And Dual-Frequency GPS and GLONASS Observations on Point Accuracy Under Forest Canopies

Effects of Differential Single- and Dual-Frequency GPS and GLONASS Observations on Point Accuracy under Forest Canopies

Erlk Naesset

Deckert and Bolstad (1996) and Sigrist et al. (1999) reported A 20-channel, dual-frequency receiver observing dual-fie- accuracies of approximately 3.1 to 4.4 m and 1.8 to 2.5 m for the quency pseudorange and carrier phase of both GPS and average position of 500 and 480 repeated measurements of indi- GLONASS was used to determine the positional accuracy of 29 vidual points under tree canopies, respectively, based on differ- points under tree canopies. The mean positional accuracy ential pseudorange. Nsesset (1999)found that, even under tree based on differential postprocessing of GPS+GLONASS single- canopies, carrier phase observations represent valuable addi- frequency observations ranged from 0.16 m to 1.I 6 m for 2.5 tional information as compared to traditional pseudorange min to 20 min of observation at points with basal area ranging acquisition. By using both single-frequency pseudorange and from <20 m2/ha to 230 m2/ha. The mean positional accuracy carrier phase observations in an adjustment with coordinates of differential postprocessing of dual-frequency GPS+GLONASS and carrier phase ambiguities as unknown parameters (float observations ranged from 0.08 m to 1.35 m. Using the dual- solution), an accuracy of 0.8 m was reported for two 12-chan- frequency carrier phase as main observable and fixing the nel receivers based on 30 min of observation. The correspond- initial integer phase ambiguities, i.e., a fixed solution, gave ing accuracy using pseudorange only was 1.2 to 1.9 m. the best accuracy. However, searching for fixed solutions Recently, Naesset et al. (2000)argued that, under less favor- increased the risk of large individual positional errors due to able conditions such as under forest canopies, the number of "false" fixed solutions. available satellites is a critical factor for a high positional accu- The accuracy increased with decreasing density of forest, racy. With additional satellites beyond those of the GPS pro- increasing length of observation period, and decreasing a gram, the probability of receiving signals from a required priori standard error as reported by the postprocessing soft- number of satellites with a good geometric distribution will ware. increase. This would be particulary useful in order to take full advantage of the carrier phase observations. By acquisition of Introduction the pseudorange and L1 carrier phase of both GPS and the Rus- Many forest survey applications need highly accurate spatial sian Global Navigation Satellite System (GLONASS),an accu- location of timber measurements made in the field. One such racy of approximately 0.4 m (float solution) was reported after example is the determination of tree heights and timber volume 30 min of observation. The corresponding accuracy using only from airborne laser scanner data (Naesset, 1997; Naesset and GPS observations was 0.7 m. Bjerknes, 2001). Global Positioning System (GPS)technology Furthermore, Naesset et al. (2000) showed that even under can provide few-millimeter accuracy with a surveying-grade tree canopies that are not too dense it might be possible to solve receiver under "clear sky." In forested landscapes, however, the initial carrier phase ambiguity, i.e., to obtain a so-called biologic and topographic obstacles tend to degrade the accu- fixed solution. Such solutions will often represent centimeter- racy obtained from the GPS observations and at times prevent level accuracy. In land surveyor applications with the highest the radio signals from reaching the GPS antenna on the ground. accuracy requirements, dual-frequency (LI+LZ) receivers are Differential positioning in forest environments, i.e., the often used. For ambiguity resolution, observation of both LI utilization of two GPS receivers-one base receiver sited at a and LZ is superior to L1 only (e.g., Hofrnan-Wellenhof et al., known position and a rover receiver used in the forest at 1997). The objective of this study was to compare the point unknown positions-has been applied both in traverse sur- accuracy of single-frequency (LI) carrier phase differential veys (Liu and Brantigan, 1995) and in the determination of the GPS+GLONASS under forest canopies with corresponding accu- geographical