Contributions of Differential GPS and GLONASS Observations to Point Accuracy under Forest Canopies
Erlk Naesset, Trygve Bjerke, Ola Bvstedal, and Lorentz H. Ryan
Abstract 1996; Naesset, 1999).When differential positioning is used, the A &&channel,single-frequency receiver observing the C/A code two receivers collect data simultaneously, and common errors and carrier phase of both GPS and GLONASS was used to deter- in the two receivers are limited. However, site-dependent mine the positional accuracy of 27 points under tree canopies. errors are not reduced by differencing between receivers. The mean positional accuracy based on combined differential Two observables are available for positioning with GPS,i.e., postprocessing of GPS C/A code and carrier phase observations the pseudorange determined from the CIA code and the carrier ranged from 0.20 m to 5.72 m for 2.5 min to 30 min of observa- phase. The carrier phase is the basis of the techniques used for tion at points with basal area rangingfrom
PHOTOGRAMMETRIC ENGlNEERlNQ & REMOTE SENSING observations, at least in some cases. We evaluated whether it station for differentialcorrection sited at the university campus was possible to achieve fixed solutions under tree canopies ("University Station") and one used as a rover receiver in the with the combined use of GPS+GLONASS, and whether the forest at the sub-canopy sites. The University Station was chances to obtain a fixed solution could be predicted from located 2.0 to 5.5 km from the sub-canopy sites. The Ashtech characteristics observed in advance. GG24 are 24-channel single-frequency receivers observing CIA code and carrier phase of both GPS and GLONASS. Material and Methods The GPS and GLONASS observations for the 27 sub-canopy Field Reference Data points were acquired during the period 05 to 08 October 1997. The study was accomplished in a forest in the municipality of In that period 25 operating GPS satellites (Anon., 1997b) and 15 As (N 59'40' E 10°45', 40 to 120 m a.s.l.),southeast Norway, operating GLONASS satellites (Anon., 1998) were available. No near the Agricultural University of Norway. The field reference mission planning was done to survey under optimal satellite data were collected by Naesset (1999). Seven sites within a configurations. The rover receiver was positioned accurately radius of 5 km were selected for the trial. Each site comprised a with a tripod over each sub-canopy point. The antenna height mixture of open areas and closed forest stands. The closed ranged from 1.43 m to 1.69 m. The base and rover receivers stands represented different combinations of tree heights, were set with an elevation mask of 10" and 11°,respectively. A stand densities, and tree species. In an open area at each of the lower elevation mask was used for the base to ensure that all seven sites, the positions of two subjectively selected points satellites observed by the rover could be observed by the base were accurately determined by means of differential GPS. as well. Both receivers used a position dilution of precision Static observations over a period of about 60 min were carried (PDOP) mask of 20 and a two-second logging rate. Collection of out using an Ashtech Dimension single-frequency receiver observations lasted for exactly 30 rnin at each point. observing carrier phase. An Ashtech Dimension receiver served as the base station. The distance between the sites and GPS and GLONASS Data Processing and Analysis the base station was less than 5.5 km. Fixed solutions were Differential combined pseudorange and carrier phase postpro- found for all these 14 points, i.e., the carrier phase ambiguity cessing was performed at the Institute of Geodesy and Naviga- was solved, which indicates an a priori positional standard tion of the University of Federal Armed Forces, Munich, error on the order of about 2 cm or less (Anon., 1993). Germany, with a computer program developed by Rossbach and In closed stands adjacent to each of the seven open areas, Hein (1996).For each sub-canopy point, 12 different positions 27 sub-canopy points were selected with desired canopy char- were computed based on six observation periods and two dif- acteristics. The age of the forest ranged from 15 years to 111 ferent satellite combinations. The six different observation years with an average of 58 years (Table 1)."True" reference periods were (1)the first 2.5 min, (2)the first 5 min, (3) the first positions were found for each of the 27 points by using the 10 min, (4) the first 15 min, and (5) the first 20 min, respectively, points located in the open areas and traverses performed with of the 30-min period of observation, and finally, (6) the entire standard surveying methods, which indicated that the