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This paper describes the implementation of the Wide Area Differential Global Positioning System (WADGPS) system in order to evaluate the operational performance of a satellite based aviation navigation system within Taipei Flight Information Region (FIR). The main objective of the WADGPS is to provide real time integrity information regarding the use of GPS for civil aviation applications. This paper uses the e-GPS observation stations operated by the Taiwan Ministry of Interior (MOI) as the WADGPS reference stations to collect the L1-L2 dual-frequency GPS measurements. A WADGPS master station is also implemented to process all GPS measurements sent from each reference station, and then generate the vector corrections. These vector corrections consist of the satellite ephemeris and clock errors, and a grid of ionospheric delays. The data stream also includes confidence bounds for the corrections and “Use/Do Not Use” messages to provide integrity. These messages are then passed to the WADGPS user through the Internet. This paper discusses the WADGPS system architecture and the system performance analysis. A five-day operation performance in Taipei Flight Information Region (FIR) is presented in this paper. The results show that the WADGPS can improve the accuracy performance of GPS positioning and fulfill the integrity performance required by Non-Precision Approach (NPA) defined by the International Civil Aviation Organization (ICAO).

The Global Positioning System (GPS) provides positioning, navigation and timing services to around 400 million users in sea, air, terrestrial, and space applications [

Similar to this work, in the early 1990s, the Federal Aviation Administration (FAA) implemented the National Satellite Test Bed (NSTB) as a WAAS prototype system to ensure the success of the WAAS. In 2006, the authors co-developed one of the RSs of the Asia-Pacific Economic Cooperation (APEC) Global Navigation Satellite System (GNSS) test bed which is a WADGPS-like system to conduct the preliminary analysis of the SBAS performance within Asia-Pacific [

Accordingly, this paper is organized as follows: In Section 2, we define the metrics that are normally used to quantify the performance of GPS-based aircraft approach systems. In Section 3, we describe the details of the WADGPS architecture. Section 4 shows the main processes of the WADGPS master station. In Section 5, we first validate the implementation of the WADGPS using the U.S. NSTB data, and we then conduct several experiments to evaluate the LNAV performance of the WADGPS within Taipei FIR. Finally, Section 6 presents the summary and concluding remarks.

The Protection Level (PL) calculation [

The weighting matrix, ^{th}

The position error is proportional to the measurement errors and the satellite geometry through the matrix (^{T}^{−l}. This matrix is composed of the variance from each direction as indicated in

The Horizontal Protection Level (HPL) is:
_{H}^{−7}), the tolerable probability of Hazardously Misleading Information (HMI). The protection level calculation is specified in the WAAS MOPS Appendices A and J [

On the other hand, this paper uses a triangular chart as our WADGPS system performance indicator, called the Stanford Chart [^{−7} and should be avoided. As a result, this Stanford Chart can intuitively present system performance in terms of accuracy, availability and integrity. The availability of the system can be determined by examining the percentage of points that lie within the service available region [

The WADGPS is a network composed of several Reference Stations (RSs) and a Master Station (MS). The RSs are distributed geographically at the precisely known locations that 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 MS 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 the rationalities of the code and carrier phase measurement at L1 and L2 frequencies, Signal-to-Noise Ratios (SNR), and Doppler frequency. The raw GPS observations are subsequently processed to reduce local errors by the carrier smoothing method [

The WADGPS master station (MS) receives and processes the measurements from all WADGPS reference stations (RSs). The data collected from each RS is calibrated and used to generate the differential corrections to ionosphere and satellite errors. There are two main correction generation modules: one is for the ionosphere and the other is for satellite errors. WADGPS provides the user with the differential corrections and two system accuracy metrics, namely, the user differential range error (UDRE) and the grid ionospheric vertical error (GIVE) [

Each RS uses a dual-frequency receiver to receive code and carrier phase observations at the L1 and L2 frequencies. These raw observations are sent to the WADGPS master station to process the corrections for common errors and the corresponding confidences [

The differences in these observation equations are the ionospheric delays. The pseudorange (code phase) measurement is delayed and the carrier phase is advanced, and this is the reason of the sign difference of

To mitigate the measurements noise and multipath effects, a dual-frequency carrier smoothing filter is used after raw GPS observations collecting from each RS [

_{L1} is ionospheric delay at the L1 frequency, the extra subscripts present the observations used in the combination,

_{PR} > v_{L1} > v_{ϕ}[

The dual-frequency carrier smoothing filter is depicted in _{smth}, and smoothed ionosphere-free pseudorange, _{L1}. The first step in the filter is to generate _{smth} and its confidence by smoothing the _{L1,PR} with the low noise _{L1,ϕ}. Then combining the _{smth} and _{L1}_{L1} by moving average. If the cycle slip is not present, the N_{L1}λ_{L1} is constant. Finally, substituting _{smth} and N_{L1}_{L1} into the L1 carrier phase, _{L1} (_{L1}, is obtained [

The major functions of the WADGPS master station (MS) are the ionospheric corrections model and the satellites ephemeris and clock errors estimation algorithms. After the dual-frequency carrier smoothing filter outputs the smoothed ionospheric delay, the MS then converts all ionospheric slant delays to the vertical delays at the Ionosphere Pierce Points (IPPs) by the Obliquity Factor (_{G}. The Grid Ionospheric Vertical Error (

_{i} is the weight of the ^{th} IPP measurement,

_{Klobuchar,G} is the vertical ionospheric delay at the grid point using the Klobuchar model parameters [

_{Measure,i} is the vertical ionospheric delay measurement at the pierce point, and

_{Klobuchar,i} is the vertical ionospheric delay at the pierce point using the Klobuchar model parameters.

The weight is calculated by the inverse of the vertical delay measurements variance according to the correlation distance between the grid point and the IPP as shows in

_{i} is ^{th} vertical ionospheric delay measurements variance [

Δ is a function of the correlation distance of the ionosphere [

Specifically, this model scales the measurements using the Klobuchar model to transport the measurement from the IPP location to the location of the desired grid point through the relationship of latitude and longitude dependence provided by the Klobuchar model [

The bottom plot of

^{th} IPP, estimated with the broadcasted ionospheric corrections,

_{i}(_{IPP,i},_{IPP,i}) is the weighting factor of the ^{th} IPP whose location is (_{IPP,i},_{IPP},_{i}) [

_{IGP,V,i} is the broadcast vertical ionospheric delay at ^{th} IGP,

_{IPP,i} is the user ionospheric vertical error (UIVE) which is a 99.9% confidence (error bound) on the post-correction ionospheric vertical delay residual [

_{i} is a confidence bound of the corrected ionospheric delay residual at the ^{th} IGP.

The MS generates the grid model and its confidence with feedback information to ensure that GIVE covers 99.9% of the corrected ionospheric residuals statistically. Therefore, the MS uses the grid model to estimate the vertical ionospheric delays of the RSs and their confidences (UIVE). Then, the master station can determine if the UIVE bounds the difference of ionospheric delays from the grid model (based on above user algorithms,

This section describes the MS procedures for satellite ephemeris and clock errors estimations.

The CVTT filter synchronizes the measurements with a common reference time and decouples the measurements sequentially for each satellite to eliminate the receiver clock bias. To find the difference of the clock biases between two RSs, CVTT filter obtains the synchronized pseudorange residuals from the first difference between the pseudorange residuals of two stations as shown in

Δ^{j} is the ephemeris error,

Δ_{i},_{I} is the clock difference, and

Then, the clock bias difference, Δ_{i,I}, is described in

Through the CVTT module, the pseudorange residuals from all RSs are synchronized based on a common clock, and the pseudorange residuals consist of satellite ephemeris and clock errors. The corrections to the ephemeris error and the clock error have to be sent frequently, and they occupy lots of bandwidth. To reduce the bandwidth, separating the satellite clock error term is necessary. Therefore, the single difference is used to remove the satellite clock error term as shown in the following equation:

Δ^{j} is ephemeris error which is this process solving for, and

the subscript “

Then, the

Δ^{j} is the ephemeris error which will be denoted as

As indicated in

After estimating the ephemeris error by the minimum variance method, the clock error measurements for all satellites can be derived from the synchronized pseudorange residuals. ^{th} satellite from the ^{th} RS [

Then, the

the subscript

_{c} is a column vector with all 1’s,

_{c} is the measurement noise with covariance matrix _{c}.

In

Finally, to bound and indicate the uncertainty of the satellite ephemeris and clock corrected pseudorange, UDRE is calculated for each visible satellite as in

The UDRE value is calculated in _{UDRE,ii} is the ^{th} diagonal element of the _{UDRE}.

When the WADGPS users receive the satellite ephemeris and clock corrections, the corrections need to be converted to the pseudorange domain.

^{i} is pseudorange from the ^{th} visible satellite,

Δ^{i} is satellite ephemeris corrections,

^{i} is line of sight vector from the user to the satellite, and

Δ^{i} is clock corrections.

To implement the WADGPS system in Taipei flight information region (FIR), the stable RSs collection of dual-frequency GPS observations are essential. This paper uses the e-GPS observation stations in Taiwan as the WADGPS RSs, and the e-GPS observation stations are operated by Taiwan Ministry of Interior. The WADGPS RSs send four types of raw dual-frequency GPS observations to the WADGPS MS including:

■ Range data: it is composed of L1-L2 dual-frequency pseudorange, carrier phase, Doppler frequency, and signal to noise ratio of each satellite in view by the network [

■ Ephemeris data [

■ Almanac data [

■ The Klobuchar model coefficients [

The WADGPS system implemented in this paper is based on that of the NSTB which is operated by FAA in the United States. Therefore, the NSTB archive data are used to verify the WADGPS performance. On the other hand, the GPS receivers used in the e-GPS observation stations might be different, for ease of data processing, the common GPS observation data format, the Receiver INdependent EXchange format (RINEX), is adopted for this work. Before the WADGS MS can use the observations to generate the WADGPS messages, the RINEX data needs to be decoded and organized in a proper format.

To evaluate the performance of the WADGPS developed in this work, a WADGPS user monitor is developed based on WAAS MOPS [

This paper first used four NSTB reference stations to validate the implementation of the WADGPS system, and three of them are used as the WADGPS RSs and one acts as the WADGPS user. The RSs distribution is shown in

Next, this work uses the e-GPS observation stations operated by Taiwan MOI to evaluate the LNAV performance of the WADGPS implementation. The e-GPS observation stations distribution is shown in

For the WADGPS system with three RSs in Taipei FIR,

To achieve possible improvement of the system performance, this WADGPS implementation adds one more e-GPS observation station (Station number 4 in

This paper implemented a Wide Area Differential Global Positioning System (WADGPS) system in Taipei Flight Information Region. The National Satellite Test Bed (NSTB) Reference Stations (RSs) were first used as the WADGPS RSs to validate the implementation. As shown in the three days validation results, the WADGPS system can provide enhanced GPS positioning services with full integrity required by the Lateral NAVigation (LNAV) service for civil aviation. This paper then used the e-GPS observation stations operated by Taiwan Ministry of Interior (MOI) as the WADGPS RSs in Taipei FIR. Two kinds of WADGPS RSs constellations were utilized in this work, and one used three RSs and the other used four RSs. Five-day data were used to analyze both WADGPS implementations. The results showed that the WADGPS system with four RSs performed slightly better than that with three RSs. Importantly, in Taipei FIR, both WADGPS implementations can successfully provide LNAV service with integrity required by civil aviation.

The work presented in this paper is supported by Taiwan National Science Council under the research grant NSC 98-2221-E-006-122. The authors gratefully acknowledge this support. The authors would also like to thank Taiwan Ministry of Interior, FAA Technical Center (NJ., USA), and Stanford GPS Research Laboratory of Stanford University for providing the GPS observation data sets and their thoughtful comments.