positions of individual points under forest cano- racies of dual-frequency (LI+LZ) observations. Fixed solutions pies (Deckert and Bolstad, 1996; Naesset, 1999; Sigrist et al., were also compared with float solutions, i.e., an adjustment 1999;Barrette et al., 2000; N~ssetet al., 2000). When differen- with both coordinates and carrier phase ambiguities as un- tial positioning is used, the two receivers collect data simulta- known parameters. neously, and common errors in the two receivers are elimi- In practical field surveys of remote forest areas, it is not nated. However, site-dependent errors are not reduced by dif- economically feasible to revisit a site. It is therefore important ferencing between receivers. to ensure that a proper quality of all the collected GPS+GLONASS Two observables are available for positioning with GPS, i.e., the pseudorange and the carrier phase. The carrier phase is the basis of the techniques used for high-precision GPS surveys. Photogrammetric Engineering & Remote Sensing Vol. 67, No. 9, September 2001, pp. 1021-1026. Department of Forest Sciences, qgricultural University of 0099-1112/01/6709-1021$3.00/0 Norway, P.O. Box 5044, N-1432 As, Norway (erik.naesset@ O 2001 American Society for Photogrammetry isf.nlh.no). and Remote Sensing

PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING September 2001 1021 observations be obtained on the first attempt. To achieve a TABLE1. SUMMARYOF FOREST STAND CHARACTERISTICS FOR 29 SUB required accuracy at sites with high tree densities, it may be CANOPYPOINTS~ necessary that a position in an adjacent opening be measured Range Mean and that the position of the object of interest be computed from measurements of distance and bearing. However, it would be Age (years) 18-115 68 useful if the surveyor could decide in the field whether it is h~ [m) 5.1-28.2 17.8 likely that an accurate position can be obtained. Forest density, G [m2/ha) 5.0-42.0 24.7 V (m3/ha) 15.0-508.5 226.8 tree height, length of the observation period, and geometric sat- % spruce 0.0-100.0 55.2 ellite distribution are factors that affect accuracy (Deckert and % pine 0.0-100.0 28.6 Bolstad, 1996; Naesset, 1999; Naesset et al., 2000) and that may % birch 0.0-100.0 16.2 be considered by planning in advance or by tree measurements No. of sites dominated by in situ. How these factors affect accuracy was, therefore, spruce 16 evaluated. pine 9 Furthermore, when the field measurements are completed deciduous 4 and the positions finally are computed by differential post- "hL= Lorey's mean height, G = basal area, V = total timber volume. processing, it is useful to assess the reliability of the computed positions. Because no ground truth will exist, the expected accuracy has to be computed from indicators that are known to sample trees and expressed by the so-called Lorey's mean be correlated with the accuracy and that are made available height (ht),i.e., mean height weighted by basal area. during the field work or after the postprocessing. These indicators comprise the factors mentioned above and the a priori stan- GPS and GLONASS Data Collection dard errors of the computed coordinates reported by the Two identical Javad Legacy receivers (Javad Positioning Sys- postprocessing software. I evaluated how these factors and tems, San Jose, California) were used to collect the GPS and indicators affect the observed accuracy. GLONASS observations, one receiver serving as a base station for differential correction sited at the university campus ("Base Material Methods Station 1") and near the Oslo International Airport ("Base Sta- and tion 2") and one used as a rover receiver in the forest at the sub- Field Reference Data canopy sites. The base stations were located 0.8 to 5.5 km from The study was accomplished in a forest in the municipality of the respective sub-canopy sites. The Javad Legacy are 20-chan- As (N 5g040' E 10°45', 40 to 120 m a.s.l.1, near the Agricultural nel dual-frequency receivers observing pseudorange and car- University of Norway, and in the municipality of Ullensaker rier phase (LI+L~)of both GPS and GLONASS. (N 60°11' E 11°13', 200 m a.s.l.), southeast Norway, near the The GPS and GLONASS obs~rvationsfor the 23 sub-canopy Oslo International Airport. points in the municipality of As were acquired on 20 and 21 Ten sites were selected forethetrial. Eight of them were July 1999. For the six sub-canopy sites in the