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1.
Considering the contribution of the hardware biases to the estimated clock errors, an improved method for estimating the satellite inter-frequency clock bias (IFCB) is presented, i.e., the difference in the satellite clock error as computed from ionospheric-free pseudorange and carrier phase observations using L1/L2 and P1/P2 versus L1/L5 and P1/P5. The IFCB is composed of a constant and a variable part. The constant part is the inter-frequency hardware bias (IFHB). It contains the satellite and receiver hardware delays and can be expressed as a function of the DCBs [DCB (P1 ? P2) and DCB (P1 ? P5)]. When a reference satellite is selected, the satellite IFHB can be computed but is biased by a reference satellite IFHB. This bias will not affect the utilization of IFCB in positioning since it can be absorbed by the receiver clock error. Triple-frequency observations of 30 IGS stations between June 1, 2013, and May 31, 2014, were processed to show the variations of the IFHB. The IFHB values show a long-term variation with time. When a linear and a fourth-order harmonic function are used to model the estimated IFCB, which contains contributions of the hardware delays and clock errors, the results show that 89 % of the IFCB can be corrected given the current five triple-frequency GPS satellites with the averaged fitting RMS of 1.35 cm. Five days of data are processed to test the estimated satellite clock errors using the strategy presented. The residuals of P1/P5 and L1/L5 have a STD of <0.27 m and 0.97 cm, respectively. In addition, most predicted satellite IFCBs reach an accuracy of centimeter level and its mean accuracy of 5 days is better than 7 cm.  相似文献   

2.
Absolute orientation is a basic technical work in digital image geologic logging of underground coal mine. Traditional control-point-based absolute orientation method requires setting object space control points of the known three-dimensional coordinates, which may lead to low efficiency. Therefore, this paper proposed a point-free close-range photogrammetry absolute orientation algorithm, which utilized direction line segments including plumb line segments and line segments with known directions and lengths to identify the dimensional orientation of a stereoscopic model. Experiment results show that the precision of the orientation results is favorable. σ X and σ Y are as high as 0.5 mm, and σ Z is 0.3 mm. Finally, this paper introduced the application of the proposed algorithm in rapid geological logging of coal mine roadway, which was fast and reliable, convenient and feasible.  相似文献   

3.
Assessment of area under agroforestry in Tehri district of North Western Himalaya, Uttarakhand, India has been done using GIS and remote sensing technology. The study district characterized by hilly terrain with varying elevations from 288 m to more than 2800 m and generally gentle slopes, valleys, flat land covers and agricultural terraces. High-resolution satellite imageries (spatial resolution 5.8 m) were used in this study for land uses and land covers classification. According to unsupervised classification, highest area was found under forest class (65.22%) followed by cropland (20.41%). Considerable area was also found under snow cover (9.45%) in the district. Area under agroforestry was estimated to be 5572.26 ha (1.53%) by this method, whereas it was estimated to be 7029.06 ha (1.93%) by supervised classification. Estimated cropland area comes out to be about 20.0%. An accuracy of 86.5% was found in this classification for agroforestry class. Highest area under agroforestry of 3707.36 ha was obtained in 1200–2000 m elevations followed by 2231.26 ha in 288–1200 m elevations. Negligible area was found on high elevation zones of more than 2800 m. The major agroforestry systems of dominated by Grewia oppositifolia (Bhimal), Celtis australis (Kharik) and Quercus leucotrichophora (Banj) were identified and mapped and remaining systems were grouped as others class. Estimated area under G. oppositifolia, C. australis and Q. leucotrichophora based systems come out to be 2330.82, 1456.80 and 1129.10 ha, respectively. These systems are multiple usufructs are food, fuelwood, fodder, fiber and small timber. It has been observed from the accuracy assessment that the estimates of area under agroforestry obtained under this study are reliable.  相似文献   

