estimate missing or unobserved values in a dataset integrating both spatial and temporal records. Although space-time interpolation plays a key role in space-time modeling, existing methods were mainly developed for space-time processes that exhibit stationarity in space and time. It is still challenging to model heterogeneity of space-time data in the interpolation model. To overcome this limitation, in this study, a novel space-time interpolation method considering both spatial and temporal heterogeneity is developed for estimating missing data in space-time datasets. The interpolation operation is first implemented in spatial and temporal dimensions. Heterogeneous covariance functions are constructed to obtain the best linear unbiased estimates in spatial and temporal dimensions. Spatial and temporal correlations are then considered to combine the interpolation results in spatial and temporal dimensions to estimate the missing data. The proposed method is tested on annual average temperature and precipitation data in China (1984–2009). Experimental results show that, for these datasets, the proposed method outperforms three state-of-the-art methods—e.g., spatio-temporal kriging, spatio-temporal inverse distance weighting, and point estimation model of biased hospitals-based area disease estimation methods.

An inter-comparison of soil moisture data products from satellite remote sensing and a land surface model

Significant advances have been achieved in generating soil moisture (SM) products from satellite remote sensing and/or land surface modeling with reasonably good accuracy in recent years. However, the discrepancies among the different SM data products can be considerably large, which hampers their usage in various applications. The bias of one SM product from another is well recognized in the literature. Bias estimation and spatial correction methods have been documented for assimilating satellite SM product into land surface and hydrologic models. Nevertheless, understanding the characteristics of each of these SM data products is required for many applications where the most accurate data products are desirable. This study inter-compares five SM data products from three different sources with each other, and evaluates them against in situ SM measurements over 14-year period from 2000 to 2013. Specifically, three microwave (MW) satellite based data sets provided by ESA's Climate Change Initiative (CCI) (CCI-merged, -active and -passive products), one thermal infrared (TIR) satellite based product (ALEXI), and the Noah land surface model (LSM) simulations. The in-situ SM measurements are collected from the North American Soil Moisture Database (NASMD), which involves more than 600 ground sites from a variety of networks. They are used to evaluate the accuracies of these five SM data products. In general, each of the five SM products is capable of capturing the dry/wet patterns over the study period. However, the absolute SM values among the five products vary significantly. SM simulations from Noah LSM are more stable relative to the satellite-based products. All TIR and MW satellite based products are relatively noisier than the Noah LSM simulations. Even though MW satellite based SM retrievals have been predominantly used in the past years, SM retrievals of the ALEXI model based on TIR satellite observations demonstrate skills equivalent to all the MW satellite retrievals and even slightly better over certain regions. Compared to the individual active and passive MW products, the merged CCI product exhibits higher anomaly correlation with both Noah LSM simulations and in-situ SM measurements.

Probability hypothesis density filter for radar systematic bias estimation aided by ADS-B

This paper provides a solution for systematic bias estimation of radar without priori information of data association based on the probability hypothesis density (PHD) filter aided by automatic dependent surveillance broadcasting (ADS-B). Novel dynamics model and measurement model of systematic bias are developed by using ADS-B surveillance data as the high-accuracy reference source. The Gaussian mixture probability hypothesis density (GM-PHD) filter is applied for recursive estimation of systematic bias by introducing the novel dynamics model and measurement model of systematic bias into the filter. Numerical results are provided to verify the effectiveness and improved performance of the proposed method for systematic bias estimation.

The nature of GPS differential receiver bias variability: An examination in the polar cap region

AbstractWhile modern GPS receiver differential code bias estimation techniques have become highly refined, they still demonstrate unphysical behavior, namely, notable solar cycle variability. This study investigates the nature of these seasonal and solar cycle bias variabilities in the polar cap region using single‐station bias estimation methods. It is shown that the minimization of standard deviation bias estimation technique is linearly dependent on the user's choice of shell height, where the sensitivity of this dependence varies significantly from 1 total electron content unit (1 TECU = 1016 el m−2) per 4000 km in solar minimum winter to in excess of 1 TECU per 90 km during solar maximum summer. Using an ionosonde, we find appreciable shell height variability resulting in bias variabilities of up to 2 TECU. Comparing northward face Resolute Incoherent Scatter Radar (RISR‐N) measurements to a collocated GPS station, we find that RISR‐derived GPS receiver biases vary seasonally but not with solar cycle. RMS differences between bias estimation methods and observation between 2009 and 2013 were found to range from 2.7 TECU to 3.4 TECU, depending on method. To account for the erroneous solar cycle variability of standard bias estimation approaches, we linearly fit these biases to sunspot number, removing the trend. RMS errors after sunspot detrending these biases are reduced to 1.91 TECU. Also, these ISR‐derived and sunspot‐detrended biases are fit to ambient temperature, where a significant correlation is found. By using these temperature‐fitted biases we further reduce RMS errors to 1.66 TECU. These results can be taken as further evidence of temperature‐dependent dispersion in the GPS cabling and antenna hardware.

