表一、GPS Required Navigation Performance (RNP)
15
Aviation Navigation Requirements
LPV 350 ft DH 50 m VAL, 40 m HAL
Approach with Vertical Guidance
(APV)
CAT I
CAT II
CAT III 200ft DH
12m VAL 100ft DH 5.3m VAL
0~100ft DH 5.3m VAL
DH: decision height VAL:vertical alert limit HAL: horizontal alert limit
Requirement: More Accuracy, Tighter Bounds
圖一、各種降落標準
圖二、GPS、DGPD 與 GBAS 定位結果比較
Master Station Reference
Station
Data Arrange Measurement
s Almanac
Ephemeris
Integrity Monitoring
Algorithm Results of
Evaluation
圖三、陸基增強系統原型機資料流程
圖四、品質監控組成圖
PRN# 1 2 3 4 5 6 7 8 9
RECV1 T T T T T T N N T
RECV2 T T T T T N T T N
RECV3 T T T T F N F F F
17
圖五、Common Set 示意圖
圖六、一致性驗證流程圖
圖七、陸基增強系統原型機實驗設定與儀器配置圖
圖八、訊號強度測試結果
圖九、相異測試結果
19
圖十、資料品質監控結果。(A)為長效型與短效型星曆比較結果。(B)為新舊星曆 比較結果
圖十一、鎖定時間確認結果
圖十二、載波測試結果(acceleration)
圖十三、載波測試結果(ramp)
21
圖十四、載波測試結果(step)
圖十五、電碼測試結果
圖十六、1 號參考站的 11 號衛星的 B 值與其門檻值
圖十七、sigma monitor 結果
23
圖十八、修正量範圍測試結果
圖十九、通過所有測試後之Common Set 裡的衛星數量
出席 2009 International Symposium on GPS/GNSS 國際學術研 討會議心得報告
計畫編號 NSC 98-2221-E-006-122
計畫名稱 建置民用航空全球衛星定位系統陸基增強系統測試平台之研究發展與評估 成果報告
出國人員姓名
服務機關及職稱 詹劭勳 國立成功大學航太系助理教授 會議時間地點 November 04-06, 2009, Cheju, Korea.
會議名稱 2009 International Symposium on GPS/GNSS (2009 國際衛星導航系統學術研 討會)
發表論文題目
1. Implementation of the Wide Area Differential GPS Master Station Algorithms in Taipei Flight Information Region
2. Development and Implementation of RAIM to Support the New ATM System
一、 參加會議經過
赴韓國濟州島參加 2009 國際衛星導航系統學術研討會發表學術論文，論文題目為:
1. Implementation of the Wide Area Differential GPS Master Station Algorithms in Taipei Flight Information Region
2. Development and Implementation of RAIM to Support the New ATM System
本學術會議以全球衛星導航系統等前瞻性發展研究分析為主軸之大型國際學術研討會議，
本次會議之重點著重於國際上各國相關系統之發展現況及其未來展望與其訊號規劃與分析，而 本次大會中有大量針對衛星定位系統訊號使用完整性(integrity)之研究，隨著 GPS 全球衛星定 位與導航應用的日漸普及，因為 GPS 並沒有針對大眾運輸安全有相對的要求，因此，使用 GPS 於大眾運輸系統將沒有安全之保障，這次大會中開始針對航海及陸地交通運輸的 GPS 使用定 義其導航性能要求(Required Navigation Performance, RNP)，並因應此導航性能要求(RNP)設計 GPS 之即時監測(real time monitoring)機制與相對完整性訊號設計，使 GPS 未來可以安全的使 用於航海及陸地交通運輸。本會議參與人士包括世界各知名大學，國際民航組織，與獨立實驗 室。
二、 與會心得
第一篇發表的論文”Implementation of the Wide Area Differential GPS Master Station Algorithms in Taipei Flight Information Region”是以民用航空使用者未來導航為目的所設計與 建置的寬域衛星導航系統之擴增系統，其目的是開發一級時監測機制及訊息發布系統保障GPS 使用者安全的效能測試平台，包括其精確性(accuracy)，完整性(integrity)，連續性(continuity)，
和可用性(availability)的效能評估與分析。
第二篇發表的論文”Development and Implementation of RAIM to Support the New ATM System”則是以開發民航交通管理系統使用GPS作為其輔助導航系統(supplemental navigation system)以及主要導航系統(primary navigation system)之完整性預測及即時監測系統，其提供未 來GPS完整性72小時之預測結果作為未來飛航計劃的基礎，而即時監測機制則提供於機場特定 地點的GPS完整性現況提供管制員做相關管理與規畫之依據。
本學術研討會為亞太最重要之衛星導航相關學術研討會，有超過200位註冊參與會議者，
超過100篇學術論文發表，成功大學在此領域有相當傑出的表現，因此本大會組織決定明年將 在台灣由成功大學主辦2010 International Symposium on GPS/GNSS。
三、 發表之論文共二篇
1. Implementation of the Wide Area Differential GPS Master Station Algorithms in Taipei Flight Information Region
2. Development and Implementation of RAIM to Support the New ATM System
Implementation of the Wide Area Differential GPS Master Station Algorithms in Taipei Flight Information Region
Shih-Chieh Lu and Shau-Shiun Jan*
Institute of Civil Aviation, National Cheng Kung University, Tainan 70101, Taiwan (Tel: +886-6-2349294, E-mail: [email protected])
Abstract: This paper implements the Wide Area Differential GPS (WADGPS) master station algorithms to facilitate the operation of a satellite based aviation navigation system in Taipei Flight Information Region (FIR). The WADGPS master station algorithms used in this paper are based on that of the National Satellite Test Bed (NSTB) operated by Federal Aviation Administration (FAA).