4.
Cotton aphid (Aphis gossypii) is considered as one of the most important agriculture pest for the cotton production. However, it is generally labor-intensive and time-consuming to obtain some information of Cotton aphid with conventional methods through direct measurement by sampling in the field. This study explores the potential of using a new method to obtain information of the Cotton aphid rapidly. In our study, the cotton canopy spectral indices (NDVI, VI_2, REDrefc, NIRrefc) and chlorophyll concentration, obtained from hand-held high spectrometer GreenSeeker and chlorophyll meter SPAD-502 and Cotton aphid amount derived from the artificial field-based survey were used to uncover the relationship between Cotton aphid amount and canopy spectral index and SPAD value of the cotton in city of Shihezi, China. The results showed that NDVI and NIRrefc were negatively related to Cotton aphid amount. VI_2 content had a significant and positive relationship with its amount. The non-linear three cubic models with alate Aphid amount as independent variables have been established between VI_2 value and alatae Aphid amount, which could explain 92.37 % of VI_2 value variance. SPAD values were also significantly and negatively correlated to the Aphid amount. The non-linear logarithm model with wingless Aphid amount as independent variables was the best for uncovering the relationship between SPAD value and wingless Aphid amount, which could explain 85.48 % of SPAD value variance. The results demonstrate the establishment of the function model provides a theoretical basis and techniques for indirect and rapid monitoring and management of Cotton aphid.  相似文献   

5.
Chlorophyll fluorescence is an indicator of plant photosynthetic activity and has been used to monitor the health status of vegetation. Several studies have exploited the application of red/far-red chlorophyll fluorescence ratio in detecting the impact of various types of stresses in plants. Recently, sunlight-induced chlorophyll fluorescence imaging has been used to detect and discriminate different stages of mosaic virus infection in potted cassava plants with a multi-spectral imaging system (MSIS). In this study, the MSIS is used to investigate the impact of drought and herbicide stress in field grown crop plants. Towards this control and treatment groups of colocasia and sweet potato plants were grown in laterite soil beds and the reflectance images of these crop plants were recorded up to 14-days of treatment at the Fraunhofer lines of O2 B at 687 nm and O2 A at 759.5 nm and the off-lines at 684 and 757.5 nm. The recorded images were analyzed using the Fraunhofer Line Discrimination technique to extract the sunlight-induced chlorophyll fluorescence component from the reflectance images of the plant leaves. As compared to the control group, the chlorophyll fluorescence image ratio (F 687/F 760) in the treatment groups of both the plant varieties shows an increasing trend with increase in the extent of stress. Further, the F 687/F 760 ratio was found to correlate with the net photosynthetic rate (Pn) and stomatal conductance (gs) of leaves. The correlation coefficient (R 2) for the relationship of F 687/F 760 ratio with Pn were found to be 0.78, 0.79 and 0.78, respectively for the control, herbicide treated and drought treated colocasia plants, while these were 0.77, 0.86 and 0.88, respectively for sweet potato plants. The results presented show the potential of proximal remote sensing and the application F 687/F 760 fluorescence image ratio for effective monitoring of stress-induced changes in field grown plants.  相似文献   

6.
We address the problem of estimating the carrier-to-noise ratio (C/N0) in weak signal conditions. There are several environments, such as forested areas, indoor buildings and urban canyons, where high-sensitivity global navigation satellite system (HS-GNSS) receivers are expected to work under these reception conditions. The acquisition of weak signals from the satellites requires the use of post-detection integration (PDI) techniques to accumulate enough energy to detect them. However, due to the attenuation suffered by these signals, estimating their C/N0 becomes a challenge. Measurements of C/N0 are important in many applications of HS-GNSS receivers such as the determination of a detection threshold or the mitigation of near-far problems. For this reason, different techniques have been proposed in the literature to estimate the C/N0, but they only work properly in the high C/N0 region where the coherent integration is enough to acquire the satellites. We derive four C/N0 estimators that are specially designed for HS-GNSS snapshot receivers and only use the output of a PDI technique to perform the estimation. We consider four PDI techniques, namely non-coherent PDI, non-quadratic non-coherent PDI, differential PDI and truncated generalized PDI and we obtain the corresponding C/N0 estimator for each of them. Our performance analysis shows a significant advantage of the proposed estimators with respect to other C/N0 estimators available in the literature in terms of estimation accuracy and computational resources.  相似文献   

