Performance Evaluation of GPS Augmentation Using Quasi-Zenith Satellite System

Transcription

1 I. INTRODUCTION Performance Evaluation of GPS Augmentation Using Quasi-Zenith Satellite System FALIN WU, Student Member, IEEE NOBUAKI KUBO AKIO YASUDA, Member, IEEE Tokyo University of Marine Science and Technology The current Global Positioning System (GPS) provides limited availability and capability for a country like Japan where mountainous terrain and urban canyons do not allow a clear skyline to the horizon. At present, the Japanese Quasi-Zenith Satellite System (QZSS) is under investigation through a cooperative effort between the government and the private sector. QZSS is considered a multi-function satellite system, as it is able to provide communication, broadcasting, and positioning services for mobile users in a specified region with a high elevation angle. The additional GPS compatible signals from QZSS can remarkably improve the availability, accuracy, and capability of GPS positioning. This work focuses on the performance of GPS augmentation using the proposed QZSS. The QZSS satellite constellation and signal structure are briefly reviewed. Positioning with pseudo-range and carrier phase are discussed. The performance of GPS augmentation using QZSS in the Asian-Pacific and Australian area is studied using software simulations. The results are presented using the number of visible satellites as a measure of availability, GDOP as a measure of accuracy, and ambiguity success rate as a measure of capability of carrier-phase-based positioning with spatial and temporal variations. The results show that the QZSS will improve not only the availability and accuracy of GPS positioning, but will also enhance the capability of the GPS carrier-phase-based positioning in Japan and neighboring regions. Manuscript received July 2, 2003; revised April 13, 2004; released for publication July 12, IEEE Log No. T-AES/40/4/ Refereeing of this contribution was handled by G. Lachapelle. This work was supported by the Tokyo University of Marine Science and Technology. Authors address: Laboratory of Communication Engineering, Tokyo University of Marine Science and Technology, Etchujima, Koto-ku, Tokyo , Japan, (fwu@e.kaiyodai.ac.ip) /04/$17.00 c 2004 IEEE Currently Japan leads the world in the various applications of GPS equipment and services for civil use. About 5.7 million GPS-equipped cellular phones are in use, and approximately 2 million GPS-equipped car navigation units are sold annually in Japan with a cumulative total of more than 12.2 million units sold from 1993 to 2003 [1, 2]. The spread of the civil applications of GPS in such areas as air navigation, land navigation, maritime navigation, mapping, land surveying, and telecommunications, calls for high reliability and availability of the positioning service, which at present has some limitations due to reduced satellite visibility typical in Japan because of its mountainous terrain and urban canyons. Augmentation using a GEO-stationary satellite system cannot make up for these shortcomings because it has an approximate 45 elevation angle limitation in mid-latitude regions. However, the planned Japanese Quasi-Zenith Satellite System (QZSS) will augment GPS to meet these requirements. QZSS is a constellation consisting of several highly elliptic orbit (HEO) satellites orbiting in different high inclination planes with a GEO-synchronous orbital period. Each satellite is placed in orbit so as to pass over the same ground track at a constant interval. Eccentricity and inclination are chosen so that users are able to receive the signal from at least one of the satellites near the zenith direction (i.e., with a high elevation angle) at any time. This is the origin of the name Quasi-Zenith Satellite System. Satellite systems like QZSS that operate in a high inclination orbit are especially indispensable in high latitude regions. Russia has used the Molniya orbit for satellite communications since In mid-latitude regions, although GEO satellite systems have been used in the past, some systems have, however, just been implemented for broadcastings. Sirius Satellite Radio has started to provide its digital audio broadcasting (DAB) services for mobile users in North America via three HEO satellites. In Europe, Global Radio is also planning to begin a similar DAB service in a couple of years using a similar HEO satellite system [3]. We focus here on the performance of GPS augmentation using the Japanese QZSS. The constellation and signal structure of QZSS is briefly reviewed in Section II. Positioning with pseudo-range and carrier phase is discussed, and the measures for performance evaluation are described in Section III. The performance of GPS augmentation using QZSS is shown in terms of the number of visible satellites, geometric dilution of precision (GDOP), and ambiguity success rate with spatial and temporal variations in Section IV. IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 40, NO. 4 OCTOBER

2 Fig. 1. Ground tracks of three QZSS satellite constellation options. (a) Option 1. (b) Option 2. (c) Option 3. II. JAPANESE QUASI-ZENITH SATELLITE SYSTEM QZSS is being developed by the private sector with the government sector assuming responsibility for the associated technology development, and especially the portion of the project concerned with the positioning service. This effort has taken place in the context of Japan-United States cooperation over GPS, formalized by the GPS joint statement signed on November 22, The 1998 policy statement established a cooperative mechanism that provided for annual plenary meetings and working groups. Japan s stated policy objective is to secure and enhance user interest, and the QZSS initiative is a logical outcome of this policy [1]. A. Satellite Constellation Five types of satellite constellations that are being considered for the QZSS were registered with the International Telecommunications Union in November 2002 [1]. It is yet to be decided which satellite constellation will be adopted for the QZSS because investigations are still under way. Table I summarizes the main characteristics of the three most favored satellite constellation options that are investigated in this study. Each QZSS satellite constellation is composed of three satellites in orbit and one spare satellite on the ground. The lengths of the semi-major axis of three satellite constellations are all 42,164 km. Different eccentricity and inclination are selected for the three QZSS satellite constellation options. The eccentricities of the three satellite constellations are approximately 0.099, 0.360, and 0.000, respectively. The inclinations of the three satellite constellations are approximately 45:0,52:6, and 45:0, respectively [3, 4]. Fig. 1 illustrates the ground tracks of the three satellite constellations [5]. 1) QZSS Option 1: With an eccentricity of and an inclination of 45:0, the ground track of the satellite constellation scribes an asymmetrical figure 8 shape. This satellite constellation offers an advantage for mobile communication users with tracking TABLE I Parameters of the Three QZSS Satellite Constellation Options QZSS Ground Number of Eccentri- Inclina- Semi-major Option Track Satellites city tion Axis 1 Asymmetrical :0 42,164 km 8 shape 2 Egg-shape :6 42,164 km 3 Symmetrical 8 shape :0 42,164 km antenna and feeder link stations in Japan. Another one advantage of this satellite constellation is that various services, such as communication, broadcasting, and positioning, are available equally to users in Japan and neighboring regions [3]. 2) QZSS Option 2: With an eccentricity of and an inclination of 52:6, the ground track of the satellite constellation scribes an egg-shaped figure. The advantage of this satellite constellation is that broadcasting related services will be provided somewhat more effectively for users in Japan and neighboring regions than in the case of the other two satellite constellation options [3]. 3) QZSS Option 3: With an eccentricity of and an inclination of 45:0, the ground track of the satellite constellation scribes a symmetrical 8 shape centered on the equator, and users in both hemispheres can receive services equally. However, this satellite constellation has to maneuver the satellite frequently to avoid collisions as it passes through the highly populated geostationary satellite belt. In addition, this satellite constellation would provide less favorable visibility over the northern hemisphere compared with the other two satellite constellation options [1]. Fig. 2 shows the temporal variations of elevation for the three QZSS satellite constellations in Tokyo. It is shown that a user located in Tokyo can track at least one QZSS satellite with a 70 mask elevation and two QZSS satellites with a 30 mask elevation for each of the three QZSS constellations [5] IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 40, NO. 4 OCTOBER 2004