municipality of located in the municipality of As within a radius of 5 km and Ullensaker, the data were collected on 30 October 1999. On two of them were located in the municipality of Ullensaker both occasions 27 operating GPS satellites were available within a radius of 0.8 km. Each site was comprised of a mixture (Anon., 1999a),whereas the number of operating GLONASS sat- of open areas and closed forest stands. The closed stands repre- ellites in July and October were 16 and 10, respectively (Anon., sented different combinations of tree heights, stand densities, 1999b).No mission planning was done to survey under opti- and tree species. In an open area at each of the ten sites, the posi- mal satellite configurations. The rover receiver was positioned tions of two subjectively selected points were accurately deter- accurately with a tripod over each sub-canopy point. The an- mined using differential GPS. Static observations over a period of tenna height ranged from 1.50 m to 1.85 m. The base and rover about 60 rnin were carried out using an Ashtech Dimension sin- receivers were set with an elevation mask of 12" and 15", gle-frequency receiver (Ashtech Inc., Sunnyvale, California) respectively. A lower elevation mask was used for the base sta- observing carrier phase. An Ashtech Dimension receiver sewed tions to ensure that all satellites observed by the rover could be as the base station. The distance between the sites and the base observed at the bases as well. Both receivers used a two-second station was less than 5.5 km. Fixed solutions were found for all logging rate. Collection of observations lasted for exactly 20 these 20 points, i.e., the carrier phase ambiguity was solved, rnin at each point. which indicates an a priori positional standard error on the order of about 2 cm or less (Anon., 1993). GPS and GLONASS Data Processing and Analysis In closed stands adjacent to each of the ten open areas, 29 Differential postprocessing of the GPS+GLONASS observations sub-canopy points were selected with desired canopy character- was accomplished with the Pinnacle software, version 1.00 istics. The age of the forest ranged from 18 years to 115 years (Anon., 1999~).For each sub-canopy point, 20 different posi- with an average of 68 years (Table 1)."True" reference positions were computed based on five observation periods, two tions were found for each of the 29 points using the points different GPS+GLONASS frequency combinations, and two dif- located in the open areas and traverses performed with standard ferent processing modi. The five different observation periods surveying methods, which indicated that the expected stan- were (1)the first 2.5 min, (2) the first 5 min, (3)the first 10 min, dard error of the reference positions was approximately 2 cm. (4) the first 15 min, respectively, of the 20-min period of obser- For each of the 29 sub-canopy points, the forest canopy was vation, and finally, (5) the entire 20-minperiod. For each of the characterized by forest stand attributes (Table 1).Stand density five time intervals, coordinates were computed from (1)the was expressed by basal area (G). A relascope, which measures pseudorange and L1 carrier phase observations of GPS+GLO- the basal area per hectare directly, was used. Basal area ranged NASS as float solutions, (2) the pseudorange and L1+L2 carrier from 5 m2/hato 42 m2/ha (Table 1).Tree species composition phase observations of GPS+GLONASS as float solutions, (3) the was expressed according to the basal area of each species. The L1 carrier phase observations of GPS+GLONASS searching for tree species in the study were Norway spruce (Picea abies (L.) fixed solutions. and (41 the Ll+LZ carrier uhase observations of Karst.), silver birch (Betula pendula Roth), and Scots pine GPS+GLONASS kearchiAg for fixed solutitns. In (I)and (2) the (Pinus sylvestris L.). Five sample trees were selected by hori- positions were computed as static double-difference float solu- zontal point sampling and their heights were measured by a tions using a least-squares technique. By assigning a value of Vertex hypsometer. Stand mean height was computed from the 1.0 to the "contrast threshold" parameter, the postprocessing