7.
GOCE gravitational gradiometry   总被引：16，自引：6，他引：10  
GOCE is the first gravitational gradiometry satellite mission. Gravitational gradiometry is the measurement of the second derivatives of the gravitational potential. The nine derivatives form a 3 × 3 matrix, which in geodesy is referred to as Marussi tensor. From the basic properties of the gravitational field, it follows that the matrix is symmetric and trace free. The latter property corresponds to Laplace equation, which gives the theoretical foundation of its representation in terms of spherical harmonic or Fourier series. At the same time, it provides the most powerful quality check of the actual measured gradients. GOCE gradiometry is based on the principle of differential accelerometry. As the satellite carries out a rotational motion in space, the accelerometer differences contain angular effects that must be removed. The GOCE gradiometer provides the components V xx , V yy , V zz and V xz with high precision, while the components V xy and V yz are of low precision, all expressed in the gradiometer reference frame. The best performance is achieved inside the measurement band from 5 × 10–3 to 0.1 Hz. At lower frequencies, the noise increases with 1/f and is superimposed by cyclic distortions, which are modulated from the orbit and attitude motion into the gradient measurements. Global maps with the individual components show typical patterns related to topographic and tectonic features. The maps are separated into those for ascending and those for descending tracks as the components are expressed in the instrument frame. All results are derived from the measurements of the period from November to December 2009. While the components V xx and V yy reach a noise level of about \({10\;\rm{\frac{mE}{\sqrt{Hz}}}}\), that of V zz and V xz is about \({20\; \rm{\frac{mE}{\sqrt{Hz}}}}\). The cause of the latter’s higher noise is not yet understood. This is also the reason why the deviation from the Laplace condition is at the \({20 \;\rm{\frac{mE}{\sqrt{Hz}}}}\) level instead of the originally planned \({11\;\rm{\frac{mE}{\sqrt{Hz}}}}\). Each additional measurement cycle will improve the accuracy and to a smaller extent also the resolution of the spherical harmonic coefficients derived from the measured gradients.  相似文献   

8.
Estimating the water budgets of large basins is a challenge because of the lack of data and information. It becomes more complicated in endorheic basins that consist of separate land and water phases. The application of remotely-sensed data is one solution in this regard. The present study addresses this issue and develops a modeling framework to evaluate a water budget based on remotely-sensed data for endorheic basins. To explore the methodology, Lake Urmia basin was selected as a case study. The lake water level has declined steeply since 1995 and stakeholders have agreed to allocate 3100 MCM of water per year to the lake. This makes it necessary to monitor river inflow into the lake to fulfill the agreement. Gauging stations have been employed around the lake, but they could not account for shortages such as water uptake below the stations. To do this, separate water budgets for the water body and the land were required. More specifically, it was necessary to estimate actual evapotranspiration (ET a ) from freshwater (E f ) and saltwater (E s ) estimated using the SEBAL model. Different methods were applied to estimate soil moisture, groundwater exploitation, and surface-groundwater inflow into the lake. A comparison of the observed and estimated amounts showed good agreement. For instance, the coefficient of determination for the observed/reported and estimated ET a and E f were 0.83 and 0.84, respectively. The average annual inflow was estimated to be 2.2 BCM/year for 2002–2008 using the RS model, which is about 84 % of the total inflow from the last recording stations before the lake and shows influence of water exploitation after these stations. Future study should focus on increasing temporal and spatial resolution of the method  相似文献   

9.
The initial acquisition of direct-sequence spread-spectrum (DSSS) signal transmitted in bursts by ground terminals at satellite-borne receiver poses an engineering challenge. We propose a low-complexity acquisition algorithm that is capable of capturing extremely weak DSSS signal in the presence of large Doppler dynamics. The algorithm uses fast Fourier transform (FFT)-based frequency-domain techniques to implement circular correlations between the received signal and the local pseudo-random noise (PRN) code, and it coherently accumulates the correlation results across multiple PRN code periods, to achieve a sufficient signal–noise ratio for reliable acquisition. We invoke another FFT procedure to perform the coherent accumulation and the fine compensation for the residual Doppler frequency offset. To highlight the advantage of the proposed algorithm, we make a complexity comparison among the proposed algorithm and two other benchmark strategies, namely the modified double block zero padding (MDBZP) and two-dimensional exhaustive search (2D-ES). It is shown that the proposed algorithm has the lowest complexity, which is particularly desirable for satellite-borne receivers where the computational resource is limited. The acquisition performance of the proposed algorithm is verified by theoretical analysis and Monte Carlo simulations and compared with that of MDBZP and 2D-ES. Moreover, we have carried out extensive tests on a hardware verification system, and we show the claimed tradeoff between performance and cost is indeed attainable with the suggested algorithm. Numerically, it is found the proposed algorithm can achieve a detection rate of 0.9 and a false alarm rate of \(10^{ - 5}\) at C/N 0 = 29.5 dBHz over a Doppler frequency offset range of \(\left[ { - 7.5\,{\text{kHz}},7.5\,{\text{kHz}}} \right]\) in floating-point simulation, which coincides with the analytical results. The same performance is achieved at C/N 0 = 31 dBHz in fixed-point simulation and at C/N 0 = 31.5 dBHz on a hardware system.  相似文献   

10.
An Effective Model to Retrieve Soil Moisture from L- and C-Band SAR Data   总被引：1，自引：0，他引：1  
This study investigated an appropriate method for soil moisture retrieval from radar images and coincident ground measurements acquired over bare soil and sparsely vegetated regions. The adopted approach based on a single scattering integral equation method (IEM) was developed to establish the relationship between backscatter coefficient and surface soil parameters including volumetric soil moisture content and surface roughness. The performance of IEM in 0–7.6 cm is better than that in 0–20 cm. Moreover, IEM can simulate correctly the backscatter coefficients only for the root mean square (RMS) height s < 1.5 cm at C-band and s < 2.5 cm at L-band by using an exponential correlation function and for s > 1.5 cm at C-band and s > 2.5 cm at L-band by using Gaussian function. However, due to the difficulties involved in the parameterization of soil surface roughness, the estimated accuracy is not satisfactory for the inversion of IEM. This paper used a combined roughness parameter and Fresnel reflection coefficient to develop an empirical model. Simulations were performed to support experimental results and to highlight soil moisture content and surface roughness effects in different polarizations. Results showed that a good agreement was found between the IEM simulations and the SAR measurements over a wide range of soil moisture and surface roughness characteristics. The model had a significant operational advantage in soil moisture retrieval. The correlation coefficients were 77.03 % at L-band and 81.45 % at C-band with the RMSEs of 0.515 and 0.4996 dB, respectively. Additionally, this work offered insight into the required application accuracy of soil moisture retrieval at a large area of arid regions.  相似文献   

11.
Soil moisture estimation from satellite earth observation has emerged effectively advantageous due to the high temporal resolution, spatial resolution, coverage, and processing convenience it affords. In this paper, we present a study carried out to estimate soil moisture level at every location within Enugu State Nigeria from satellite earth observation. Comparative analysis of multiple indices for soil moisture estimation was carried out with a view to evaluating the robustness, correlation, appropriateness and accuracy of the indices in estimating the spatial distribution of soil moisture level in Enugu State. Results were correlated and validated with In-Situ soil moisture observations from multi-sample points. To achieve this, the Topographic Wetness Index (TWI), based on digital elevation data, the Temperature Vegetation Dryness Index (TVDI) and an improved TVDI (iTVDI) incorporating air temperature and a Digital Elevation Model (DEM) were calculated from ASTER global DEM and Landsat images. Possible dependencies of the indices on land cover type, topography, and precipitation were explored. In-Situ soil moisture data were used to validate the derived indices. The results showed that there was a positive significant relationship between iTVDI versus TVDI (R = 0.53, P value < 0.05), while in iTVDI versus TWI (R = 0.00, P value > 0.05) and TVDI versus TWI (R = ?0.01, P value > 0.05) no significant relationship existed. There was a strong relationship between iTVDI and topography, land cover type, and precipitation than other indices (TVDI, TWI). In situ measured soil moisture values showed negative significant relationship with TVDI (R = ?0.52, P value < 0.05) and iTVDI (R = ?0.63, P value < 0.05) but not with TWI (R = ?0.10, P value > 0.05). The iTVDI outperformed the other two index; having a stronger relationship with topography, precipitation, land cover classes and soil moisture. It concludes that although iTVDI outperformed other indices (TVDI, TWI) in soil moisture estimation, the decision of which index to apply is dependent on available data, the intent of usage and spatial scale.  相似文献   

12.
The correlation between the rate of TEC index (ROTI) and scintillation indices S 4 and σ Φ for low-latitude region is analyzed in this study, using data collected from a Global Positioning System (GPS) scintillation monitoring receiver installed at the south of Hong Kong for the periods June–August of 2012 and May 2013 and July–December of 2013. The analysis indicates that the correlation coefficient between ROTI and S 4/σ Φ is about 0.6 if data from all GPS satellites are used together. If each individual satellite is considered, the correlation coefficients are above 0.6 on average and sometimes above 0.8. The analysis also shows that the ratio of ROTI and S 4 varies between 1 and 4. The ratio ROTI/σ Φ, varies between 2 and 9. In addition, it is also found that there is a good consistency between the temporal variations of ROTI with scintillation activity under different ionospheric conditions. ROTI has a high correlation relationship with scintillation indices on geomagnetically disturbed days or in solar active months. Moreover, the data observed at low elevation angles have weak correlation between ROTI and scintillation indices. These results demonstrate the feasibility of using ROTI derived from GPS observations recorded by common non-scintillation GPS receivers to characterize ionospheric scintillations.  相似文献   

13.
A new approach for deformation monitoring of super high-rise building using GPS/BDS technology is proposed for the case when prior coordinates are known and the baseline is short but has a large height difference. The approach is based on the ambiguity function method (AFM). Considering that the double-differenced (DD) troposphere delay residual error cannot be ignored, the relative zenith tropospheric delay (RZTD) parameter is introduced into the original AFM equation. Thus, the RZTD and 3D coordinate parameters are together obtained through the modified AFM (MAFM). Due to the low computational efficiency of conventional AFM, an improved particle swarm optimization (IPSO) algorithm is used to search the four optimal parameters X/Y/Z/RZTD and replaces the grid search method. In this study, GPS/BDS deformation monitoring data for buildings with approximately 290 m height difference were used to verify the feasibility of the proposed MAFM. Numerical results show a single-epoch average computation time of approximately 0.3 s, which meets the requirements of near-real-time dynamic monitoring. The average accuracy of the GPS single-epoch RZTD solution is better than 1 cm, the combined GPS/BDS MAFM performance outperforms the GPS-only system, and using multi-epoch observations can further improve the accuracy of the RZTD solution. After RZTD correction, GPS/BDS monitoring precision can be improved, particularly the height dimension, whose precision is improved by approximately 6 cm.  相似文献   

14.
Error analysis in length measurements is an important problem in geographic information system and cartographic operations. The distance between two random points—i.e., the length of a random line segment—may be viewed as a nonlinear mapping of the coordinates of the two points. In real-world applications, an unbiased length statistic may be expected in high-precision contexts, but the variance of the unbiased statistic is of concern in assessing the quality. This paper suggesting the use of a k-order bias correction formula and a nonlinear error propagation approach to the distance equation provides a useful way to describe the length of a line. The study shows that the bias is determined by the relative precision of the random line segment, and that the use of the higher-order bias correction is only needed for short-distance applications.  相似文献   

15.
Precise point positioning with integer ambiguity resolution requires precise knowledge of satellite position, clock and phase bias corrections. In this paper, a method for the estimation of these parameters with a global network of reference stations is presented. The method processes uncombined and undifferenced measurements of an arbitrary number of frequencies such that the obtained satellite position, clock and bias corrections can be used for any type of differenced and/or combined measurements. We perform a clustering of reference stations. The clustering enables a common satellite visibility within each cluster and an efficient fixing of the double difference ambiguities within each cluster. Additionally, the double difference ambiguities between the reference stations of different clusters are fixed. We use an integer decorrelation for ambiguity fixing in dense global networks. The performance of the proposed method is analysed with both simulated Galileo measurements on E1 and E5a and real GPS measurements of the IGS network. We defined 16 clusters and obtained satellite position, clock and phase bias corrections with a precision of better than 2 cm.  相似文献   

16.
Applying a one-step integrated process, i.e. by simultaneously processing all data and determining all satellite orbits involved, a Terrestrial Reference Frame (TRF) consisting of a geometric as well as a dynamic part has been determined at the observation level using the EPOS-OC software of Deutsches GeoForschungsZentrum. The satellite systems involved comprise the Global Positioning System (GPS) as well as the twin GRACE spacecrafts. Applying a novel approach, the inherent datum defect has been overcome empirically. In order not to rely on theoretical assumptions this is done by carrying out the TRF estimation based on simulated observations and using the associated satellite orbits as background truth. The datum defect is identified here as the total of all three translations as well as the rotation about the z-axis of the ground station network leading to a rank-deficient estimation problem. To rectify this singularity, datum constraints comprising no-net translation (NNT) conditions in x, y, and z as well as a no-net rotation (NNR) condition about the z-axis are imposed. Thus minimally constrained, the TRF solution covers a time span of roughly a year with daily resolution. For the geometric part the focus is put on Helmert transformations between the a priori and the estimated sets of ground station positions, and the dynamic part is represented by gravity field coefficients of degree one and two. The results of a reference solution reveal the TRF parameters to be estimated reliably with high precision. Moreover, carrying out a comparable two-step approach using the same data and models leads to parameters and observational residuals of worse quality. A validation w.r.t. external sources shows the dynamic origin to coincide at a level of 5 mm or better in x and y, and mostly better than 15 mm in z. Comparing the derived GPS orbits to IGS final orbits as well as analysing the SLR residuals for the GRACE satellites reveals an orbit quality on the few cm level. Additional TRF test solutions demonstrate that K-Band Range-Rate observations between both GRACE spacecrafts are crucial for accurately estimating the dynamic frame’s orientation, and reveal the importance of the NNT- and NNR-conditions imposed for estimating the components of the dynamic geocenter.  相似文献   

17.
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18.
There has been a significant advancement in the application of remote sensing from various space altitudes for inventorying and monitoring ofjhum (shifting) cultivation associated forest loss. The dynamic nature ofjhum system, complex physiography, small size of individualjhum plots and their discontinuous nature of distribution, highly heterogeneous vegetation and ever-changing atmospheric condition in the Arunachal Himalaya posses a great challenge to local flora and fauna. Indian Remote Sensing (IRS)-1C/1D LISS-III data were used to classify the current and abandonedjhum areas in Dibang valley district. The amount of area occupied by current and abandonedjhum corresponds to 199.34 km2(1.53%) and 225.40 km2(1.73%) respectively. Field data were collected following stratified random sampling method to gather information on plant community occurring in abandonedjhum cultivated areas. It was observed that only nine species out of 45 contribute to 50% of the important value index (IVI). Of the 45 species, 7 species (15.56%) have been found to be endemic to Eastern Himalayas. Population inducedjhum cultivation has led to deforestation, biodiversity loss, increased surface soil erosion, and sedimentation of water bodies in this area. The potential use of satellite-derived maps can best be used for better management and land use planning.  相似文献   

19.
It has been noted that the satellite laser ranging (SLR) residuals of the Quasi-Zenith Satellite System (QZSS) Michibiki satellite orbits show very marked dependence on the elevation angle of the Sun above the orbital plane (i.e., the \(\beta \) angle). It is well recognized that the systematic error is caused by mismodeling of the solar radiation pressure (SRP). Although the error can be reduced by the updated ECOM SRP model, the orbit error is still very large when the satellite switches to orbit-normal (ON) orientation. In this study, an a priori SRP model was established for the QZSS Michibiki satellite to enhance the ECOM model. This model is expressed in ECOM’s D, Y, and B axes (DYB) using seven parameters for the yaw-steering (YS) mode, and additional three parameters are used to compensate the remaining modeling deficiencies, particularly the perturbations in the Y axis, based on a redefined DYB for the ON mode. With the proposed a priori model, QZSS Michibiki’s precise orbits over 21 months were determined. SLR validation indicated that the systematic \(\beta \)-angle-dependent error was reduced when the satellite was in the YS mode, and better than an 8-cm root mean square (RMS) was achieved. More importantly, the orbit quality was also improved significantly when the satellite was in the ON mode. Relative to ECOM and adjustable box-wing model, the proposed SRP model showed the best performance in the ON mode, and the RMS of the SLR residuals was better than 15 cm, which was a two times improvement over the ECOM without a priori model used, but was still two times worse than the YS mode.  相似文献   

20.
López et al. (Reg Sci Urban Econ 40(2–3):106–115, 2010) introduce a nonparametric test of spatial dependence, called SG(m). The test is claimed to be consistent and asymptotically Chi-square distributed. Elsinger (Reg Sci Urban Econ 43(5):838–840, 2013) raises doubts about the two properties. Using a particular counterexample, he shows that the asymptotic distribution of the SG(m) test may be far from the Chi-square family; the property of consistency is also questioned. In this note, the authors want to clarify the properties of the SG(m) test. We argue that the cause of the conflict is in the specification of the symbolization map. The discrepancies can be solved by adjusting some of the definitions made in the original paper. Moreover, we introduce a permutational bootstrapped version of the SG(m) test, which is powerful and robust to the underlying statistical assumptions. This bootstrapped version may be very useful in an applied context.  相似文献   

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