The master station processes include the GPS L1-L2 dual frequency observation data collector, the ionospheric delay estimation module, and the satellite ephemeris and clock error estimation modules.
At first, the data collector checks for the reasonableness of Signal-to-Noise Ratio (SNR) for each satellite in view, and it also implements the dual frequency carrier smooth to reduce the code noise and multipath effects. The ionospheric delay model used in this work is a thin shell model at the altitude of 350 km above the earth surface, and the planar fit method is implemented to generate the ionospheric grid model based on the L1-L2 dual frequency observation data. Furthermore, the pseudorange residuals from the reference stations to satellites are synchronized to a common clock by the Common View Time Transfer (CVTT). These synchronized residuals are used to estimate the satellites ephemeris and clock errors by the minimum-variance method. This master station provides the differential positioning services to users, and the confidence bounds of these correction messages which will be computed by the protection level calculation.
To validate the implemented WADGPS master station algorithms, this paper uses the archive data from NSTB reference stations to generate the WADGPS corrections and then compare them with the archive WAAS correction messages provided by the FAA WAAS website. After the validation processes, this paper uses the local reference stations which are e-GPS observation stations operated by the Ministry of Interior (MOI) in Taiwan to evaluate the performance of WADGPS in Taipei Flight Information Region.
Keywords: WADGPS, NSTB, the integrity messages
1. Introduction
The Global Positioning System (GPS) provides positioning, navigation and timing services for several applications.
However, GPS without the monitoring system cannot provide the service for civil aviation users. Therefore, an augmentation system is essential for GPS to supply a comprehensive service to civil aviation users. As a result, the goal of this paper is to develop a Wide Area Differential GPS (WADGPS) to enhance the GPS performance for civil aviation users in Taipei Flight Information Region (FIR).
The WADGPS is guaranteed to provide service which satisfies the safety requirements of certain phases of flight to civil aviation users [1]. The WADGPS developed in this work consists of a Master Station (MS) and several Reference Stations (RS) [2]. The GPS dual frequency measurements collected by each local RS are transmitted to the master station. The master station generates vector corrections for satellite ephemeris and clock errors, and ionospheric delays, as shown in Figure 1 [3].
Finally, the WADGPS messages can be transmitted to users via radio, Internet, or GEO. Similar to this work, the Federal Aviation Administration (FAA) implemented the National Satellite Test Bed (NSTB) as a prototype system to evaluate the
Wide Area Augmentation System (WAAS) algorithms [4]. The WADGPS master station algorithms developed in this paper are based on the NSTB algorithms. As for the WADGPS reference stations, the e-GPS observation stations built by Ministry of Interior (MOI) in Taiwan are used to be the reference stations to collect the dual frequency GPS data.
Figure 1. The Wide Area Differential GPS
This paper focuses on the implementation of the WADGPS master station algorithms. Accordingly, this paper is organized as follows: Section 2 describes the details of the WADGPS
architecture and GPS measurements. Based on the error sources, the main function of the WADGPS is divided into two parts; therefore, Section 3 shows the main processes of the WADGPS. In Section 4, several experiments are conducted to evaluate the navigation performance of the WADGPS in Taipei FIR. Finally, Section 5 presents the summary and concluding remarks.
2. Wide Area Differential GPS (WADGPS) Architecture
The WADGPS is a network composed of several Reference Stations (RS) and a Master Station (MS). The RSs are distributed at the precise known locations to receive GPS L1-L2 dual-frequency signals and archive the raw observations from the monitored GPS satellites. The GPS L1-L2 dual frequency measurements collected at each RS are sent to the MS. The WADGPS MS focuses on the correction processes for the ionospheric delay, and the satellites ephemeris and clock errors [5]. Figure 2 shows the flow chart of the data process in the MS:
1. The data collector receives GPS raw measurements from each RS and updates the previous measurements in real time.
Moreover, the statuses of GPS signals for all monitored satellites are checked including their rationalities of the code and carrier phase measurement at L1 and L2 frequencies, Signal-to-Noise Ratios (SNR), and Doppler frequency.
2. The raw GPS observations are processed to reduce local errors by the carrier smoothing.
3. The MS estimates the satellite clock and ephemeris errors and models the ionospheric delays.
4. All corrections with corresponding integrity messages are packed into SBAS message format and then transmitted to users via Internet according to the appropriate scheduling time.
Figure 2. The WADGPS Architecture
3. The WADGPS Master Station Algorithms
3.1 GPS observations
The RSs receive code and carrier measurements at L1 and L2 frequencies. They are expressed as follows [6]:
1 , 1 integer ambiguities of the carrier phase observations, λ is the wavelength and the subscripts L1 and L2 indicates L1 and L2 frequencies, respectively; I is the ionospheric delay on L1; T is the tropospheric delay; b is the receiver clock bias, and B is the satellite clock error; ν is the pseudorange measurements noise and e is the carrier phase measurements noise; ρ is the true range, the superscript j is the jth satellite, and the subscript i is the ith receiver [6]. Equation (6) shows the geometric range between the surveyed locations, Ri, and satellites location, Rj.
j j
i R Ri
ρ = − (6)
3.1 The dual-frequency carrier smoothing
To reduce the measurements noise and multipath effect, the smoothing filter is used after data collecting from each RS.
Because the measurement noise of the carrier phase are much smaller than that of the pseudorange measurements, the pseudorange and carrier phase are combined to reduce the measurement noise [7].
The ionospheric delay measurements could be derived by the liner combination of GPS L1 and L2 pseudorange and carrier phase measurements:
Where the IL1 is ionospheric delay at the L1 frequency; the subscripts present the observations used in the combination; the Amb is the combination of ambiguities from the L1 and L2 carrier phases, and the noise vPR>vL1> [1]. vφ
As shown in Figure 3, the filter estimated the smoothed ionospheric delay, ˆIsmth , and ionospheric-free pseudorange,
1
More detailed description of the Stanford dual frequency carrier smoothing algorithm can be found in [7].
Figure 3. Dual frequency smoothing of ionospheric delay and pseudorange
3.2 Ionospheric delay model
The major functions of the WADGPS master station are the ionospheric delay model and the satellites ephemeris and clock error estimation algorithms. In Figure 4, the MS process converts all ionospheric slant measurements to the vertical delays at Ionosphere Pierce point (IPP) locations by the Obliquity Factor (OF). The location of IPP is defined as the intersection of the line segment from the RS network to the satellite and an ellipsoid with constant high above 350 km from earth’s surface [8]. The next step is to create a vertical delay model from the IPP measurements to estimate the ionospheric vertical delay at the Ionosphere Grid Points (IGP), IG. The Grid Ionospheric Vertical Error (GIVE) is provided for each IGP which is a confidence bound of the corrected ionospheric delay residual error at the IGP. The following Equations (10) and (11) estimate the IG and GIVE by the weighted least-squared algorithm. onospheric delay at the grid point using Klobuchar model p arameters; Imeasure i, is vertical ionospheric delay at the pie rce point using the Klobuchar model parameters [1];
, Klobuchar i
I is the measured vertical ionospheric delay at th e IPP; the weight is conducted by inverse of vertical delay measurements variance according to distance between the g rid point and the IPP as shows in Equation (12).