September 2001 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING program was enforced to compute float solutions. In (3) and (4) postprocessing modus based on single-frequency observa- it was searched for fixed or partial fixed solutions. A default tions; LlFIXED = 1, LlLZFLOAT = 0, and LlLZFIXED = 0 if fixed contrast threshold value of 0.95 was used. The positions were postprocessing modus based on single-frequency observa- computed as static double-difference solutions using a least- tions; LlFIXED = 0, LlLPFLOAT = 1,and LlLZFIXED = 0 if float squares technique. In cases where the postprocessing program postprocessing modus based on dual-frequency observations; did not find any fixed or partial fixed solution, a float solution and LlFIXED = 0, LlLZFLOAT = 0, and LlLZFIXED = 1 if fixed was reported. Thus, sometimes it happened that the solution postprocessing modus based on dual-frequency observations. in (1)and (3) and in (2) and (4) were equal. The second, third, and fourth models (Equations 2,3, and Arithmetic mean PDOP values were computed from the 4) were estimated as a linear regression using the ordinary GPS+GLONASS observations at the base stations for each of the least-squares method (Anon., 1989). 2.5-min, 5-min, 10-min, 15-min, and 20-min intervals. Mean PDOP ranged from 1.4 to 2.7. Results The positional accuracy of each computed position was Adequate coordinates were obtained by postprocessing for all calculated as the horizontal distance (D, m) between the satel- sub-canopy points and all observation periods except for 2.5 lite-acquired position and the "true" reference position. The rnin of observation of one of the points where the postproc- precision was also calculated. It was computed as the standard essing software did not report any solution. For the remaining error of D. However, the standard error depicts the deviation observations, positional accuracy varied by GPS+GLONASSfre- from the mean and not from the truth. In error budgets in which quencies, postprocessing modi, observation period, and stand the total effect on precision of several independent error factors density as expressed by basal area (Table 2). For positions deter- is estimated, it is often useful to know the deviation from the mined from 2.5 to 20 rnin of single-frequency observations, the truth and not from the mean. The root-mean-square error mean accuracy ranged from 0.19 m to 0.83 m for the low density (RMSE) was therefore reported. points (G < 20 m2/ha)based on float processing modus and Regression analysis was applied to the data to assess how from 0.16 m to 0.86 m based on fixed processing modus. For the factors that may be recorded in the field or in advance affect highest densities (G 2 30 m2/ha),the mean accuracy ranged accuracy. Positional accuracy as expressed by D was the depen- from 0.66 m to 1.13 m and from 0.68 m to 1.16 m for the float dent variable, and continuous independent variables were Lor- and fixed processing modi, respectively. ey's mean tree height (hL,m), stand density as expressed by basal For dual-frequency observations, the mean accuracy for area (G, m2/ha),and observation period (t, min). Furthermore, points with G < 20 m2/hawas in the range between 0.15 m and mean PD~Pvalues of the base stations were included as an inde- 0.72 m and between 0.08 m and 0.63 m for float and fixed modi, pendent variable to represent geometric satellite distribution. respectively. For points with G r 30 m2/ha,the corresponding PDOP values of the base stations were used rather than the values accuracies rangedfrom 0.67 m to 0.99 m and from 0.52 m to 1.35 observed under tree canopies with the rover in order to separate m after 2.5 to 20 min of observations. the effects of canopy characteristics and satellite configuration The maximum error for a single position was 3.41 m, and (Naesset, 1999). The relationships between accuracy and the the root-mean-square error ranged from 0.10 m to 1.58 m for the independent variables are not strictly linear (Nmsset, 1999; various combinations of frequencies, processing modi, obser- Sigrist et al., 1999; Naesset et d.,2000). A multiplicative model vation periods, and stand densities. was therefore used in the regression analysis: i.e., According to the regression analysis of the second model (Equation 2), which comprised factors that could be assessed during field work as independent variables, the accuracy improved significantly by decreasing mean tree height (lnhL) where D is the horizontal distance between satellite-acquired and stand density (1nG) (Table 3) and by increasing observation and the "true" reference position (m);hL is