_{1}

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The standalone Global Positioning System (GPS) does not meet the higher accuracy requirements needed for approach and landing phase of an aircraft. To meet the Category-I Precision Approach (CAT-I PA) requirements of civil aviation, satellite based augmentation system (SBAS) has been planned by various countries including USA, Europe, Japan and India. The Indian SBAS is named as GPS Aided Geo Augmented Navigation (GAGAN). The GAGAN network consists of several dual frequency GPS receivers located at various airports around the Indian subcontinent. The ionospheric delay, which is a function of the total electron content (TEC), is one of the main sources of error affecting GPS/SBAS accuracy. A dual frequency GPS receiver can be used to estimate the TEC. However, line-of-sight TEC derived from dual frequency GPS data is corrupted by the instrumental biases of the GPS receiver and satellites. The estimation of receiver instrumental bias is particularly important for obtaining accurate estimates of ionospheric delay. In this paper, two prominent techniques based on Kalman filter and Self-Calibration Of pseudo Range Error (SCORE) algorithm are used for estimation of instrumental biases. The estimated instrumental bias and TEC results for the GPS Aided Geo Augmented Navigation (GAGAN) station at Hyderabad (78.47°E, 17.45°N), India are presented.

The Global Positioning System (GPS) is a satellite-based navigation system capable of providing three dimensional position, velocity and timing information to users anywhere on or above the surface of the earth. GPS has been in use for a wide variety of applications. These include during flight in oceanic routes, enroute over the domestic airspace, and in crowded metropolitan airspaces. Aircraft on the final approach to airports, demands the greatest safety and reliability. To use GPS for precision approach (PA) and landings of civil aviation, the navigation system has to meet the Required Navigation Performance (RNP) parameters. These include accuracy, integrity, availability and continuity of service. Standalone GPS does not meet these precision approach requirements. The horizontal and vertical accuracy required for Category-I PA is 16 m and 4 m (95%) respectively [

As a part of the global Communications, Navigation, and Surveillance/Air Traffic Management (CNS/ATM) plan adopted by the International Civil Aviation Organisation (ICAO), the Airports Authority of India (AAI) and Indian Space Research Organisation (ISRO) have jointly undertaken a programme for implementation of the Indian Satellite Based Augmentation System (SBAS) known as GPS Aided Geo Augmented Navigation (GAGAN) [

Several error sources that affect the positional accuracy of GPS are ionosphere, troposphere, satellite and receiver clock offsets, instrumental biases of the receiver and satellite, receiver measurement noise and multipath. Among all of these, the ionospheric delay is the most predominant error in GPS precise positioning and navigation. The measurement of ionospheric delay involves estimation of ionospheric total electron content (TEC). TEC is defined as number of free electrons contained in a tube of 1 m^{2} cross-section extending from the satellite to the receiver. The dual frequency GPS observations can be used to estimate the TEC, taking advantage of the

dispersive nature of the ionosphere. However, line-of-sight ionosphere measurements derived from dual frequency GPS data are corrupted by instrumental biases in both the receiver and GPS satellite transmitters. The instrumental biases occur due to the frequency dependent delays of analog hardware within the GPS satellite and receiver [

Two prominent techniques based on the Kalman filter and the Self Calibration Of pseudoRange Error (SCORE) algorithm are applied to the low latitude GAGAN station data for estimation of TEC and instrumental bias. The Kalman filter is a computational algorithm that can optimally estimate the states of a system from a multidimensional signal contaminated by noise. Both these techniques use dual frequency GPS data of a single station to estimate the instrumental bias.

The TEC measurements from a dual frequency GPS receiver are affected by the thermal noise as well as the differential instrumental biases within the satellite and receiver hardware. A two step method is proposed to optimally combine both code and carrier phase observables for improving the TEC estimation accuracy. The ionospheric delay measurements derived from the code observables are unambiguous but are affected by the measurement noise and multipath errors. In the first step, line-of-sight ionospheric delay derived from the code observables is smoothed using the carrier phase derived ionosphere measurements. In the second step, a single layer ionosphere model is used to estimate the vertical TEC and instrumental biases from the smoothed line-of- sight TEC, using a five state Kalman filter.

The dual frequency GPS code and carrier phase measurements in metres can be described by the following equations (subscript i = 1, 2, refers to GPS frequencies, f_{1} and f_{2}) [

where r is the true geometric range (m);

c is the speed of light (m/s);

dt_{u}, dt^{s} are the receiver and satellite clock offsets, respectively (s); TD is the tropospheric delay (m);

I_{i} is the ionospheric delay at frequency f_{i} (m);

SB_{Pi} and RB_{Pi} are the satellite and receiver instrumental group delay biases at frequency f_{i}, respectively (m);

SB_{Li} and RB_{Li} are the satellite and receiver instrumental phase delay biases at frequency f_{i}, respectively (m);

λ_{i} is the carrier wavelength at frequency f_{i} (m);

N_{i} is the carrier phase integer ambiguity (cycles);

e(.) includes measurement noise and multipath error (m).

The ionospheric delay at frequency f_{i} can be expressed as,

where

Using the Equations (1), (2) and (3), the differential ionospheric delay, I can be obtained as,

where SB_{P} = SB_{P}_{1} − SB_{P}_{2}, RB_{P} = RB_{P}_{1} − RB_{P}_{2}, SB_{L} = SB_{L}_{1} − SB_{L}_{2}, and RB_{L} = RB_{L}_{1} − RB_{L}_{2}. SB_{P} and RB_{P} are referred to as the satellite and receiver differential instrumental biases respectively.

The smoothing procedure used in this paper is described in [

The vertical TEC and instrumental biases are estimated using a five state Kalman filter. The biased smoothed line-of-sight TEC is represented using a single layer ionosphere model as [

where A_{1}, A_{2}, and A_{3} are the parameters for the spatial linear approximation of vertical TEC;

S is the slant function and e is elevation angle;

dl_{IP} is the difference between the geomagnetic longitude of the ionospheric pierce point (IPP) and the mean longitude of the Sun;

df_{IP} is the difference between the geomagnetic latitude of the ionospheric pierce point and that of the receiver.

Equation (6) forms the measurement model of the Kalman filter. The parameters A_{1}, A_{2}, and A_{3} describing the vertical TEC on the IPP are estimated for each time t along with the instrumental biases using a five state Kalman filter. In this investigation, the instrumental bias obtained using Fitted Receiver Bias (FRB) method is used as the initial state of the receiver bias in the Kalman filter. However, only nighttime data are used in the FRB method for achieving better results. The details of the FRB method are discussed in a later section.

The Self-Calibration Of pseudo Range Error (SCORE) technique can be used to improve the accuracy of TEC measurement from the GPS observations. A dual frequency receiver contains several components such as antenna, low noise amplifier (LNA), cables, and filters in the RF and IF sections, which contribute to instrumental bias errors. SCORE technique can be used to calibrate such a dual frequency GPS receiver system. With this ability to calibrate and monitor the integrity of pseudo range measurements, SCORE algorithm can be used for ionospheric error measurement for GAGAN. The SCORE technique does not require use of any hardware calibrators or ionospheric models.

The SCORE technique can be applied to estimate the combined satellite plus receiver instrumental biases for each satellite. It uses a self-consistency constraint on the receiver’s measurements of ionospheric delay to derive the instrumental bias errors. This self-consistency can be understood by considering a conjunction occurring between two satellite paths, i.e. the two satellite paths arrive at the same moment at an ionospheric pierce point. In such an event, the same ionospheric pseudo range error (TEC value) should be seen on each satellite [

The mathematical quantity E describes the equivalent vertical TEC difference for multiple observations [

where, α: satellite PRN number; i: sample number;

_{i} and β_{j};

T_{γk} = calculated equivalent vertical TEC for sample γ_{k}, using the appropriate local zenith angle and satellite bias,

for S_{γk} = slant TEC for the data sample;

B_{γ} = combined satellite plus receiver bias for PRN γ, in TECu;

ε_{γk} = elevation angle for satellite sample, at observing site;

μ = altitude scale factor for conversion to IPP zenith angle,

where R_{e} = 6378 km (earth radius);

H_{IPP} = 350 km (altitude of ionospheric pierce point);

The Gaussian function is chosen as an appropriate weighting factor,

for θ_{k} = Latitude for sample k (degrees).

λ_{k} = MJD + LT/24

where MJD is Modified Julian Day (day) and LT is local time (fraction of day), for sample k;

θ_{0} = reference latitude difference, for scaling (degrees);

λ_{0} = reference local time difference, for scaling (days).

For selection of IPP crossover points, an IPP latitude band of 4˚, centered 3˚ north of the receiver is considered. For Hyderabad station (Longitude: 78.47˚E, Latitude: 17.45˚N), this corresponds to 20.47˚N ± 2˚. In the computations, latitude scale parameter (θ_{0}) is chosen as 16˚. This is much larger than the IPP latitude band range (4˚). The local time scale parameter (λ_{0}) corresponds to a smaller spatial domain than θ_{0}, and is comparable to the IPP latitude band range [_{0} is chosen as 4.5˚ in longitude.

A method for estimating the receiver bias of a single receiver is described by [_{o}) for which the standard deviation sum is minimum is considered as the correct receiver bias.

The standard deviation of VTEC data over the measurement period is given as,

where

where M_{t} denotes the total number of satellites and N_{t} is duration of the desired measurement time interval in samples. In equation (11), the total standard deviation is obtained by summing the standard deviation values of each measurement sample where N_{t} is chosen equal to the number of measurement samples present in 24 hours

of GPS data. _{t} satellites.

In this analysis, dual frequency GPS data of Hyderabad GAGAN station is used. The data is provided by the Space Applications Centre (SAC), Indian Space Research Organisation, Ahmedabad, India. The raw data obtained from the NovAtel GPS card is converted into the desired Receiver Independent Exchange (RINEX) format using the “Convert” software. The RINEX navigation and observation data files are used in the processing.

From the navigation data, position of all the visible satellites in the Earth Centered Earth Fixed (ECEF) reference system is computed [

The computed biased phase smoothed slant TEC, slant factor, geomagnetic latitude and longitude of IPP, geomagnetic latitude of receiver, and the mean longitude of Sun form the inputs to the Kalman filter. The satellite instrumental biases determined by the Centre for Orbit Determination (CODE), Europe are used as initial state of the biases of various satellites, in the proposed Kalman filter model.

Normally, FRB method is used for rough estimation of instrumental bias of GPS receiver considering the 24-hour data of several days. The FRB method is applied to GPS data of Hyderabad GAGAN station (0 - 24 hours LT, March 4, 2005). In this method, the slant TEC is converted into equivalent vertical TEC using the

slant function. The sampling period of the data is 60 s. Hence, N_{t} is chosen as 1440. Literature suggests that the receiver bias can be as large as about ±15 ns [

The estimated vertical TEC after removal of the instrumental bias error is shown in

The estimated maximum vertical TEC of two satellites (PRN 4 and PRN 7) visible during mid-day, after correcting for the instrumental biases are 47.12 and 52.87 TECU. The mean value of the receiver bias estimated using the Kalman filter is obtained as 3.2 ns (1 ns of differential delay = 2.852 TECU).

The ionospheric TEC and the combined instrumental bias of satellite and receiver are estimated using SCORE technique. The dual frequency GPS data of Hyderabad GAGAN station is used in the estimation. The slant TEC is estimated using carrier phase measurements for all the visible satellites over a 24 hour period (4 March 2005). Knowing the satellite and receiver position information, elevation and azimuth angles due to various satellites are computed. Further, the IPP coordinates, and mapping (slant) function is computed for later use. The slant TEC values are converted into equivalent vertical TEC estimates by using the mapping function.

For input to the SCORE algorithm, vertical TEC values and the IPP latitudes over a narrow band of 4˚, centered 3˚ north of the receiver (i.e. 20.5˚N ± 2˚) is considered. The vertical TEC and IPP latitude variation over this limited band are shown in

The vertical TEC values of each satellite pair (corresponding to the crossover points) in the chosen latitude band are used in computing E. The combined satellite plus receiver biases due to various satellites are estimated using a minimization procedure for E. The estimated biases due to various satellites are shown in

The absolute values of the combined biases are found to range from 0.66 to 20 TECU over a 24 hour observation period. The system calibration parameter (SCP) is computed by taking the average of bias corrections of all the visible satellites. This can be used to calibrate the GPS receiver system. The SCP is estimated as −8.29 TECU. The vertical TEC profile after application of the SCORE algorithm is shown in

S. No. | Satellite PRN # | Bias values (TECU) |
---|---|---|

1. | 1 | −1 |

2. | 2 | −7.75 |

3. | 4 | 3 |

4. | 5 | −14 |

5. | 6 | −13 |

6. | 9 | −18.2 |

7. | 10 | −1 |

8. | 11 | −13 |

9. | 14 | −6 |

10. | 15 | −2.8 |

11. | 18 | −8.8 |

12. | 19 | −9 |

13. | 22 | −11 |

14. | 24 | −18.5 |

15. | 25 | −20 |

16. | 26 | 1 |

17. | 29 | −8.5 |

18. | 30 | −0.66 |

In this paper, two prominent techniques based on Kalman filter and SCORE algorithms are used for estimation of TEC and instrumental biases. In order to reduce the noise level in the GPS pseudorange data, ionospheric delay measurements are smoothed using precise carrier phase data. The phase smoothed slant TEC measurements obtained using the Hatch filter technique show considerable improvement over the code derived slant TEC. To further improve the accuracy of TEC estimation, a five state Kalman filter is developed for estimating the differential instrumental bias. An FRB method is used for estimating the initial state of the receiver bias. However, only nighttime data are considered in the estimation of receiver bias using FRB method, as TEC variations are relatively small during nighttime. The biases are found to be consistent over the observation period and agree with other reported values in open literature. Using the SCORE technique, the combined satellite and receiver biases are estimated. The SCORE approach is distinct in that it allows the dual frequency GPS receivers to autonomously maintain its pseudorange accuracy without use of any hardware calibrators or ionospheric models. The ionospheric delay corrections obtained after removal of instrumental bias would enable the user aircraft having a SBAS enabled GPS receiver to determine its position accurately for Category-I Precision Approach applications.

The author would like acknowledge the Director, Space Applications Centre, Indian Space Research Organisation, Ahmedabad, India for providing the data.

DhirajSunehra, (2016) TEC and Instrumental Bias Estimation of GAGAN Station Using Kalman Filter and SCORE Algorithm. Positioning,07,41-50. doi: 10.4236/pos.2016.71004