expec- 30-min period. For each of the six time intervals, coordinates ted standard error of the reference positions was approxi- were computed from (1)the CIA code and carrier phase obser- mately 2 cm. vations of the GPS satellites and (2) the C/A code and carrier For each of the 27 sub-canopy points, the forest canopy was phase observations of the GPS+GLONASS satellites. Positions characterized by forest stand attributes (Table 1).Stand density were computed as sequential kinematic epoch-by-epoch dou- was expressed by basal area (G).A relascope, which measures ble difference float solutions. the basal area per hectare directly, was used. Basal area ranged Arithmetic mean PDOP values were computed from the from 1mz/ha to 42 mz/ha (Table 1).Tree species composition observations at the University Station for each of the 2.5-min, was expressed according to the basal area of each species. The 5-min, 10-min, 15-min, 20-min, and 30-min intervals for GPS tree species in the study were Norway spruce (Picea abies (L.) and GPS+GLONASS,respectively. Karst.), silver birch (Betula pendula Roth), and Scots pine The positional accuracy of each computed position was (Pinus sylvestris L.). Four sample trees were selected by hori- calculated as the horizontal distance (D, m) between the satel- zontal point sampling and their heights were measured with a lite-acquired position and the "true" reference position. Vertex hypsometer. Stand mean height was computed from the Regression analyses were applied to the data. Positional accu- sample trees and expressed by the so-called Lorey's mean racy as expressed by D was the dependent variable, and contin- height (hL),i.e., mean height weighted by basal area. uous independent variables were stand density as expressed by basal area (G, m2/ha)and observation period (t, min). Fur- GPS and GLONASS Data Collection thermore, mean PDOp values of the University Station were Two identical Ashtech GG24 receivers were used to collect the included as an independent variable to represent geometric sat- GPS and GLONASS observations: one receiver serving as a base ellite distribution. PDOP values of the base station were used rather than the values observed under tree canopies with the TABLE1. SUMMARYOF FOREST STAND CHARACTERISTICS FOR 27 SUB- rover in order to separate the effects of canopy characteristics CANOPYPOINTS= and satellite configuration (Naesset, 1999). The relationships between accuracy and basal area, obser- Range Mean vation period, and PD~Pobserved at the base station are proba- Age (years) 15-111 58 bly not strictly linear (Naesset, 1999). A multiplicative model h~ (ml 5.2-34.8 17.6 was therefore used in the regression analysis: i.e., G (mz/ha) 1.0-42.0 19.5 V (m3/ha) 3.1-416.2 181.0 Percent spruce 0.0-100.0 53.0 Percent pine 0.0-100.0 19.3 Percent birch 0.0-100.0 27.8 This model (Equation 1)was log-transformed to No. of sites dominated by spruce 15 pine 5 deciduous 7
OhL = Lorey's mean height, G = basal area, V = total timber volume. Different satellite combinations (GPS versus GPS+GLONASS)
404 April 2000 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING were coded as a dummy variable (SATELLITE = 0 if GPS and SAT- ELLITE = 1if GPS+GLONASS)and added to the log-transformed model (Equation 2): i.e.,
Maximum-likelihood computations for fitting of the logis- tic model in Equation 4 was performed with the LOGISTIC regression procedure of the SAS package (Anon., 1989). An option for stepwise selection of variables was used to find the The second and third models (Equations 2 and 3) were esti- "best" model. mated as a linear regression using the standard least-squares No independent data were available to test whether the method (Anon., 1989). selected model could be used to predict the probability of Differential postprocessing of the GPS+GLONASS carrier obtaining a fixed solution. Cross validation was used to verify phase observations was accomplished to find fixed solutions the predictions. One of the 27 observations was removed from for the 27 sub-canopy points. Observation periods shorter than the data set at a time, and the "best" model was fitted to the data 30 min were not considered. The processing was carried out from the 26 remaining observations. The probability of obtain- with the AOS software (Anon., 1997~).First, all carrier phase ing a fixed solution was predicted for the removed observation. observations for 30 min for each of the 27 points were included The prediction was assessed according to a deterministic in a static postprocessing. Second, the "scan menu" of AOS was approach, i.e., if the predicted probability was greater than 0.5. used to "edit" manually the carrier phase observations. The it was classified as FIXED. "scan menu" displays the appearance of each satellite, and it shows whether and when continuous reception of signals is Results broken. Satellites with frequent signal blocking were discarded Positional accuracy varied by satellite combination, observa- and the static postprocessing was repeated. tion period, and stand density as expressed by basal area (Table Based on the results of the static postprocessing of the 2). For positions determined from 2.5 to 30 min of C/A code and edited carrier phase observations, we modeled the probability carrier phase GPS observations, the mean accuracy ranged from of obtaining a fixed solution (~(FULED))by multiple logistic 0.20 m to 0.62 m for the low density points (G < 15 m2/ha)and regression. The basic independent variables were basal area from 1.24 m to 5.72 m for the highest densities (G 2 25 m2/ha). (G, m2/ha) and the mean PDOP of the University Station. The largest error for a single position was 19.61 m. Because the relationships between positional accuracy and G For combined use of GPS+GLONASS,the mean accuracy for and PDOP as observed at the base are probably nonlinear points with G < 15 m2/hawas in the range between 0.09 m and (Nasset, 1999), it is likely that the relationships between 0.78 m. For points with G 25 mz/ha, the mean accuracy FIXED) and G and mean PDOP are nonlinear as well. On the ranged from 0.51 m to 2.85 m after 2.5 to 30 min of observa- basis of the results from estimation of the third model (Equa- tions. The maximum error for a single position was 6.17 m. tion 3), square-root transformations of G and PDOP were com- According to the regression analysis (Table 3), the accuracy puted, and G and PD~Pwere represented by a polynomial of improved significantly by decreasing stand density (1nG) and second degree based on the square-root transformations, which by increasing the observation period (lnt) (Figure 1). gave the following model: The analysis of the third model (Equation 3) also revealed
TABLE2. MEAN POSITIONALACCURACY BASED ON GPS AND GPS+GLONASS SATELLITESFOR DIFFERENT BASAL AREAS AN0 OBSERVATIONPERIODS. MIN. ERROR, MAX. ERROR,AND STD.ERROR ARE SHOWNUNDER EACHMEAN Observation Period (min] Basal Area Satellites (m2/ha) 2.5 5 10 15 20 30 GPS Mean (m) Min. (m) Max.Std.err. (m) (m) GPS
GPS
GPS + GLONASS
---
PHOTOGRAMMETRIC ENGINEERING 81 REMOTE SENSING TABLE3. REGRESSION COEFFICIENTSAND THEIRSTANDARD ERRORS AND TABLE4. POSITIONALACCURACY AND NUMBEROF OBSERVATIONS FOR FIXEDAND COEFFICIENTOF DETERMINATION (RZ) FOR REGRESSIONANALYSIS OF FLOATSOLUTIONS BASED ON 30 MINOF OBSERVATIONOF GPS+GLONASS POSITIONALACCURACYB ~ATELL~TESFOR DIFFERENTBASAL AREAS (G) Equation (2) Equation (3) G (m2/ha) Accuracy (m) No, of Coefficient Estimate Std. Error Estimate Std. Error Solution Range Mean Mean Min. Max. Std. Error Observations - - lnPo -2.44*** 0.25 -2.02*** 0.31 Fixeda el5 7.4 0.03 0.01 0.09 0.02 10 InG O.9OX** 0.06 0.91*** 0.06 15-25 20.5 0.01 0.01 0.02 0.01 2 lnt -0.54*** 0.06 -0.54*** 0.06 225 31.0 0.06 0.06 0.06 - 1 lnPDOP 1.15*** 0.23 0.69* 0.31 Floatb <15 - - - - - 0 SATELLITE -0.31* 0.13 15-25 20.7 0.45 0.07 0.80 0.29 7 No. of observation 324 324 225 33.7 0.54 0.04 1.12 0.40 7 RZ 0.52 0.53 "Carrier phase observations processed by the AOS software (Anon., "Level of significance: *<0.05; ***<0.001. 1997c) after manual editing. bCombined processing of CIA code and carrier phase observations according to Rossbach and Hein (1996). that the difference between the satellite combinations IGPS ver- sus GPS+GLONASS)was statistically significant (Table 3). The remaining 14 points based on float solutions ranged from 0.04 negative sign of the estimated coefficient (SATELLITE) indicated m to 1.12 m (Table 4). Fixed solutions were found for all the ten that the accuracy of GPS+GLONASSwas better than the accuracy low density points (G < 15 m2/ha).The mean basal area for obtained from GPS measurements only. Furthermore, the accu- racy increased as the geometric satellite distribution at the base these locations was 7.4 m2/ha.Fixed solutions were found for two of the nine points with medium stand density (15 < G I25 station improved (~~PDoP). However, because the number of satellites increases when m2/ha),whereas a fixed solution was found for only one point with G r 25 m2/ha. the GLoNASS satellites are taken into consideration in addition The logistic regression analysis based on stepwise selec- to the GPS satellites, the PDOP values of GPS+GLONASS will tion of variables and the 27 sub-canopy points with the 30-min improve accordingly. The GPS PDOP at the base ranged from 1.60 to 3.25 with an average of 2.13, whereas the GPS+GLONASS observations of GPS+GLONASSsatellites revealed that the proba- bility of obtaining a fixed solution could be related to the PDOP ranged from 1.20 to 2.50 with a mean value of 1.60. Thus, square-root of basal area. The "best" logistic regression model the SATELLITE dummy in the third model (Equation 3) will tend to be highly correlated with I~PDOP.The Spearman rank correla- was tion coefficient between SATELLITE and ~~PDOPwas -0.71. The second and third models (Equations 2 and 3) therefore re- vealed similar proportions of explained variation. The R2val- ues for the second and third models (Equations 2 and 3) were 0.52 and 0.53, respectively (Table 3). with p < 0.05 and p < 0.01 (Wald chi-square statistic) for the Static differential postprocessing of the 30-min observa- two estimated regression coefficients, respectively. The tions of the GPS+GLONASS carrier phase gave fixed solutions for Hosmer-Lemeshow statistic (Hosmer and Lemeshow, 1989, p. 2 of the 27 points. Repeated processing based on edited carrier 140) indicated a decent fit for the selected model (p = 0.43). phase observations gave 14 fixed solutions, of which 13 were However, it is likely that the probability of obtaining a fixed "true" fixed solutions. The accuracy of these 13 positions solution is related to the PDOP at the base as well. The backward ranged from 0.01 m to 0.09 m, whereas the accuracy of the selection indicated that F FIXED) is related to transformations of both G and PDOP. Cross validation of the selected logistic regression model revealed an agreement between the observed and predicted types of differential processing solutions (fixed versus float) of 81.5 percent (Table 5). The user's and producer's accuracies (Story and Congalton, 1986) were of similar magnitude and ranged from 76.9 percent to 85.7 percent. +- GPS Discussion and Conclusions .-0 -.GPS+GLONASS The results of this study revealed that the highest accuracy was obtained by combining GPS and GLONASS. The accuracy of the double difference float solutions of GPS+GLONASSwas superior
TABLE5. ERRORMATRIX OF OBSERVED AND PREDICTED~~FFERENT~AL PROCESSINGSOLUTIONS OF 27 SUB-CANOPY POINTSBASED ON 30 MINUTES OF OBSERVATIONOF GPS+GLONASS SATELLITES.PREDICTIONS CARRIED OUT BY MEANSOF LOGISTIC REGRESSIONEQUATIONS AND CROSS VALIDATION Observed Predicted Fixed Float Totals User's Accuracy (%) 0 5 I0 15 20 25 30 Obsewatlon period (mln) Fixed 10 2 12 83.3 FIoat 3 12 15 80.0 Figure 1. Mean positional accuracy based on GPS and Totals 13 14 27 GPS+GLONASS satellites for different observation periods. Producer's accuracy (%) 76.9 85.7 Overall agreement (%) 81.5
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING to the corresponding GPS accuracy for different combinations example geo-referencing of field sample plots to determine tim- of stand density and observation period. This was not surpris- ber volume from airborne laser scanner data (Naesset, 1997),it ing because it is a critical factor in satellite surveying under tree is essential that one can take advantage of all possible satellites canopies to receive unobstructed signals without serious available. Thus, it is a serious concern that the GLONASS pro- multipath effects from a required number of satellites over an gram seems to have degraded over last two years. In March extended period of time. 1996, GLONASS comprised 24 operating satellites, whereas the After 15 rnin of observation of GPS+GLONASS, its seems number of satellites was reduced to 15 in October 1997 and to possible to obtain an accuracy better than 0.8 m for low and 14 one year later (Anon., 1998). The future development of GLO- moderate stand densities (G < 25 m2/ha)(Table 2). Even for the NASS and other planned systems such as the European GALILEO highest stand densities (G 2 25 m2/ha),the mean accuracy was may be a key to the most accurate applications of satellite sur- 2.85 m after 2.5 min of observation, 1.30 m after 15 min, and veying in forest environments. 0.51 m after 30 min (Table 2). Deckert and Bolstad (1996) reported an accuracy of 3.1 m and 4.4 m for deciduous and coni- Acknowledgme& fer sites with average densities of 23 m2/ha and 31 m2/ha, This research was funded by the Borregaard Research Fund, respectively. They used differential GPS CIA code collected by a Norway. GPS receivers and software for the study were pro- six-channel receiver. Naesset (1999) used two 12-channel vided by Blinken A/S, Norway. We thank Rof. Giinter W. Hein receivers observing GPS CIA code and carrier phase, and found and Dr. Udo Rossbach at the University of Federal Armed accuracies of 0.90 m and 1.13 m for G 2 25 m2/ha after 30 min Forces, Munich, Germany, who accomplished some of the data of observation. processing and thus made important parts of this study pos- Although the positional accuracy of the current study was sible. higher than the accuracy