Real-Time PPP Based on the Coupling Estimation of Clock Bias and Orbit Error with Broadcast Ephemeris.

Satellite orbit error and clock bias are the keys to precise point positioning (PPP). The traditional PPP algorithm requires precise satellite products based on worldwide permanent reference stations. Such an algorithm requires considerable work and hardly achieves real-time performance. However, real-time positioning service will be the dominant mode in the future. IGS is providing such an operational service (RTS) and there are also commercial systems like Trimble RTX in operation. On the basis of the regional Continuous Operational Reference System (CORS), a real-time PPP algorithm is proposed to apply the coupling estimation of clock bias and orbit error. The projection of orbit error onto the satellite-receiver range has the same effects on positioning accuracy with clock bias. Therefore, in satellite clock estimation, part of the orbit error can be absorbed by the clock bias and the effects of residual orbit error on positioning accuracy can be weakened by the evenly distributed satellite geometry. In consideration of the simple structure of pseudorange equations and the high precision of carrier-phase equations, the clock bias estimation method coupled with orbit error is also improved. Rovers obtain PPP results by receiving broadcast ephemeris and real-time satellite clock bias coupled with orbit error. By applying the proposed algorithm, the precise orbit products provided by GNSS analysis centers are rendered no longer necessary. On the basis of previous theoretical analysis, a real-time PPP system was developed. Some experiments were then designed to verify this algorithm. Experimental results show that the newly proposed approach performs better than the traditional PPP based on International GNSS Service (IGS) real-time products. The positioning accuracies of the rovers inside and outside the network are improved by 38.8% and 36.1%, respectively. The PPP convergence speeds are improved by up to 61.4% and 65.9%. The new approach can change the traditional PPP mode because of its advantages of independence, high positioning precision, and real-time performance. It could be an alternative solution for regional positioning service before global PPP service comes into operation.

Combining Some Biased Estimation Methods with Least Trimmed Squares Regression and its Application

<p>In the case of multicollinearity and outliers in regression analysis, the researchers are encouraged to deal with two problems simultaneously. Biased methods based on robust estimators are useful for estimating the regression coefficients for such cases. In this study we examine some robust biased estimators on the datasets with outliers in x direction and outliers in both x and y direction from literature by means of the R package ltsbase. Instead of a complete data analysis, robust biased estimators are evaluated using capabilities and features of this package.</p>

Principal Component Regression by Principal Component Selection

Abstract We propose a selection procedure of principal components in principal component regression. Our methodselects principal components using variable selection procedures instead of a small subset of major principalcomponents in principal component regression. Our procedure consists of two steps to improve estimation andprediction. First, we reduce the number of principal components using the conventional principal componentregression to yield the set of candidate principal components and then select principal components among thecandidate set using sparse regression techniques. The performance of our proposals is demonstrated numericallyand compared with the typical dimension reduction approaches (including principal component regression andpartial least square regression) using synthetic and real datasets.Keywords: Biased estimation, dimension reduction, penalized regression, principal componentregression, principal component selection. 1. Introduction Regression model is a popular statistical model for data analysis. Under fairly general conditions,the ordinary least squares (OLS) estimator of the regression model has many desirable properties,including unbiasedness and minimum variance. Multicollinearity deteriorates OLS estimator quality.Multicollinearity often arises in many real-world applications where the set of explanatory variableshas the nearly linear dependence or the sample size is smaller than the variable size. Two types ofbias estimation are widely used to address such situation. One of them is regularization method,where model parameters are selected under a certain constraint. Popular regularization methods forregressionareridgeregression,Lasso,andotherpenalizedregressionmethods. Theotherisdimensionreductionmethods(suchasprincipalcomponentregression(PCR)andpartialleastsquaresregression(PLSR)) where explanatory variable space is decomposed into orthogonal directions and only someof them are used for model building. Both of approaches produce biased estimators, but often have asmaller variance than OLS estimators. This property (incurring bias and reducing variance) improvesestimation and prediction, and this is the reason why biased estimation methods are popular. Moreaccounts can be found in standard textbooks (Bishop, 2006; Hastie

한국형 위성항법시스템의 UDRE 모니터링 분석

This paper is about analysis of UDRE monitoring method for Korean Satellite navigation system, which is the correction parameter of satellite measurements. New receiver clock bias and tropospheric delay error estimation method to make pseudo-range residual for UDRE monitoring is proposed. Saastamoinen model and Neill mapping function are used for estimate the tropospheric delay and EKF is used for estimgate the receiver clock bias. Through the satellite measurements and regional weather data received directly from the domestic is using for UDRE monitoring analysis, more suitable UDRE monitoring threshold can be deducted and it is expected to be utilized for fault detection technique of Korean Satellite Navigation System.