3 Fig. 2. Elevation temporal variations of three QZSS constellation options in Tokyo. (a) QZSS option 1. (b) QZSS option 2. (c) QZSS option 3. The performance of GPS augmentation using the three QZSS options is analyzed in Section IV. Further information about the QZSS satellite constellations can be found in [1 13]. B. Signal Structure At the GPS-QZSS Technical Working Group meeting in early December 2002, Japanese and United States government representatives discussed the creation of QZSS. The representatives from the two nations deliberated on the technical requirements of the QZSS signal structure, codes, and power. To date, the positioning service of the QZSS is considered to be an advanced space augmentation system for GPS. The QZSS will use the same signal structure as GPS, and use a pseudorandom noise (PRN) code which is used by both GPS and the wide area augmentation system (WAAS). Other types of signal modulation are also under consideration. Currently, the governmental institutions involved continue to work towards a definition of the signal structure. At the time of writing of this paper, the most recent meeting was held in May, 2003 [1, 3]. Table II gives an overview of possible GPS and QZSS signals, with corresponding frequencies, TABLE II Possible Signals of GPS and QZSS, with Corresponding Frequencies, Wavelengths, and Typical Code Measurement Accuracies Frequency Wavelength Typical Code Measurement Signal [MHz] [m] Accuracy ¾ P [m] L L L wavelengths, and typical code measurement accuracies [14 16] that are used in this study. III. GPS AUGMENTATION USING QUZSI-ZENITH SATELLITE SYSTEM The measured ranges from GPS and QZSS satellites to receiver, by pseudo-range and carrier phase, respectively, are related to the unknown parameters via the following generic measurement equations [17] P s L1 fi 2 r,i = ½s r + d r,i ds,i + f2 L1 fi 2 s r,i = ½s r + ± r,i ±s,i f2 I s r + Ts r + ²s r,i (1) Ir s + Ts r + ins r,i + "s r,i (2) WU ET AL.: PERFORMANCE EVALUATION OF GPS AUGMENTATION 1251

4 where P and are the code and carrier phase observations, respectively. ½ is the geometric range from satellite s to receiver r. i is the L-band frequency signals of GPS and QZSS; i = L1, L2, and L5. f is the frequency of the signals. I represents ionospheric delay on L1 frequency, and T is the tropospheric delay. d and ± are the clock error for code and carrier phase measurements, respectively. and N are the wavelength and cycle ambiguity number of signal i carrier phase, respectively. " and ² are the effect of receiver noise on the carrier phase and the pseudo-range, respectively. A. Positioning with Code The linearized code measurement is given by [18] ±x ±P = G + ẽ P (3) ±b where ±P is the vector of predicted minus actual code measurement. The vector ±x has three components, which are the position offset of the user from the linearization point, ±b is the offset of the user time bias. The geometry matrix G is a (m 4) matrix characterizing the satellite-receiver geometry; G only depends upon the line-of-sight effect. m is the number of measurements, and ẽ P is the residual error vector. The dilution of precision (DOP) is a measure for the geometrical strength of the observation model. Different types of DOP values are distinguished. Here only GDOP is considered. The DOP values depend on the cofactor matrix, Q =(G T G) 1. The GDOP is defined as [18] GDOP = tr(q) = Q 11 + Q 22 + Q 33 + Q 44 : (4) The estimate of the rms value of the three position errors and the clock error, rms(x,b), may thus be given as rms(x,b)=¾ UERE GDOP (5) where ¾ UERE is the accuracy of the range measurements. The achievable position accuracy depends both on the accuracy of the range measurements and the satellite-receiver geometry. Themorefavorablethegeometry,thelowertheDOP will be. The lower the DOP is, the higher the quality of the position estimate, in general. In this study the GDOP is applied to evaluate the performance of positioning with code. B. Precise Positioning with Carrier Phase 1) Carrier-Phase-Based Positioning: From (1) and (2), the measurements, with or without parameterization in terms of the baseline components, are collected by type, code, and carrier phase, on all used frequencies. Then the carrier phase based positioning model can be cast in the following linear observation equation [15, 18 20] y = Aa + Bb + e (6) where y is the given data vector of order m; a and b are the unknown parameter vectors, respectively, of order n and p, ande is the noise vector of order m. The matrices A and B are the corresponding design matrices of order m n and m p, respectively. The data vector y will usually consist of the observed minus computed single-, dual-, or triple-frequency double difference carrier phase and/or code observations, accumulated over all observation epochs. The entries of vector a are then the double difference carrier phase ambiguities, expressed in units of cycles rather than range. They are known to be integers, a Z n. The entries of vector b will consist of the remaining unknown parameters, such as double difference ranges in the case of the geometry-free model or baseline components in the case of the stationary receiver geometry-based model and the roving receiver geometry-based model, possibly together with atmospheric delay parameters (troposphere, ionosphere) and/or other parameters of interest. The entries of b are known to be real values, b R p. For a more extensive review of the geometry-free model, stationary receiver geometry-based model and roving receiver geometry-based model, we refer to [5, 16, 21]. The procedure which is usually followed for solving the carrier phase based positioning model can be divided into three steps [22]. In the first step, one simply disregards the integer constraints a Z n on the ambiguities and performs a standard least-squares adjustment min y Aa a,b Bb 2 Qy 1 with a R n, b R p (7) where Q y is the variance-covariance matrix of the double difference observations y. Q y is given in Section IIIB2. As a result one obtains the real-valued estimates of a and b together with their variance-covariance matrix â ˆb, Qâ Qˆbâ Qâˆb Qˆb : (8) This solution is referred to as the float solution. In the second step, the float ambiguity estimate â is used to compute the corresponding integer ambiguity estimate ²a ²a = M(â) (9) with M : R n Z n, a mapping from the n-dimensional space of real numbers to the n-dimensional space of 1252 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 40, NO. 4 OCTOBER 2004

5 integers. The mapping methods (i.e., M) isgivenin Section IIIB3. Once the integer ambiguities ²a are fixed, they are used in the third step to correct the float estimate of ˆb. As a result one obtains the ambiguity resolved unknown parameters solution ²b = ˆb Q Qˆbâ 1 â (â ²a): (10) This solution is usually referred to as the fixed solution. 2) Stochastic Model: Itisassumedthatthe variance-covariance matrix of the observations of one satellite, without elimination of the ionospheric parameters, is given as CP C P = (11) where C P and C are the variance-covariance matrices of the code and phase observations, respectively. Thus, there may be correlations between the code observations and between the phase observations on different frequencies. Since the ionospheric parameters were eliminated from the measurement equations using a pseudo-observable, the variance-covariance matrix of observation becomes ¹ ¹ T C = C P +2s 2 (12) ¹ ¹ where ¹ =(¹ i(1),:::,¹ i(l) ) T ; l is the number of frequencies used for each solution and ¹ i = fl1 2 =f2 i, i = L1, L2, and L5. s 2 is the undifferenced ionospheric weighing factor in units of square meters. When ionospheric delays are absent or assumed known, we have s 2 = 0, which may be the case when the baseline is sufficiently short. This is referred to as the ionosphere-fixed. When it is assumed that the ionospheric behavior is not completely known, it is common to choose s 2 depending on the baseline length, referred to as the ionosphere-weighted model. For long baselines, when the ionospheric behavior is completely unknown, the ionosphere-float model should be used, which means that s 2, see [21] and [23]. No satellite-dependent weighting is applied. The complete variance-covariance matrix of double difference observations is then given as [16] Q y = I k C E (13) where E = D T D,andD T is the (m 1) m double differencing operator. The notation I k denotes an identity matrix of order k; k is the number of epochs used for each solution. is Kronecker product. 3) Integer Ambiguity Estimation: Various methods (i.e., integer ambiguity estimator) for mapping â into ²a have been proposed. Three different admissible integer ambiguity estimators are considered. They are integer rounding estimator, bootstrapped estimator, C and integer least-squares estimator; see [24]. These methods have been discussed at length elsewhere [18, 21, 25]. The simplest integer ambiguity estimator is the integer rounding estimator. This estimator rounds each of the entries of â to its nearest integer. Let â =(â 1,:::,â n ) T R n be the ambiguity float solution. The corresponding integer estimator would then be defined as ²a R =([â 1 ],:::,[â n ]) T (14) where [ ] denotes rounding to the nearest integer. Note that this estimator does not take into account the correlation between the elements of the integer ambiguity vector. A more advanced but still relatively simple integer ambiguity estimator is the bootstrapped estimator. This estimator still makes use of integer rounding, but it also takes some of the correlation between the ambiguities into account. Letting ²a B = (²a B,1,:::,²a B,n ) T Z n denotes the corresponding integer bootstrapped solution. The entries of the bootstrapped ambiguity estimator are then defined as ²a B,1 =[â 1 ] ²a B,2 =[â 2 1 ]=[â 2 ¾â2 â 1 ¾ 2 â 1 (â 1 ²a B,1 )]. n 1 ²a B,n =[â n (n 1) ]= â n ¾ân â i I ¾ 2 â i I (â i I ²a B,i ) i=1 (15) where ¾âi â i I denotes the covariance between â i and â i I,and¾ 2 â i I is the variance of â i I. The shorthand notation â i I stands for the ith least-squares ambiguity obtained through a conditioning on the previous I = 1,:::,(i 1) sequentially rounded ambiguities. Note that the bootstrapped estimator is not unique. Changing the order in which the ambiguities appear in vector â will produce a different bootstrapped estimator. For a more extensive review of the theory of integer bootstrapping we refer to [24] and [26]. The integer least-squares estimator is defined as ²a LS =argmin z Z n(â z)t Q 1 (â z) (16) â where ²a LS Z n denotes the corresponding integer least-squares solution. This type of least-squares problem was first introduced in [22] and has been labeled as the integer least-squares. It is a nonstandard least-squares problem due to the integer constraints z Z n. For an extensive review of the theory of integer least-squares we refer to [26]. 4) Ambiguity Success Rate: For carrier-phasebased positioning, it is important to estimate the integer ambiguities correctly. The ambiguity success rate is the probability that the integer ambiguities are correctly estimated. It can be written in equation form WU ET AL.: PERFORMANCE EVALUATION OF GPS AUGMENTATION 1253

6 TABLE III Configuration of all Scenarios Considered in the Simulations System GPS, GPS+QZSS (three options) Baseline model Single medium length baseline (20 km), roving-receiver geometry-based model Functional model Mask elevation 30 Number of epochs used for each solution 1 Number of frequencies 2 (L1 and L2) Code standard deviation ¾ P =0:300 m Stochastic model Phase standard deviation ¾ =0:003 m Ionospheric model Ionosphere-weighted model, ¾ I =0:020 m Tropospheric delay ¾ T =0:010 m Integer Ambiguity Estimation Bootstrapped Estimator Spatial simulation Date and time May 15, 2003, 12:00 Location Asian-Pacific and Australian area (Latitude: 90 S 90 N, Longitude: ) Temporal simulation Date and time May 15, 2003, 00:00 May 15, 2003, 24:00 Location Tokyo ( N, E) Output Spatial variation Number of visible satellites, GDOP, Temporal variation and ambiguity success rate as [27 29] P(²a = a)= pâ(x)dx (17) S a where pâ(x) is the probability density function of the float ambiguities; S a is the pull-in region, or area around the correct integer for which any float solution gets pulled towards the correct fixed solution. The ambiguity success rate depends on three contributing factors: the functional model (i.e., observation equations), the stochastic model (i.e., distribution and precision of the observations) which governs the distribution pâ, and the chosen method of integer estimation which governs the shape of the pull-in region S a. Changes in any one of these will affect the ambiguity success rate. A more extensive description of the ambiguity success rate is given in [27]. The ambiguity success rate of the bootstrapped estimator could be given explicitly as [15, 20] n 1 P(²a B = a)= 2 1 (18) i=1 2¾âi I where n is the number of ambiguities and x 1 (x)= exp 12 À2 dà: (19) 2¼ The conditional standard deviations ¾âi I can be obtained directly as the square roots of the entries of the diagonal matrix D in the triangular decomposition of the variance-covariance matrix Qâ = LDL T. An exact evaluation of the ambiguity success rates of the integer rounding estimator and the integer least-squares estimator is complicated. In [24], it was proven that the integer least-squares estimator maximizes the ambiguity success rate, where P(²a R = a) P(²a B = a) P(²a LS = a): (20) The ambiguity success rate of the bootstrapped estimator is a safe lower bound since it is always lower than or equal to that of the integer least-squares estimator. Therefore, in practice, the ambiguity success rate corresponding to the bootstrapped estimator is used. The ambiguity success rate can be obtained once the functional model, the stochastic model, and the integer ambiguity estimator are known. Similar to the usage of DOP measures, it can be computed without having the actual measurements available. The ambiguity success rate is used to elevate the capability of carrier-phase-based positioning in this study. The higher the ambiguity success rate is, the better the performance of capability of carrier-phase-based positioning will be. Further information about ambiguity success rate can be found in [15], [16], and [27] [29]. IV. PERFORMANCE EVALUATION In this section the expected performance of GPS augmentation using the proposed Japanese QZSS is studied using software simulations. The performance of GPS augmentation is evaluated spatially as well as temporally by analyzing the spatial and the temporal variations of the number of visible satellites, GDOP, and ambiguity success rate. Two simulations, spatial simulation and temporal simulation, were conducted. Table III 1254 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 40, NO. 4 OCTOBER 2004

7 TABLE IV Spatial Variations of the Number of Visible Satellites, GDOP, and Ambiguity Success Rate for Different Constellations System GPS Only GPS+QZSS 1 GPS+QZSS 2 GPS+QZSS 3 Whole Area Number of Visible Satellites % 95.67% 92.21% 95.40% Number of MIN visible satellites MAX MEAN Positioning MIN available area GDOP MAX (GPS only) MEAN Ambiguity MIN 28.93% 28.93% 28.93% 28.93% success rate MAX 98.78% 99.81% 99.81% 99.82% MEAN 64.53% 84.27% 78.05% 84.02% gives a summary of all scenarios considered in the simulations. A GPS constellation with 29 satellites and the three QZSS satellite constellation options were simulated. Because a user may be more interested in the unknown baseline coordinates than in the receiver-satellite ranges and because the stationary receiver geometry-based model is a typical form of the roving receiver geometry-based model, only a single medium length baseline (20 km) and the roving receiver geometry-based model were used. It has been shown in Section II that a user located in Tokyo can track at least two QZSS satellites with a 30 mask elevation; the visible satellites were masked by a 30 elevation angle cutoff. Only single epoch data was used for each solution. The observations of L5 were not considered in the simulations, and the accuracies of all code and carrier phase observations were set at a standard deviation of m (see Table II) and m [16], respectively. It is known that for a medium length baseline, the ionospheric behavior cannot be assumed known or absent. We used the ionosphere-weighted model. The ionospheric slant delay and tropospheric zenith delay were included as unknown parameters. Variations in the delays of ionosphere and troposphere were tolerated to a reasonably small extent for a medium length baseline (¾ I =0:020 m and ¾ T =0:010 m) [23]. The bootstrapped estimator was used in the calculation of the ambiguity success rate. In the spatial simulation, the receiver-satellite geometries were simulated at 12:00 on May 15, 2003 in the Asian-Pacific and Australian area with asamplinggridof0:4 0:4. In the temporal simulation, the receiver-satellite geometries were simulated in Tokyo, from May 15, 2003, 00:00 to May 15, 2003, 24:00 with a sampling interval of 120 s. The spatial simulation and temporal simulation yielded spatial variations and temporal variations of the number of visible satellites, GDOP, and ambiguity success rate, in the case of GPS only or augmented GPS using the three QZSS options, respectively. A. Spatial Variations Before considering the temporal performance of GPS augmentation using QZSS, the spatial performance is analyzed. Table IV summarizes the spatial variations of the number of visible satellites, GDOP, and ambiguity success rate in the case of GPS only and augmented GPS using the three QZSS constellation options at 12:00 on May 15, It is shown that with the augmentation by the three QZSS constellation options, the area where positioning is available (i.e., the number of visible satellites is larger than three) will be extended from 85.51% to 95.67%, 92.21%, and 95.40%, respectively for each constellation. Because augmentation using QZSS cannot only extend the positioning available area but also enable some locations that have a very high GDOP and a very low ambiguity success rate, only the area where positioning is available in the case of GPS only is considered to evaluate the performance of GPS augmentation using the three QZSS constellation options presented in this subsection. Fig. 3 shows the number of visible satellites as a function of geographic location in the case of GPS only and augmented GPS using the three QZSS constellation options, respectively. The maximum number of visible satellites of GPS only is eight, but augmented GPS using the three QZSS options increases the number to eleven for all cases. The average number of visible satellites of GPS only is about 5.20, but the values of augmented GPS using the three QZSS options are about 6.40, 6.17, and 6.46, respectively. Fig. 4 shows the spatial variations of GDOP for the GPS only and augmented GPS using the three QZSS options. The minimum GDOP of GPS only is about 2.98, but augmented GPS using the three QZSS options give values of 2.48, 2.63, and 2.46, respectively. The average GDOP of GPS only is about 14.15, but the average GDOPs of augmented GPS using the three QZSS options are 7.10, 10.01, and 6.90, respectively for each constellation. WU ET AL.: PERFORMANCE EVALUATION OF GPS AUGMENTATION 1255

8 Fig. 3. Spatial variations of number of visible satellites for different constellations. (a) GPS only. (b) GPS and QZSS option 1. (c) GPS and QZSS option 2. (d) GPS and QZSS option 3. Fig. 4. Spatial variations of GDOP for different constellations. (a) GPS only. (b) GPS and QZSS option 1. (c) GPS and QZSS option 2. (d) GPS and QZSS option 3. Fig. 5 shows the spatial variations of the ambiguity success rate for the GPS only and augmented GPS using the three QZSS options. The maximum ambiguity success rate of GPS only is 98.78%, but augmented GPS using the three QZSS options give values of 99.81%, 99.81%, and 99.82%, respectively. The average ambiguity success rate of GPS only is about 64.53%, but augmented GPS using the three QZSS options give values of 84.27%, 78.05%, and 84.02%, respectively IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 40, NO. 4 OCTOBER 2004

9 Fig. 5. Spatial variations of ambiguity success rate for different constellations. (a) GPS only. (b) GPS and QZSS option 1. (c) GPS and QZSS option 2. (d) GPS and QZSS option 3. TABLE V Temporal Variations of the Number of Visible Satellites, GDOP and Ambiguity Success Rate for Different Constellations in Tokyo System GPS Only GPS+QZSS 1 GPS+QZSS 2 GPS+QZSS 3 Whole Time Number of Visible Satellites % % % % Number of MIN visible satellites MAX MEAN Positioning MIN available time GDOP MAX (GPS only) MEAN Ambiguity MIN 28.93% 72.40% 40.79% 49.23% success rate MAX 98.27% 99.47% 99.43% 99.55% MEAN 60.25% 93.03% 91.75% 92.05% It has been shown that any of the three QZSS options will not only improve the satellite visibility, extend the positioning available area, and offer better GDOP, but also improve the capability of carrier phase positioning in Japan and neighboring regions. Among the three QZSS options, the third QZSS option can provide a little more favorable availability and accuracy than the other two QZSS options. But the first QZSS option can provide a little more favorable availability, accuracy, and capability of carrier-phase-based positioning than the second QZSS option. B. Temporal Variations Table V summarizes the temporal variations of the number of visible satellites, GDOP, and ambiguity success rate in the case of GPS only and augmented GPS for the three QZSS options in Tokyo from May 15, 2003, 00:00 to May 15, 2003, 24:00. It is shown that with the augmentation by any of the three QZSS options, the time when positioning is available will be improved from 91.40% to %. For temporal variations, augmentation using the three QZSS options can improve the positioning available time and enable some periods of time that have a very high GDOP and a very low ambiguity success rate. To evaluate the performance of GPS augmentation using QZSS, the time when positioning is available in the case of GPS only is considered in this subsection. Fig. 6 shows the temporal variations of the number of visible satellites of GPS only and augmented GPS using the three QZSS options from May 15, 2003, 00:00 to May 15, 2003, 24:00. The maximum WU ET AL.: PERFORMANCE EVALUATION OF GPS AUGMENTATION 1257

10 Fig. 6. Temporal variations of number of visible satellites for different constellations. (a) GPS only. (b) GPS and QZSS option 1. (c) GPS and QZSS option 2. (d) GPS and QZSS option 3. Fig. 7. Temporal variations of GDOP for different constellations. (a) GPS only. (b) GPS and QZSS option 1. (c) GPS and QZSS option 2. (d) GPS and QZSS option IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 40, NO. 4 OCTOBER 2004

11 Fig. 8. Temporal variations of ambiguity success rate for different constellations. (a) GPS only. (b) GPS and QZSS option 1. (c) GPS and QZSS option 2. (d) GPS and QZSS option 3. number of visible satellites of GPS only is eight, but augmented GPS using the three QZSS options gives values of ten for all cases. The average number of visible satellites of GPS only is about 4.93, but the values of augmented GPS using the three QZSS options are about 6.94, 7.07, and 6.81, respectively. Fig. 7 shows the GDOPs of GPS only and augmented GPS using the three QZSS options as a function of time, respectively. The minimum GDOP of GPS only is about 2.88, but the augmented GPS using the three QZSS options gives values of 2.37, 2.43, and 2.44, respectively. The average GDOPs of GPS only and augmented GPS using the three QZSS options are about 11.78, 4.78, 5.44, and 4.85, respectively. Fig. 8 shows the temporal variations of the ambiguity success rate of GPS only and augmented GPS using the three QZSS options. The maximum ambiguity success rate of GPS only is about 98.27%, but the values of augmented GPS using the three QZSS options are 99.47%, 99.43%, and 99.55%, respectively. The average ambiguity success rate of GPS only is 60.25%, but the values of augmented GPS using the three QZSS options are about 93.03%, 91.75%, and 92.05%, respectively. The results show that any of the three QZSS options will not only improve the satellite visibility, extend the positioning available time, and offer better GDOP, but also improve the capability of carrier phase positioning in Japan. Among the three QZSS options, the second QZSS option can provide a little more favorable availability than the other two QZSS options. But the first QZSS option can provide a little more favorable accuracy and capability of carrier-phase-based positioning than the other two QZSS options. V. CONCLUSION This paper focuses on the performance of the GPS augmentation using the proposed Japanese QZSS. The QZSS satellite constellation and signal structure have been briefly reviewed. Positioning with pseudo-range and carrier phase have been discussed, and the measures for performance evaluation have been described. The achievable performance of the GPS augmentation using QZSS has been obtained using software simulations and described by the spatial and temporal variations of the number of visible satellites, GDOP and ambiguity success rate. Three QZSS satellite constellation options have been investigated. It has been shown that QZSS will not only improve the satellite visibility, extend the positioning available area and time, and offer better GDOP, but also enhance the capability of carrier-phase-based positioning in Japan and neighboring regions. Among the three QZSS satellite constellation options, the first QZSS option is the best option for Japan, although the third QZSS option is the best option for the whole Asian-Pacific and Australian area. WU ET AL.: PERFORMANCE EVALUATION OF GPS AUGMENTATION 1259

12 ACKNOWLEDGMENT The authors would like to acknowledge Dr. Tomoyuki Miyano, Tokyo Metropolitan College of Aeronautical Engineering and Mr. Masayuki Saito, Advanced Space Business Corporation, Japan, for generously providing information about QZSS satellite constellation. The authors would also like to acknowledge Mr. Peter Joosten and Ms. Sandra Verhagen at the faculty of Aerospace Engineering of the Delft University of Technology, the Netherlands, for software support. REFERENCES [1] Petrovski, I. G., Ishii, M., Torimoto, H., Kishimoto, H., Furukawa, T., Saito, M., Tanaka, T., and Maeda, H. (2003) QZSS Japan s new integrated communication and positioning service for mobile users. GPS World, 14, 6 (June 2003), [2] Kogure, S., Kawano, I., and Kajii, M. (2003) The status and experiment plan for GPS augmentation using quasi-zenith satellite system (QZSS). In Presentations at 4th CGSIC IISC Asia Pacific Rim Meeting, Tokyo, Japan, Nov. 16, [3] Kogure, S., and Kawano, I. 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13 [25] Strang, G., and Borre, K. (1997) Linear Algebra, Geodesy, and GPS. Wellesley-Cambridge Press, [26] Teunissen, P. J. G. (2001) Statistical GNSS carrier phase ambiguity resolution: Areview. In Proceedings of 2001 IEEE Workshop on Statistical Signal Processing, Signapore, Aug. 6 8, 2001, [27] Joosten, P., and Tiberius, C. (2000) Fixing the ambiguities are you sure they re right? GPS World, 11, 5 (May 2000), [28] Teunissen, P. J. G. (2000) The success rate and precision of GPS ambiguities. Journal of Geodesy, 74, 3/4 (2000), [29] Verhagen, S. (2002) Studying the performance of global navigation satellite systems A new software tool. GPS World, 13, 6 (June 2002), Falin Wu (S 04) is a Ph.D. candidate at the Laboratory of Communication Engineering of the Tokyo University of Marine Science and Technology (TUMST), Japan. He received his B.Sc. and M.Sc. degrees from Dalian Maritime University, P.R. China, in 1995 and 1998, respectively. He worked at China Transport Telecommunication Center, P.R. China, from 1998 to His current research interests are software and algorithm development for the carrier-phase-based positioning and software receiver. Mr. Wu is a member of the Institute of Navigation (ION), the Institute of Electronics, Information and Communication Engineers (IEICE) and the Japan Institute of Navigation. Nobuaki Kubo graduated from Hokkaido University, Japan, in 1996 with a Bachelor of Engineering (electrical) and with a Master of Engineering (electrical) in He joined the NEC Company in 1998 and was engaged in LAAS System research for three years. He is currently a research associate at the Laboratory of Communication Engineering of the Tokyo University of Marine Science and Technology. He is interested in multipath estimating in GPS. Akio Yasuda (M 88) received his Dr. Eng. degree from Nagoya University, Japan. He is a professor at the Laboratory of Communication Engineering of the Tokyo University of Marine Science and Technology. His major subjects are satellite communication and positioning systems, including GPS application and development of instruments for marine application. Dr. Yasudo is the president of the GPS Society, Japan Institute of Navigation (JIN GPS). WU ET AL.: PERFORMANCE EVALUATION OF GPS AUGMENTATION 1261