The Wide Area Differential GPS.

The Stanford Chart.

The WADGPS architecture.

The dual-frequency smoothing of ionospheric delay and pseudorange.

The WADGPS ionospheric vertical delay grid model flow chart.

The feedback algorithm for GIVE.

Ephemeris and clock errors estimation flow chart.

The common view time transfer flow chart.

Experiment setup.

The procedures of the WADGPS user software.

The WADGPS satellites corrections status window.

The WADGPS ionospheric grid corrections status window.

The WADGPS reference stations status window.

The NSTB reference stations distribution.

(a) The positioning error distribution and 95% error bound in east direction using NSTB data. (b) The positioning error distribution and 95% error bound in north direction using NSTB data.

The vertical positioning error and 95% error bound using NSTB data.

The HPL and horizontal positioning error (NSTB).

The LNAV (NPA) performance of the implemented WADGPS with NSTB data.

The number of satellites used in positioning solutions (NSTB).

The e-GPS observation stations distribution map.

(a) The positioning error distribution and 95% error bound in east direction in Taipei FIR (3 RSs). (b) The positioning error distribution and 95% error bound in north direction in Taipei FIR (3 RSs).

Te vertical positioning error and 95% error bound in Taipei FIR (3 RSs).

The HPL and horizontal position error in Taipei FIR (3 RSs).

The LNAV (NPA) performance of the developed WADGPS with 3 RSs in Taipei FIR.

The number of satellites used in positioning in Taipei FIR (3 RSs).

The HPL and horizontal position error in Taipei FIR (4 RSs).

The LNAV (NPA) performance of the developed WADGPS with 4 RSs in Taipei FIR.

Required Navigation Performance (RNP) [

| ||||||
---|---|---|---|---|---|---|

En route (continental) | H: 740 m |
15 s | 1 × 10^{−7} /h |
H: 3,704 m |
1 × 10^{−5}/hr |
0.99 to 0.99999 |

Terminal | H: 220 m |
15 s | 1 × 10^{−7} /h |
H: 1,852 m |
1 × 10^{−5}/h |
0.99 to 0.99999 |

LNAV(NPA) | H: 220 m |
10 s | 1 × 10^{−7} /h |
H: 556 m |
1 × 10^{−5}/h |
0.99 to 0.99999 |

LNAV/VNAV | H: 220 m |
10 s | 2 × 10^{−7} /approach |
H: 556 m |
5.5 × 10^{−5} /approach |
0.99 to 0.999 |

LPV | H: 16 m |
6 s | 2 × 10^{−7} /approach |
H: 40 m |
5.5 × 10^{−5} /approach |
0.99 to 0.99999 |

Mean of the positioning error (NSTB).

| ||
---|---|---|

−0.506 | 0.090 | |

0.436 | −0.085 | |

15.707 | −7.968 |

Accuracy of the positioning performance (NSTB).

| ||
---|---|---|

7.10 | 3.55 | |

16.10 | 8.10 |

The e-GPS observation stations’ names and locations.

| |||
---|---|---|---|

1 | Longdong | 25° 5′50″N | 121° 55′5″E |

2 | Shoufeng | 23° 52′12″N | 121° 36′53″E |

3 | Fugang | 22° 47′26″N | 121° 12′32″E |

4 | Kaohsiung | 22° 37′52″N | 120° 17′18″E |

User | Taichung | 24° 17′27″N | 120° 32′6″E |

Mean of positioning error (Taipei FIR).

| |||
---|---|---|---|

0.182 | 0.220 | 0.169 | |

1.785 | 1.362 | 1.498 | |

13.400 | −2.431 | −2.440 |

Accuracy of positioning performance (Taipei FIR).

| |||
---|---|---|---|

10.970 | 5.587 | 4.0893 | |

19.360 | 11.248 | 11.485 |