A new differential code bias (C1–P1) estimation method and its performance evaluation

The current satellite clock products are computed using the ionosphere-free phase (L1/L2) and code (P1/P2) observations. Thus, if users conduct undifferenced positioning using these clock products together with C1 and P2 observations, the differential code bias (DCB) (C1---P1) should be properly compensated. The influence of DCB (C1---P1) on the undifferenced ambiguity solutions is investigated. Based on the investigation, we propose a new DCB (C1---P1) estimation method. Using it, the satellite DCB (C1---P1) can be computed. A 30-day (DOY 205---234, 2012) dual-frequency GPS data set is processed to estimate the DCB (C1---P1). Comparing the estimated results with that of IGS DCB products, the accuracy is better than 0.13 m. The performances of DCB (C1---P1) in the code-based single-point positioning, precise point positioning (PPP) convergence and wide-lane uncalibrated phase delay (UPD) estimation are investigated using the estimated DCB (C1---P1). The results of the code-based single-point positioning show that the influence of DCB (C1---P1) on the up direction is more evident than on the horizontal directions. The accuracy is improved by 50 % and reaches to decimeter level with DCB (C1---P1) application. The performance of DCB (C1---P1) in PPP shows that it can accelerate PPP convergence through improving the accuracy of the code observation. The computed UPD values show that influence of DCB (C1---P1) on UPD of each satellite is different, and some values are larger than 0.3 cycles.

A Novel Channel Phase Bias Estimation Method for Spaceborne Multi-channel High-resolution and Wide-swath SAR

方位多通道合成孔径雷达(SAR)可有效地抑制多普勒模糊以实现高分辨率宽测绘带(High-Resolution Wide-Swath HRWS)成像。通道间幅相误差将影响多普勒模糊抑制性能。基于星载SAR系统回波特性雷达回波在多普勒带宽外的能量通常远小于多普勒带宽内能量，该文提出一种多通道HRWS SAR系统通道间相位偏差估计新方法。该方法假定多普勒带宽外的信号近似为零，将单星多通道HRWS SAR系统相位偏差估计问题转换为恒模二次规划问题，然后利用经典二次规划问题求解方法特征值松弛法(Eigen-Value Relaxation, EVR)及半正定松弛法(Semi-Definite Relaxation, SDR)求解该问题，获取HRWS SAR系统通道间的相位偏差估计值。理论分析结果表明，该文算法可视为一种自适应加权最小二乘相位偏差估计算法。多通道SAR仿真实验结果验证了该文算法的有效性。

Bias correction in the estimation of dynamic panel models in corporate finance

Dynamic panel models play an increasingly important role in numerous areas of corporate finance research, and a variety of (biased) estimation methods have been proposed in the literature. The biases inherent in these estimation methods have a material impact on inferences about corporate behavior, especially when the empirical model is misspecified. We propose a bias-corrected global minimum variance (GMV) combined estimation procedure to mitigate this estimation problem. We choose the capital structure speed of adjustment (SOA) setting to illustrate the proposed method using both simulated and actual empirical corporate finance data. The GMV estimator non-trivially reduces bias and hence meaningfully increases the reliability of inferences based on parameter estimates. This method can be readily applied to many other corporate finance contexts.

Comparison of Classical Least Squares (CLS), Ridge and Principal Component Methods of Regression Analyses using Gynecological Data

This study compares results obtained from the application of Classical Least Squares with that obtained from the two major biased estimation methods: Ridge and Principal Component Regressions in multicollinear situations using gynecological data from University College Hospital, Ibadan, Oyo State, Nigeria. Numerical values of baby's weights (less than 2.5kg) at birth were considered as response variable while mother's age, weight and height, as well as preterm delivery, multiple pregnancies, parity, graphidity, maternal infections such as malaria, tuberculosis, sexually transmitted diseases, anaemia/shortage of blood, intra-uterine infections, congenital abnormalities, etc and fetal infections serve as explanatory variables. Regression method is used as the statistical tool. A number of assumptions of the regression analysis were inspected. Normality assumption was confirmed by plotting Normal Q-Q Plot and Histogram of the Standardized Residuals. The data sets were also inspected for homoscedasticity of error variances using Residual Plot and Fligner-Killeen Test; it was established that homoscedasticity assumption was not violated. Autocorrelation problem on the data set was checked by Durbin-Watson statistic. The test revealed that autocorrelation problem can be tolerated. Existence of multicollinearity problem was further checked in the data set using Farrar-Glauber Chi-squared test. It was established that some predictors are highly correlated; this was also true when correlation matrix table was obtained. Shrinkage estimator of Ridge Regression was obtained by Iterative Method of Hoerl and Kennard. Ridge Regression coefficients were later computed. Kaiser's and Cattell's Screen Criteria were employed for determining number of principal components to be retained in the analysis. The two criteria suggested that the first three components should be retained but only one component is significant. Thereafter, Ridge Regression was finally recommended as the best method to handle multicollinearity problem under Frequentist Approach.

Real Variance Estimation by Grouping Histories in Monte Carlo Eigenvalue Calculations

It is well known that the sample variance of a tally mean in Monte Carlo (MC) eigenvalue calculations is biased because of the intercycle correlations of the fission source distribution (FSD). This paper proposes the history-based batch method as a new method that can eliminate the dependency between samples and thereby estimate the real variance of the mean of the MC tally directly from routine cycle-by-cycle MC eigenvalue calculations. The new method estimates the real variance of the MC tally by the sample variance from tally estimates of the history-based batch defined as a set of histories with the same ancestor fission neutrons determined at the first active cycle MC run. The batch averages of the MC tally necessary for this estimate are obtained by correcting the individual tallies with the batch specific weight factors that are derived from independent FSD normalization of each individual batch. Diagnostic methods are also devised for small-batch-size problems, which one may encounter in applying the history-based batch method. The effectiveness of the history-based batch method is examined as a function of the dominance ratio and the batch size for the weakly coupled fissile array problems in comparison with those of bias estimation methods currently available. Its validity is also investigated in terms of the fuel storage facility problem exhibiting a slow source convergence.

Assessment of sample frequency bias and precision in fluvial flux calculations – An improved low bias estimation method

Despite the importance of calculating the flux of solutes and particulates through the global fluvial network the number of studies that have considered the bias and precision of any method is limited. Furthermore, no study has, on the basis of the bias of the method, proposed new methods with a lower bias nor considered the implications of the bias estimation for existing published studies. Using 3 years of high frequency data (hourly) for dissolved organic carbon (DOC) this study systematically degraded the data and recalculated the flux for varying sample frequencies and considered a range of interpolation, ratio and extrapolation methods. The results show that:(i)Interpolation and ratio methods showed a consistent, small bias for sampling frequencies up to every 14 days, but bias rapidly increased for lower sample frequencies with the flux estimates being between 40% and 45% of the “true” flux at 31 day (monthly) sampling.(ii)The best ratio method was based upon correction against an unrealistic assumption that river flow was normally distributed.(iii)Extrapolation methods based on fixed sampling period monitoring proved to be erratic but no better than interpolation methods.Based upon the nature of the sources of variation within the flow and solute datasets we propose the following method for calculating the fluvial flux (F) of a solute: F=KE(Ci)Qtotalwhere: Qtotal = the total flow in a year (m3/yr); E(Ci) = the expected value of the sampled concentrations (mg/l); and K = a conversion factor. This new method preserved all the available flow information and had a bias of as low as 8% for monthly sampling. When the method was applied to DOC flux from Great Britain bias correction meant a 97% increase in the national flux over previous estimates. Interpolation and ratio methods showed a consistent, small bias for sampling frequencies up to every 14 days, but bias rapidly increased for lower sample frequencies with the flux estimates being between 40% and 45% of the “true” flux at 31 day (monthly) sampling. The best ratio method was based upon correction against an unrealistic assumption that river flow was normally distributed. Extrapolation methods based on fixed sampling period monitoring proved to be erratic but no better than interpolation methods.

A homogeneous linear estimation method for system error in data assimilation

In this paper, a new bias estimation method is proposed and applied in a regional ensemble Kalman filter (EnKF) based on the Weather Research and Forecasting (WRF) Model. The method is based on a homogeneous linear bias model, and the model bias is estimated using statistics at each assimilation cycle, which is different from the state augmentation methods proposed in previous literatures. The new method provides a good estimation for the model bias of some specific variables, such as sea level pressure (SLP). A series of numerical experiments with EnKF are performed to examine the new method under a severe weather condition. Results show the positive effect of the method on the forecasting of circulation pattern and meso-scale systems, and the reduction of analysis errors. The background error covariance structures of surface variables and the effects of model system bias on EnKF are also studied under the error covariance structures and a new concept ‘correlation scale’ is introduced. However, the new method needs further evaluation with more cases of assimilation.