the Lorey's mean period (Int) (Figure 1).The model explained 34 percent of the tree height (m);G is the basal area (m2/ha);t is the observation variation. period (min);PDOP is the mean position dilution of precision of The analysis of the third model (Equation 3), which was base stations; and Po,a, p2, P3, and p4 are the regression coeffi- intended to indicate the reliability of a position after postproc- cients to be estimated. essing, also revealed that accuracy improved significantly by This model (Equation 1)was log-transformedto decreasing stand density (1nG) and increasing observation period (lnt) (Table 3). Furthermore, the a priori standard error of the computed coordinates (~~STDERR)was highly correlated with the accuracy. The observed accuracy improved by The model used to assess the accuracy after differential decreasing standard error. As a matter of fact, regressions of postprocessing (Equation 3) comprised the independent vari- each independent variable showed that ~~STDERRwas the sin- ables in Equation (2) and the a priori standard errors of the com- gle most correlated accuracy indicator of them all, and it puted coordinates reported by the postprocessing software accounted for 38.5 percent of the variation (Table 4). It is also (STDERR):i.e., noteworthy that the third model explained 49 percent of the variation a able 3), which according to a Z-tes<(~nedecorand Cochran, 1980, p. 186)is a significantly higher proportion than the R2 value of 0.34 in model 2 (Equation 2) indicated. The geometric satellite distribution (I~PDOP)did not affect Regression analysis was also used to assess how single-fre- accuracy in any of the models. The R2value of 0.007 (Table 4) quency (LI) and dual-frequency (LI +LZ)observations and how indicated that the accuracy and ~~PDOPwere hardly correlated. postprocessjng modi (float and fixed) affect accuracy, respec- Principal component analysis based on the correlation tively. Diffefent frequency and processing modus combina- matrix was used to assess the presence of collinearity in the tions were coded as dummy variables and included in the regression analysis. The square root of the largest eigenvalue regression analysis in the following way: divided by the smallest eigenvalue (condition number) was used as a means for suggesting collinearity. The condition number (K) in Equation 3 of 2.90 (Table 3) indicated no serious collinearity problems. A condition number larger than 30 has been where LlFIXED = 0, LlLZFLOAT = 0, and LlLZFIXED = 0 if float proposed to indicate collinearity (Weisberg, 1985).However,

PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING September ZOO/ 1023 TABLE2. MEANPOSITIONAL ACCURACY BASED ON GPS+GLONASS SATELLITESFOR DIFFERENTFREQUENCIES, POSTPROCESSING MODI, BASAL AREAS, AND OBSERVATIONPERIODS. MIN. ERROR,MAX. ERROR, STD. ERROR,AND RMSE ARESHOWN UNDER EACH MEAN Observation Period (min) Frequency Modus Basal Area (m2/ha) 2.5 5 10 15 20 Float 0.19 Mean (m) 0.05 Min. (m) 0.43 Max. (m) 0.12 Std.err. (m) 0.22 RMSE (ml Float 0.50 0.13 1.29 0.36 0.60 Float 0.66 0.11 1.43 0.44 0.78 Fixed 0.16 0.02 0.43 0.16 0.22 Fixed 0.53 0.02 1.29 0.37 0.64 Fixed 0.68 0.09 1.43 0.42 0.79 Float 0.15 0.01 0.50 0.17 0.22 Float 0.50 0.02 1.31 0.38 0.61 Float 0.67 0.05 1.31 0.46 0.80 Fixed 0.08 0.01 0.22 0.08 0.10 Fixed 0.54 0.02 1.79 0.64 0.81 Fixed 0.52 0.07 1.31 0.46 0.68

the regression analysis of the third model revealed that mean Nevertheless, because tree height and density are intercorre- tree height did not affect positional accuracy although they lated variables, the analysis seems to indicate that it is sufficient were highly correlated with each other (Table 4). This seeming to relate positional accuracy to basal area and not to tree height. inconsistency may be due to high intercorrelations between The analysis of the fourth model (Equation 4) revealed that tree height (lnhL)and stand density (1nG) (RZ= 0.50) and the accuracy of the positions derived by the fixed postproc- between lnhLand standard error (~STDERR)(R2 = 0.14), essing modus of the dual-frequency observations differed sig- although this was not indicated by the collinearity diagnostics. nificantly from the accuracy obtained by float processing

1024 September 2001 PHOTOGRAMMEfRlC ENGINEERING & REMOTE SENSING - TABLE4. R2 FROM REGRESSIONANALYSIS INDICATING PROPORTION OF 1.1 VARIATIONASSOCIATED WITH EACH ~ND~V~DUALVARIABLE AS COMPAREDWITH 1 THE FULLMODEL (EQUATION 3) 0.9 +L1, f ked Variable R2 - 4- L1+L2, float 0.8 - lnh~ 0.190 p 0.7 +LI+L2, fked 1nG 0.227 - lnt 0.088 0.6 lnPDOP 0.007 5 0.5 lnSTDERR 0.385 9 0.4 Full model 0.488 0.3 0.2 0.1 0 was applied. For example, for one of the points with a stand den- 0 5 10 15 20 sity of G = 29 m2/ha, an error of 1.08 m was found for both processing modi after 2.5 min of observation (Figure 2). This was Observation period (min) evidently identical float solutions. After 5-min and 10-minperi- ods of observation, the errors obtained by the fixed modus Figure 1. Mean positional accuracy based on GPS+GLONASS satellites for different frequencies, postprocessing modi, dropped to 0.04 m, which indicates "true" fixed or partial fixed and observation periods. solutions. However, after 20 min the fixed error raised to 1.58 m whereas a moderate float error of 0.34 m was found. The latter error from the fixed processing clearly indicated a "false" fixed solution. Thus, fixed-processingaccuracies that approach the accuracy of the applied "true" reference itself, i.e., less than 0.1 modus of the single-frequencyobservables (Table 3). The nega- m, may be obtained. However, under difficult conditions, there tive sign of the estimated coefficient (LILZFIXED) indicated that is a risk that a position can erroneously be accepted as a fixed or the accuracy of LI +~2fixed was better than the accuracy partial fixed solution (Naesset et al., 2000). Thus, this trial has obtained from LI float. F-tests of linear combinations of the demonstrated that enforced float solutions should be sought for coefficients also showed that the accuracy of LI +LZ fixed was sites with high tree densities and in cases where it is of particular superior to the accuracy of LI fixed (F = 34.4, p < 0.001) and importance to avoid the largest positional errors. The "price" for LI+LZ float (F= 20.2, p < 0.001) as well (Table 3). LI fixed and such a conservative attitude would be a poorer accuracy for sev- LI+LZ float did not differ significantly from LI float. eral positions where a very high accuracy could be obtained. To improve the balance between safety and risk, the value of the Discussion and Conclusions "contrast threshold" parameter could be adjusted. A default The results of this study revealed that the highest accuracy was value of 0.95 was used in the fixed modus. According to the obtained using dual-frequency observations of GPS+GLONASS results it seems reasonable that a somewhat more conservative and the fixed processing modus. This was not surprising value of, for example, 0.99 would reduce the risk of "false" solu- because previous research has indicated that it might be possi- tions and at the same time improve the overall accuracy. The ble to solve the carrier phase ambiguity even in quite dense for- "best" parameter value for a specific application can only be est (Naesset et a]., 2000). Observation of both L1 and L2 is found by empiric verification. superior to L1alone for ambiguity resolution (Hofrnan-Wellen- After 15 rnin of observation of GPS+ GLONASS, it seems pos- hof et al., 1997). sible to obtain an accuracy better than 0.3 to 0.4 m for moderate In spite of this major finding, the single largest error of the stand densities (G < 30 m2/ha)(Table 2). Even for the highest entire trial of 3.41 m (Table 2) was produced by L1+L2 fixed processing. Several such extreme deviations as compared to the average error level occurred when the fixed processing modus I.6

1.4 - TABLE3. REGRESSIONCOEFFICIENTS AND THEIRSTANDARD ERRORS (SE), - 4- - Ll+L2, float COEFFICIENT OF DETERMINATION(R2), AND CONDITIONNUMBER (K) FOR 1.2 - L1 +L2, fked REGRESSIONANALYSIS OF POSITIONALACCURACY (n = 576)a Equation 2 Equation 3 Equation 4b Coefficient Estimate SE Estimate SE Estimate SE lnPo -4.33*** 0.41 -2.68*** 0.38 -0.73*** 0.11 Inh~ 0.66*** 0.16 0.15NS 0.15 1nG 0.88*** 0.14 0.83*** 0.12 lnt -0.56*** 0.06 -0.20** 0.06 lnPDOP -0.22NS 0.36 0.15NS 0.32 lnSTDERR 0.39*** 0.03 LlFIXED -0.05NS 0.16 0 5 10 15 20 LlLZFLOAT -0.27NS 0.16 LlL2FIXED -0.98*** 0.16 Observation period (rnin) RZ 0.34 0.49 0.08 K 2.65 2.90 2.00 Figure 2. Positional accuracy for a single subcanopy point based on dual-frequency GPS+GLONASS observations for dif- "Level of significance: NS>0.05; **<0.01; ***<0.001. ferent postprocessing modi and observation periods. bTest of Ho: hlFIxrm- hILPFmD = 0, F = 34.4***. Test of HO:~IL~F~~~T - hILZFmD= 0, F = 20.2***.

PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING September 2001 1025 stand densities (G 2 30 m2/ha),the mean accuracy was 0.99 m techniques, in which corresponding observations of the same after 2.5 rnin of observation when "false" fixed solutions were objects on the ground and from the air are utilized. Such appli- avoided, i.e., when float solutions were enforced, and after 15 cations may be very sensitive to positional errors for either of rnin an improved accuracy of 0.51 m was found. Deckert and the observations (Bolduc et al., 1999; Nesset and Bjerknes, Bolstad (1996) reported an accuracy of 3.1 m and 4.4 m for 2001). This study has revealed that a priori standard errors deciduous and conifer sites with average densities of 23 m2/ha reported by the postprocessing software and forest and tree and 31 m2/ha,respectively. They used differential GPS CIA code characteristics may be used to assess the reliability of com- collected by a six-channel receiver. Naesset (1999) used two 12- puted positions. channel receivers observing GPS pseudorange and carrier phase, and found accuracies of 0.9 m and 1.1m for G r 25 m2/ha Acknowledgments after 30 min of observation. When single-frequency GLONASS This research was funded by the Borregaard Research Fund, observations were added to the GPS observables, an improved Norway. 1wish to thank Bo Eide and Petter 0kseter who carried accuracy of 0.5 m was reported after 30 rnin of observation out some of the field work and data processing, and Ola under canopies with G r 25 m2/ha (Naesset et al., 2000). 0vstedal for his comments that significantly improved the Although the positional accuracy of the current study was manuscript. higher than the accuracy reported by Deckert and Bolstad (1996) and Naesset (1999), similar factors that affect the accuracy were found in all the three studies. In the present trial, basal area and observation period were significant factors Anon., 1989. SASISTAT User's Guide, Version 6, Fourth Edition, Vol- (Table 3). Deckert and Bolstad (1996) reported that characteris- ume 2, Sas Institute Inc., Cary, North Carolina, 846 p. tics related to canopy and number of fixes were most important, ,1993. Ashtech Dimension GPS Receiver Operating Manual and whereas Naesset (1999) found that characteristics related to Interface Guide, Document Number 600119, Revision B, Ashtech canopy (density and tree species) and observation period were Inc., Sunnyvale, California, 139 p. important variables. In the current study, the accuracy did not 1999a. GPS Satellite outagesfor 1999, Automated Data Service seem to improve beyond 15 rnin of observation. A similar pat- (ADS), United States Naval Observatory (USNO),URL: ftp:l/ tern was revealed by Naesset (1999) whereas the results tycho.usno.navy.millpub/gpslgpsout99.txt, obtained by Nzsset et al. (2000) indicated a further improve- -, 1999b. GLONASS Constellation Status, The Russian Federation ment of accuracy from 15 rnin to 30 rnin of observation. It is not Ministry of Defence, Coordinational Scientific Information Cen- unlikely that an improved accuracy could be obtained by ter, Moscow, URL: http:lllistserv.unb.caibin/. extending the observation period from 15 rnin to 20 rnin using -, 1999c. Pinnacle User's Manual, Javad Positioning Systems, dual-frequency fixed postprocessing provided that "false" San Jose, California, 123 p., URL: http:llwww.javad.com. fixed solutions are avoided. Barrette, J., P. August, and F. Golet, 2000. Accuracy assessment of It has also been reported that the geometric satellite distribu- wetland boundary delineation using aerial photography and digital orthophotography, Photogrammetric Engineering b Remote Sens- tion under canopy (Deckert and Bolstad, 1996) and geometric ing, 66(4):409-416. satellite distribution at the base (Naesset, 1999; Nesset et al., Bolduc P., K. Lowell, and G. Edwards, 1999. Automated estimation of 2000) are important factors that may explain accuracy. How- localized forest volume from large-scale aerial photographs and ever, in the current study, PDOP did not significantly affect accu- ancillary cartographic information in a boreal forest, International racy (R2= 0.007). This may be due to the fact that the PDOP Journal of Remote Sensing, 20(18):3611-3624. PDOP values just varied between 1.4 and 2.7 and that above the Deckert, C., and P.V. Bolstad, 1996. Forest canopy, terrain, and distance canopy (at the base) is a poor indicator of the conditions under effects on global positioning system point accuracy, Photogram- canopy. Similar results were obtained by Sigrist et al. (1999), metric Engineering b Remote Sensing, 62(3):317-321. who stated that "PDOP is not necessarily a good indicator for Hofmann-Wellenhof, B., H. Lichtenegger, and P. Collins, 1997. GPS - positional accuracy for sites under forest canopy". The single Theory and Practice, Fourth Revised Edition, Springer, Wien-New most important factor to explain accuracy seems to be the a pri- York, 217 p. ori standard error of the coordinates reported by the postproc- Liu, C. J., and R. Brantigan, 1995. Using differential GPS for forest essing software. This factor explained 38.5 percent of the traverse surveys, Canadian Journal of Forest Research, variation (Table 4), which is much more than the total proportion 25(11):1795-1805. of variation explained by all the other factors investigated by Nasset, E., 1997. Estimating timber volume of forest stands using Deckert and Bolstad (1996) (R2 = 0.253) and Nesset (1999) airborne laser scanner data, Remote Sensing of Environment, (R2 = 0.281). 61(2):246-253. This study has demonstrated that a high accuracy can be -, 1999. Point accuracy of combined pseudorange and carrier obtained by differential postprocessing after 15 min of phase differential GPS under forest canopy, Canadian Journal of GPS+GLONASS observations. However, a flexible and pragmatic Forest Research, 29(5):547-553. treatment of the data is necessary to get the best out of it. When Neesset, E., T. Bjerke, 0. avstedal, and L.H. Ryan, 2000. Contributions the conditions for signal reception are poor, such as under very of differential GPS and GLONASS observations to point accuracy dense canopies, it may be efficient to move the receiver to an under forest canopies, Photogrammetric Engineering & Remote adjacent opening and compute the actual position from mea- Sensing, 66(4):403-407. surements of distance and bearing or, at least, enforce a float Nasset, E.,and K.-0. Bjerknes, 2001. Estimating tree heights and num- processing solution if the receiver is placed in the actual posi- ber of stems in young forest stands using airborne laser scanner tion. It may also be wise to alter the parameter value that con- data, Remote Sensing of Environment, in press. trols the contrast test ratio, i.e., the "contrast threshold" Sigrist, P., P. Coppin, and M. Hermy, 1999. Impact of forest canopy on parameter value, during postprocessing according to the con- quality and accuracy of GPS measurements, International Journal ditions at each site. However, further research is needed to gain of Remote Sensing, 20(18):3595-3610. experience on how such a factor affects accuracy under differ- Snedecor, G.W., and W.G. Cochran, 1980. Statistical Methods, Seventh ent conditions. Finally, it should be emphasized that it some- Edition, Iowa State University Press, Ames, Iowa, 507 p. times might be efficient simply to exclude from further Weisberg, S., 1985. Applied Linear Regression, Second Edition, Wiley, analysis field observations with coordinates that are likely to be New York, N.Y., 324 p. seriously degraded by errors. This is highly relevant in multi- (Received 22 August 2000; accepted 24 January 2001; revised 22 Febru- phase sampling applications based on various remote sensing ary 2001)

1026 September 2001 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING