The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower b...The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower bounds for different channel Doppler spectra are derived. Based on the obtained lower bounds on mean squared channel estimation errors, the limits on bit error rate (BER) for maximal ratio combining (MRC) with Gaussian distributed weighting errors on independent and identically distributed (i. i. d) fading channels are presented. Numerical results show that the BER performances of ideal MRC are the lower bounds on the BER performances of non-ideal MRC and deteriorate as the maximum Doppler frequency increases or the SNR of channel estimate decreases.展开更多
In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias es...In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias estimator. Some important properties are discussed. By appropriate choices of bias parameters, we construct many interested and useful biased linear estimators, which are the extension of ordinary biased linear estimators in the full_rank linear model to the deficient_rank linear model. At last, we give a numerical example in geodetic adjustment.展开更多
To improve the classification performance of the kernel minimum squared error( KMSE), an enhanced KMSE algorithm( EKMSE) is proposed. It redefines the regular objective function by introducing a novel class label ...To improve the classification performance of the kernel minimum squared error( KMSE), an enhanced KMSE algorithm( EKMSE) is proposed. It redefines the regular objective function by introducing a novel class label definition, and the relative class label matrix can be adaptively adjusted to the kernel matrix.Compared with the common methods, the newobjective function can enlarge the distance between different classes, which therefore yields better recognition rates. In addition, an iteration parameter searching technique is adopted to improve the computational efficiency. The extensive experiments on FERET and GT face databases illustrate the feasibility and efficiency of the proposed EKMSE. It outperforms the original MSE, KMSE,some KMSE improvement methods, and even the sparse representation-based techniques in face recognition, such as collaborate representation classification( CRC).展开更多
Under analyzing several characteristics of frequency-selective fast fading channels, such as large Doppler spread and multi-path interference, a low-dimensional Kalman filter method based on pilot signals is presented...Under analyzing several characteristics of frequency-selective fast fading channels, such as large Doppler spread and multi-path interference, a low-dimensional Kalman filter method based on pilot signals is presented for the channel estimation of orthogonal frequency division multiplexing (OFDM) systems. For simplicity, a one-dimensional autoregressive (AR) process is used to model the time-varying channel, and the least square (LS) algorithm based on pilot signals is adopted to track the time-varying channel fading factor a. The low-dimensional Kalman filter estimator greatly reduces the complexity of the high-dimensional Kalman filter. To utilize the relationship of fading channel in frequency domain, a minimum mean-square-error (MMSE) combiner is used to refine the estimation results. The simulation results in the frequency band of 5.5 GHz show that the proposed method achieves a good symbol error rate (SER) performance close to the theoretical bound of ideal channel estimation.展开更多
A novel algorithm of 3-D surface image registration is proposed. It makes use of the array information of 3-D points and takes vector/vertex-like features as the basis of the matching. That array information of 3-D po...A novel algorithm of 3-D surface image registration is proposed. It makes use of the array information of 3-D points and takes vector/vertex-like features as the basis of the matching. That array information of 3-D points can be easily obtained when capturing original 3-D images. The iterative least-mean-squared (LMS) algorithm is applied to optimizing adaptively the transformation matrix parameters. These can effectively improve the registration performance and hurry up the matching process. Experimental results show that it can reach a good subjective impression on aligned 3-D images. Although the algorithm focuses primarily on the human head model, it can also be used for other objects with small modifications.展开更多
A chip-level space-time equalization receiver scheme is proposed for multiple-input multiple-output high-speed downlink packet access (MIMO HSDPA) systems to jointly combat the co-channel interference and the inter-co...A chip-level space-time equalization receiver scheme is proposed for multiple-input multiple-output high-speed downlink packet access (MIMO HSDPA) systems to jointly combat the co-channel interference and the inter-code interference. A fractional sample equalizer is also derived to further improve the performance of the receiver. Performance analysis and the calculation of the output signal to interference ratio (SINR) at each receiver antenna are presented to help direct the design of equalization weight in a more optimal manner. System simulations demonstrate the significant performance gain over conventional Rake receiver and high potential of MIMO HSDPA for high-data-rate packet transmission.展开更多
In the scenario of multiple wireless personal area networks (WPANs) accessing the home area network (HAN), the frequency-shift (FRESH)filter based on the cyclostationary theory is applied for the anti-interferen...In the scenario of multiple wireless personal area networks (WPANs) accessing the home area network (HAN), the frequency-shift (FRESH)filter based on the cyclostationary theory is applied for the anti-interference at the 2. 4 GHz spectrum. The main architecture of multiple WPANs accessing the HAN is proposed. The medium access control( MAC) -level coordination solution applied in the access point (AP)for the coexistence of different communication protocols within WPAN is discussed. The diagram of the adaptive FRESH filter is described. The anti-interference models of the FRESH filter in the scenario of multiple WPANs accessing the HAN are proposed. The minimum mean square error (MMSE)convergence property of the FRESH filter with the change in the data point number is analyzed. The simulation results indicate that the FRESH filter can effectively extract the signal of interest (SOI) from the interference with the partly overlapped spectrum. Thus, the excellent anti-interference performance of the FRESH filter is validated. Moreover, by both theoretical analysis and simulation, the MMSE convergent property of the FRESH filter is also proven.展开更多
Aiming at the optimum path excluding characteristics and the full constellation searching characteristics of the K-best detection algorithm, an improved-performance K-best detection algorithm and several reduced-compl...Aiming at the optimum path excluding characteristics and the full constellation searching characteristics of the K-best detection algorithm, an improved-performance K-best detection algorithm and several reduced-complexity K-best detection algorithms are proposed. The improved-performance K-best detection algorithm deploys minimum mean square error (MMSE) filtering of a channel matrix before QR decomposition. This algorithm can decrease the probability of excluding the optimum path and achieve better performance. The reducedcomplexity K-best detection algorithms utilize a sphere decoding method to reduce searching constellation points. Simulation results show that the improved performance K-best detection algorithm obtains a 1 dB performance gain compared to the K- best detection algorithm based on sorted QR decomposition (SQRD). Performance loss occurs when K = 4 in reduced complexity K-best detection algorithms. When K = 8, the reduced complexity K-best detection algorithms require less computational effort compared with traditional K-best detection algorithms and achieve the same performance.展开更多
The van Genuchten model is the most widely used soil water retention curve (SWRC) model. Two undisturbed soils (clay and loam) were used to evaluate the accuracy of the integral method to estimate van Genuchten mo...The van Genuchten model is the most widely used soil water retention curve (SWRC) model. Two undisturbed soils (clay and loam) were used to evaluate the accuracy of the integral method to estimate van Genuchten model parameters and to determine SWRCs of undisturbed soils. SWRCs calculated by the integral method were compared with those measured by a high speed centrifuge technique. The accuracy of the calculated results was evaluated graphically, as well as by root mean square error (RMSE), normalized root mean square error (NRMSE) and Willmott's index of agreement (1). The results obtained from the integral method were quite similar to those by the centrifuge technique. The RMSEs (4.61 ×10^-5 for Eum-Orthic Anthrosol and 2.74 × 10^-4 for Los-Orthic Entisol) and NRMSEs (1.56 × 10^-4 for Eum- Orthic Anthrosol and 1.45 ×10^-3 for Los-Orthic Entisol) were relatively small. The 1 values were 0.973 and 0.943 for Eum-Orthic Anthrosol and Los-Orthic Entisol, respectively, indicating a good agreement between the integral method values and the centrifuge values. Therefore, the integral method could be used to estimate SWRCs of undisturbed clay and loam soils.展开更多
A new multi-sensor data fusion algorithm based on EMD-MMSE was proposed.Empirical mode decomposition(EMD)is used to extract the noise of every time series for estimating the variance of the noise.Then minimum mean squ...A new multi-sensor data fusion algorithm based on EMD-MMSE was proposed.Empirical mode decomposition(EMD)is used to extract the noise of every time series for estimating the variance of the noise.Then minimum mean square error(MMSE)estimator is used to calculate the weights of the corresponding series.Finally,the fused signal is the weighted addition of all these series.The experiments in lab testified the efficiency of this method.In addition,the comparison in fusion time and fusion results with existing fusion method based on wavelet and average technique shows the advantage of this method greatly.展开更多
Vegetation fractional coverage (VFC) is one of the key indicators of vegetation distribution. In the work a measurement-based model was developed to derive total forest VFC (TG) as well as the VFC of trees (T) and shr...Vegetation fractional coverage (VFC) is one of the key indicators of vegetation distribution. In the work a measurement-based model was developed to derive total forest VFC (TG) as well as the VFC of trees (T) and shrub-grasses (G) separately in a subtropical forest area in Nanjing, China. Both upward and downward photographs were taken with a digital camera in 72 quadrats (10 m × 10 m each). Fifteen models were established and validated. Models jointly using both T and G performed better than those using the T and G separately. The best model, TG = T + G- 1.134 × T × G- 0.025 (R2 = 0.9115, P < 0.01, root mean squared error = 0.0789), is recommended for application. This model provides a good way to obtain total forest VFC values through taking tree and shrub-grass photos on ground below tree canopy rather than above tree canopy.展开更多
Sea surface winds are of great significance in scientific research. In the last few years,three series of scatterometers were launched to measure these winds,including the Advanced Scatterometer(ASCAT) aboard Meteorol...Sea surface winds are of great significance in scientific research. In the last few years,three series of scatterometers were launched to measure these winds,including the Advanced Scatterometer(ASCAT) aboard Meteorological Operational Satellite A(Met Op-A) and Met Op-B,Oceansat-2 Scatterometer(OSCAT),and HY-2A Scatterometer(HY-2A SCAT). Based on buoy wind data,validation and intercomparison of these scatterometers were performed. Scatterometer-derived wind and buoy wind data were collected only if the spatial difference was less than 0.1 degree and temporal difference less than 5 min. After discarding wind direction data outside five times the standard deviation,ASCAT wind products showed high accuracy in both wind speed and direction,with root-mean-square error(RMSE) 0.86 m/s and 17.97 degrees,respectively. HY-2A SCAT nearly meets the mission requirement,with RMSE for wind speed 1.23 m/s and 22.85 degrees for wind direction. OSCAT had poor performance when compared with the others. RMSE for wind speed was 1.54 m/s and 39.86 degrees for wind direction,which greatly exceeds the mission requirement of 20 degrees. In addition,the RMSE for wind direction shows a high-low pattern on buoy wind speed. However,a wind speed range from 14 to 15 m/s was found to be abnormal,and the reason remains unclear. There was no systematic dependency of both wind speed and direction residuals on buoy wind speed and cross-track location of the wind vector cells across the entire range. No seasonal variation was found for any scatterometer.展开更多
The performance of six statistical approaches,which can be used for selection of the best model to describe the growth of individual fish,was analyzed using simulated and real length-at-age data.The six approaches inc...The performance of six statistical approaches,which can be used for selection of the best model to describe the growth of individual fish,was analyzed using simulated and real length-at-age data.The six approaches include coefficient of determination(R2),adjusted coefficient of determination(adj.-R2),root mean squared error(RMSE),Akaike's information criterion(AIC),bias correction of AIC(AICc) and Bayesian information criterion(BIC).The simulation data were generated by five growth models with different numbers of parameters.Four sets of real data were taken from the literature.The parameters in each of the five growth models were estimated using the maximum likelihood method under the assumption of the additive error structure for the data.The best supported model by the data was identified using each of the six approaches.The results show that R2 and RMSE have the same properties and perform worst.The sample size has an effect on the performance of adj.-R2,AIC,AICc and BIC.Adj.-R2 does better in small samples than in large samples.AIC is not suitable to use in small samples and tends to select more complex model when the sample size becomes large.AICc and BIC have best performance in small and large sample cases,respectively.Use of AICc or BIC is recommended for selection of fish growth model according to the size of the length-at-age data.展开更多
Wormhole attack is one of the most devastating threats for range-free localization in wireless sensor networks. In this paper, we evaluate three statistical estimation methods with the same network model and geographi...Wormhole attack is one of the most devastating threats for range-free localization in wireless sensor networks. In this paper, we evaluate three statistical estimation methods with the same network model and geographic information obtailaed by the DV-Hop algorithm. We analyze the limits of Minimum Mean Square Estimate (MMSE), Least Median of Squares (LMS) and Enhanced greedy At- tack-Resistant MMSE (EARMMSE) and propose an improved EARMMSE with the hop-distance relationship, named EARMMSE+. Simulation results illustrate the performance of MMSE, LMS and EARMMSE+ with different anchor fraction, the length of wormhole link and the average local neighborhood and show that EARMMSE+ outperforms MMSE and LMS.展开更多
文摘The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower bounds for different channel Doppler spectra are derived. Based on the obtained lower bounds on mean squared channel estimation errors, the limits on bit error rate (BER) for maximal ratio combining (MRC) with Gaussian distributed weighting errors on independent and identically distributed (i. i. d) fading channels are presented. Numerical results show that the BER performances of ideal MRC are the lower bounds on the BER performances of non-ideal MRC and deteriorate as the maximum Doppler frequency increases or the SNR of channel estimate decreases.
文摘In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias estimator. Some important properties are discussed. By appropriate choices of bias parameters, we construct many interested and useful biased linear estimators, which are the extension of ordinary biased linear estimators in the full_rank linear model to the deficient_rank linear model. At last, we give a numerical example in geodetic adjustment.
基金The Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)the National Natural Science Foundation of China(No.61572258,61103141,51405241)+1 种基金the Natural Science Foundation of Jiangsu Province(No.BK20151530)Overseas Training Programs for Outstanding Young Scholars of Universities in Jiangsu Province
文摘To improve the classification performance of the kernel minimum squared error( KMSE), an enhanced KMSE algorithm( EKMSE) is proposed. It redefines the regular objective function by introducing a novel class label definition, and the relative class label matrix can be adaptively adjusted to the kernel matrix.Compared with the common methods, the newobjective function can enlarge the distance between different classes, which therefore yields better recognition rates. In addition, an iteration parameter searching technique is adopted to improve the computational efficiency. The extensive experiments on FERET and GT face databases illustrate the feasibility and efficiency of the proposed EKMSE. It outperforms the original MSE, KMSE,some KMSE improvement methods, and even the sparse representation-based techniques in face recognition, such as collaborate representation classification( CRC).
文摘Under analyzing several characteristics of frequency-selective fast fading channels, such as large Doppler spread and multi-path interference, a low-dimensional Kalman filter method based on pilot signals is presented for the channel estimation of orthogonal frequency division multiplexing (OFDM) systems. For simplicity, a one-dimensional autoregressive (AR) process is used to model the time-varying channel, and the least square (LS) algorithm based on pilot signals is adopted to track the time-varying channel fading factor a. The low-dimensional Kalman filter estimator greatly reduces the complexity of the high-dimensional Kalman filter. To utilize the relationship of fading channel in frequency domain, a minimum mean-square-error (MMSE) combiner is used to refine the estimation results. The simulation results in the frequency band of 5.5 GHz show that the proposed method achieves a good symbol error rate (SER) performance close to the theoretical bound of ideal channel estimation.
文摘A novel algorithm of 3-D surface image registration is proposed. It makes use of the array information of 3-D points and takes vector/vertex-like features as the basis of the matching. That array information of 3-D points can be easily obtained when capturing original 3-D images. The iterative least-mean-squared (LMS) algorithm is applied to optimizing adaptively the transformation matrix parameters. These can effectively improve the registration performance and hurry up the matching process. Experimental results show that it can reach a good subjective impression on aligned 3-D images. Although the algorithm focuses primarily on the human head model, it can also be used for other objects with small modifications.
文摘A chip-level space-time equalization receiver scheme is proposed for multiple-input multiple-output high-speed downlink packet access (MIMO HSDPA) systems to jointly combat the co-channel interference and the inter-code interference. A fractional sample equalizer is also derived to further improve the performance of the receiver. Performance analysis and the calculation of the output signal to interference ratio (SINR) at each receiver antenna are presented to help direct the design of equalization weight in a more optimal manner. System simulations demonstrate the significant performance gain over conventional Rake receiver and high potential of MIMO HSDPA for high-data-rate packet transmission.
基金The National Basic Research Program of China(973Program)(No.2007CB310606)the National Natural Science Foundation of China(No.60472053)+1 种基金the High Technology Research and Development Program of Jiangsu Province(No.BG2006002)the Specialized Development Foundation for the Achievement Transformation of Jiangsu Province(No.BA2006101)
文摘In the scenario of multiple wireless personal area networks (WPANs) accessing the home area network (HAN), the frequency-shift (FRESH)filter based on the cyclostationary theory is applied for the anti-interference at the 2. 4 GHz spectrum. The main architecture of multiple WPANs accessing the HAN is proposed. The medium access control( MAC) -level coordination solution applied in the access point (AP)for the coexistence of different communication protocols within WPAN is discussed. The diagram of the adaptive FRESH filter is described. The anti-interference models of the FRESH filter in the scenario of multiple WPANs accessing the HAN are proposed. The minimum mean square error (MMSE)convergence property of the FRESH filter with the change in the data point number is analyzed. The simulation results indicate that the FRESH filter can effectively extract the signal of interest (SOI) from the interference with the partly overlapped spectrum. Thus, the excellent anti-interference performance of the FRESH filter is validated. Moreover, by both theoretical analysis and simulation, the MMSE convergent property of the FRESH filter is also proven.
基金The National High Technology Research and Develop-ment Program of China (863Program)(No.2006AA01Z264)the National Natural Science Foundation of China (No.60572072)
文摘Aiming at the optimum path excluding characteristics and the full constellation searching characteristics of the K-best detection algorithm, an improved-performance K-best detection algorithm and several reduced-complexity K-best detection algorithms are proposed. The improved-performance K-best detection algorithm deploys minimum mean square error (MMSE) filtering of a channel matrix before QR decomposition. This algorithm can decrease the probability of excluding the optimum path and achieve better performance. The reducedcomplexity K-best detection algorithms utilize a sphere decoding method to reduce searching constellation points. Simulation results show that the improved performance K-best detection algorithm obtains a 1 dB performance gain compared to the K- best detection algorithm based on sorted QR decomposition (SQRD). Performance loss occurs when K = 4 in reduced complexity K-best detection algorithms. When K = 8, the reduced complexity K-best detection algorithms require less computational effort compared with traditional K-best detection algorithms and achieve the same performance.
基金Project supported by the International Partnership Program for Creative Research Teams of the Chinese Academy of Sciences (CAS) & the State Administration of Foreign Experts Affairs (SAFEA), China, and the Hundreds-Talent Program of the Chinese Academy of Sciences, China (No. 90502006)
文摘The van Genuchten model is the most widely used soil water retention curve (SWRC) model. Two undisturbed soils (clay and loam) were used to evaluate the accuracy of the integral method to estimate van Genuchten model parameters and to determine SWRCs of undisturbed soils. SWRCs calculated by the integral method were compared with those measured by a high speed centrifuge technique. The accuracy of the calculated results was evaluated graphically, as well as by root mean square error (RMSE), normalized root mean square error (NRMSE) and Willmott's index of agreement (1). The results obtained from the integral method were quite similar to those by the centrifuge technique. The RMSEs (4.61 ×10^-5 for Eum-Orthic Anthrosol and 2.74 × 10^-4 for Los-Orthic Entisol) and NRMSEs (1.56 × 10^-4 for Eum- Orthic Anthrosol and 1.45 ×10^-3 for Los-Orthic Entisol) were relatively small. The 1 values were 0.973 and 0.943 for Eum-Orthic Anthrosol and Los-Orthic Entisol, respectively, indicating a good agreement between the integral method values and the centrifuge values. Therefore, the integral method could be used to estimate SWRCs of undisturbed clay and loam soils.
基金The National High Technology Research and Development Program of China(863Program)(No.2001AA602021)
文摘A new multi-sensor data fusion algorithm based on EMD-MMSE was proposed.Empirical mode decomposition(EMD)is used to extract the noise of every time series for estimating the variance of the noise.Then minimum mean square error(MMSE)estimator is used to calculate the weights of the corresponding series.Finally,the fused signal is the weighted addition of all these series.The experiments in lab testified the efficiency of this method.In addition,the comparison in fusion time and fusion results with existing fusion method based on wavelet and average technique shows the advantage of this method greatly.
基金Supported by the National Basic Research Program (973 Program) of China (No.2007CB407206)the National Natural Science Foundation of China (No.40371053)
文摘Vegetation fractional coverage (VFC) is one of the key indicators of vegetation distribution. In the work a measurement-based model was developed to derive total forest VFC (TG) as well as the VFC of trees (T) and shrub-grasses (G) separately in a subtropical forest area in Nanjing, China. Both upward and downward photographs were taken with a digital camera in 72 quadrats (10 m × 10 m each). Fifteen models were established and validated. Models jointly using both T and G performed better than those using the T and G separately. The best model, TG = T + G- 1.134 × T × G- 0.025 (R2 = 0.9115, P < 0.01, root mean squared error = 0.0789), is recommended for application. This model provides a good way to obtain total forest VFC values through taking tree and shrub-grass photos on ground below tree canopy rather than above tree canopy.
基金Supported by the National Natural Science Foundation of China(Nos.U1406404,41331172,61361136001)the National High Technology Research and Development Program of China(863 Program)(No.2013AA09A505)
文摘Sea surface winds are of great significance in scientific research. In the last few years,three series of scatterometers were launched to measure these winds,including the Advanced Scatterometer(ASCAT) aboard Meteorological Operational Satellite A(Met Op-A) and Met Op-B,Oceansat-2 Scatterometer(OSCAT),and HY-2A Scatterometer(HY-2A SCAT). Based on buoy wind data,validation and intercomparison of these scatterometers were performed. Scatterometer-derived wind and buoy wind data were collected only if the spatial difference was less than 0.1 degree and temporal difference less than 5 min. After discarding wind direction data outside five times the standard deviation,ASCAT wind products showed high accuracy in both wind speed and direction,with root-mean-square error(RMSE) 0.86 m/s and 17.97 degrees,respectively. HY-2A SCAT nearly meets the mission requirement,with RMSE for wind speed 1.23 m/s and 22.85 degrees for wind direction. OSCAT had poor performance when compared with the others. RMSE for wind speed was 1.54 m/s and 39.86 degrees for wind direction,which greatly exceeds the mission requirement of 20 degrees. In addition,the RMSE for wind direction shows a high-low pattern on buoy wind speed. However,a wind speed range from 14 to 15 m/s was found to be abnormal,and the reason remains unclear. There was no systematic dependency of both wind speed and direction residuals on buoy wind speed and cross-track location of the wind vector cells across the entire range. No seasonal variation was found for any scatterometer.
基金Supported by the High Technology Research and Development Program of China (863 Program,No2006AA100301)
文摘The performance of six statistical approaches,which can be used for selection of the best model to describe the growth of individual fish,was analyzed using simulated and real length-at-age data.The six approaches include coefficient of determination(R2),adjusted coefficient of determination(adj.-R2),root mean squared error(RMSE),Akaike's information criterion(AIC),bias correction of AIC(AICc) and Bayesian information criterion(BIC).The simulation data were generated by five growth models with different numbers of parameters.Four sets of real data were taken from the literature.The parameters in each of the five growth models were estimated using the maximum likelihood method under the assumption of the additive error structure for the data.The best supported model by the data was identified using each of the six approaches.The results show that R2 and RMSE have the same properties and perform worst.The sample size has an effect on the performance of adj.-R2,AIC,AICc and BIC.Adj.-R2 does better in small samples than in large samples.AIC is not suitable to use in small samples and tends to select more complex model when the sample size becomes large.AICc and BIC have best performance in small and large sample cases,respectively.Use of AICc or BIC is recommended for selection of fish growth model according to the size of the length-at-age data.
基金Acknov,.4edgements This work was supported in part by National Basic Research Program of China ("973 program") under contract No. 2007CB307101, and in part by National Natural Science Foundation of China under Grant No. 60833002, No. 60802016 and No.60972010.
文摘Wormhole attack is one of the most devastating threats for range-free localization in wireless sensor networks. In this paper, we evaluate three statistical estimation methods with the same network model and geographic information obtailaed by the DV-Hop algorithm. We analyze the limits of Minimum Mean Square Estimate (MMSE), Least Median of Squares (LMS) and Enhanced greedy At- tack-Resistant MMSE (EARMMSE) and propose an improved EARMMSE with the hop-distance relationship, named EARMMSE+. Simulation results illustrate the performance of MMSE, LMS and EARMMSE+ with different anchor fraction, the length of wormhole link and the average local neighborhood and show that EARMMSE+ outperforms MMSE and LMS.