reported by Deckert and Bolstad (1996) and Naesset (1999),similar factors that affect the accu- racy were found in all the three studies. In the present trial, Anon., 1989. SAWSTAT User's Guide, Version 6, Fourth Edition, Vol- basal area, geometric satellite distribution, and observation ume 2, Sas Institute hc., Cary, North Carolina, 846 p. period were significant factors (Table 3). Deckert and Bolstad ,1993. Ashtech Dimension GPS Receiver OperatingManual and (1996)reported that characteristics related to canopy, the geo- Interjiace Guide, Document Number 600119, Revision B, Ashtech metric satellite distribution under canopy, and the number of Inc., Sunnyvale, California, 139 p. fixes were most important, whereas Naesset (1999) found that ,199711. Study on European Forestrylnformation and Communi- characteristics related to canopy (density and tree species), cation System, Reports on Forestry Inventory and Survey Sys- geometric- satellite distribution at the base, and observation tems, Office for Official Publication of the European Communities, period were important variables. However, in the present trial as Luxembourg, 660 p. much as 52 percent of the variation in accuracy was accounted 1997b. GPS Satellite Outages for 1997, Automated Data Service for by the factors mentioned above whereas only 25.3 percent (ADS),United States Naval Observatory (USNO) (ttp:lltycho.usno. and 28.1 percent were explained in Deckert and Bolstad's navy.miYpublgpslgpsout97.txt). (1996) and Naesset's (1999) investigations, respectively. This , 1997c. Ashtech Office Suite for Survey, User's Manual, Docu- difference may be attributed to random disturbances such as ment Number 630154, Revision A, Ashtech Inc., Sunnyvale, Cali- multipath and temporal signal blocking that may have a more fornia, 304 p. serious effect when the number of available satellites is limited. -, 1998. G~ONASSConstellation Status, The Russian Federation This study revealed that it is quite often possible to get Ministrv of Defence, Coordinational Scientific Information Cen- fixed solutions even under tree canopies, at least if the canopy ter, ~odcow(hQ:lfisEserv.unb.cdin/l. is not so dense (G < 15 m2/ha). In such cases, the accuracy Deckert, C., and P.V. Bolstad, 1996. Forest canopy, terrain, and distance approaches the accuracy of the applied "true" reference itself, effects on global positioning system point accuracy, Photogmm- i.e., less than 0.1 m. It even seems to happen now and then that metric Engineering &Remote Sensing, 62(3):317-321. fixed solutions can be found under quite dense canopies (G = Hosmer, D.W., Jr., and S. Lerneshow, 1989. Applied Logistic Regression, John Wiley & Sons, Inc., New York, 307 p. 31 m2/ha,Table 4). In fact, the logistic regression analysis indi- cated that stand density as expressed by basal area is a very Liu, Cd., and R. Brantigan, 1995. Using differential GPS for forest traverse surveys, Canadian Journal of Forest Research, good indicator of whether it is likely that a fixed solution can 25(11):1795-1805. be found. Nssset, E., 1997. Estimating timber volume of forest stands using Furthermore, it is noteworthy that fixed solutions were airborne laser scanner data, Remote Sensing of Environment, found for only 8 percent of the points when we used the AoS 61(2):246-253. proprietary software package (Anon., 1997~)without any prep- , 1999. Point accuracy of combined pseudorange and carrier aration of the carrier phase observations prior to processing. phase differential GPS under forest canopy, Canadian Journal of The fixed solutions we reached for 50 percent of the points after Forest Research, 29(5):547-553. preceding manual editing indicate that such computer pro- Rossbach, U., and G.W. Hein, 1996. Treatment of integer ambiguities grams could be made more robust to cope with the problems in DGPSIDGLONASS double difference carrier phase solutions, that arise under difficult conditions. However, under difficult Proceedings of the 9th International Technical Meeting of the Sat- conditions there is a risk that a position can erroneously be ellite Division of the Institute of Navigation, ION GPS-96, Kansas accepted as a fixed solution. In our trial it occurred once. City, 17-20 September pp. 909-916. This study has demonstrated that the point accuracy of Story, M., and R. Congalton, 1986. Accuracy assessment: A user's per- positions determined under difficult conditions is highly spective, Photogmmmetric Engineering b Remote Sensing, dependent on the number of available satellites. In forest appli- 52(3):397-399. cations that require the highest possible accuracy, such as for (Received 23 March 1999; accepted 03 June 1999; revised 28 June 1999)
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