Figure 4. The WADGPS ionospheric vertical delay grid model flow chart
The bottom plot of Figure 4 describes that the user uses the nearest IGPs around the IPP to estimate the vertical ionospheric delay at a specific IPP by the interpolation algorithm. The interpolation algorithm is expressed as
( )
Where IEstipp V, is the vertical ionospheric delay at the pierce point, estimated with the broadcasted ionospheric corrections; IGrid V i, , is the broadcast vertical ionospheric delay at ith grid point and
(
,)
i pp pp
W x y is the weighting factor of the pierce point whose location is
(
xpp,ypp)
[9].3.3 Satellite ephemeris and clock errors estimation algorithm After reducing the local noise and eliminating the ionospheric effect, the pseudorange residual approximately consists of receiver clock bias, ephemeris and clock errors and noise. This section shows the procedures for ephemeris and clock errors estimations. Figure 5 details the flow chart about the calculations of the satellites ephemeris and clock errors including the Common View Time Transfer (CVTT), ephemeris error estimation, satellite clock error estimation and the User Differential Range Error (UDRE) estimation [2].
Figure 5. Ephemeris and clock errors estimation flow chart In Figure 5, the CVTT filter synchronizes the measurements in a common reference time and decouples the measurements sequentially for each satellite to eliminate receiver clock bias.
To find the difference between the clock bias of the two RSs, CVTT filter obtains the synchronized pseudorange residuals from the first differences between the pseudorange residuals of two stations as shown in Equation (14).
, ( ) , ,
j j j j j j j
i I ρ i ρ I R l i l I bi I ν i I
Δ = Δ − Δ = Δ ⋅ − + Δ + (14)
Where lji is the unit vector of line of sight from ith reference station to the jth satellite; the subscript i, I means the difference between ith reference station and Ith reference station;
(lji−ljI) is the difference of line of sight; νji I, is the pseudorange residual noise; ΔRj is the ephemeris error.
Then, the clock bias difference ( ˆ, bi I
Δ ) is described in Equation (15).
Next, the pseudorange residuals from all RSs are synchronized based on a common clock and consist by satellite ephemeris and clock error. The ephemeris error and the clock error have to be
sent frequently, and it occupies lots of bandwidth. To reduce the bandwidth, separating the satellite clock error term is necessary. The single difference is used to remove the satellite clock error term in Equation (16).
Where ΔRj is ephemeris error which is this process solving for; the subscript “m” denotes the RS which has the smallest variance. Then, the Equation (16) is re-written as matrix forms as follows:
N is number of synchronized RSs. The matrix z and H are composed by (N-1) measurements.
By the Equation (18), satellite position errors and clock offsets with the minimum variance estimator are estimated [2].
ˆMV T( T ) 1
After estimating the ephemeris error by the minimum variance method, the clock error measurements for all satellites are derived from the synchronized pseudorange residuals. Equation (19) shows the clock error measurements.
, ˆ
j j j j j j
c i i i i
z = ΔR ⋅l − Δ = Δρ B +n (19)
Then, the Equation (19) is re-written as matrix forms as follow:
c c j c
z =H ΔB +n (20)
Where the subscript c denotes clock; Hc is a column vector with all l’s and nc is the measurement noise with covariance matrix Wc. In Equation (21), a weighted least-square method is used to derive the satellite clock error.
1 1 1
ˆWLSj ( Tc c c) Tc c c
B H W− H − H W− z
Δ = (21)
Finally, to bound and indicate the uncertainty of the ephemeris and satellite clock corrected pseudorange, UDRE is calculated for each visible satellite as in Equation (22) [10].
ˆ T
PUDRE= +R HPH (22)
Where R is measurement covariance; ˆP is covariance of the estimated ephemeris and clock error; H is observation matrix, from the RS to the satellite. The UDRE value is calculated in Equation (24). When the users receive the satellite ephemeris and clock corrections, the corrections need to be converted to the pseudorange domain. Equation (25) shows the pseudorange which is corrected by satellite ephemeris and clock errors [10].
j j j j j
corrected PR R l b
ρ = − Δ i + (25)
Where PRj is pseudorange from the jth visible satellite; Δ Rj and bj are satellite ephemeris and clock corrections, respectively; lj is line of sight vector from the user to the satellite.
4. Experiments and Performance Evaluation
To implement the WADGPS in Taipei FIR, the stable RSs to collect GPS observations are essential. This paper uses the e-GPS observation stations in Taiwan as the WADe-GPS RSs. The observations provided by the RSs consist of four major data:
To implement the WADGPS in Taipei FIR, the stable RSs to collect GPS observations are essential. This paper uses the e-GPS observation stations in Taiwan as the WADe-GPS RSs. The observations provided by the RSs consist of four major data: