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Global Positioning System provides three dimensional position, velocity and time information to users anywhere on or above the surface of the Earth. A GPS receiver uses two types of measurements, viz. code and carrier phase for determining its (user) position. The positional accuracy of GPS is limited by several sources of error such as satellite and receiver clock offsets, signal propagation delays due to ionosphere and troposphere, multipath, receiver measurement noise and instrumental biases. The ionospheric delay error is the most predominant of all the error sources. Taking advantage of the dispersive nature of the ionosphere, one can estimate the ionospheric delay using the dual frequency GPS measurements. In this paper, two prominent ionospheric delay smoothing algorithms, viz. combined code and carrier smoothing filter (CCCSF) and Hatch smoothing filter (HSF) are compared for reducing the effect of code measurement noise and multipath. The GPS data of Hyderabad GAGAN station is used in this investigation. The smoothing results are validated with the Bernese GPS data processing software. The mean, standard deviation and RMS values of the noise suppressed due to the above techniques are compared. The work presented is useful for accurate ionospheric modeling required for communication, navigation and surveillance (CNS) systems in India.
Key words: GPS, Ionospheric delay, Smoothing, Hatch filter, Bernese software.
Global Positioning System (GPS) is a satellite based navigation system, developed by the U.S. Department of Defense (DoD). It provides three dimensional user position, velocity and time (PVT) under all weather conditions. The positional accuracy of GPS is affected by several errors such as satellite and receiver clock errors, signal propagation delay errors due to ionosphere and troposphere, multipath error, receiver measurement noise and instrumental biases. Among all the error sources, ionospheric delay is the most predominant one and is of the order of 5-15m during mid-afternoon . The Indian Space Research Organisation (ISRO) and Airports Authority of India (AAI) are jointly implementing a Satellite Based Augmentation System (SBAS) known as GPS Aided Geo Augmented Navigation (GAGAN) to provide seamless coverage over the Indian airspace and meet the navigation accuracy requirements of Category-I precision approach aircraft landings. It is expected to be operational by 2010 . In order to meet these requirements, accurate estimation of ionospheric delay is necessary. One can use either the dual frequency code or carrier phase measurements for estimating the ionospheric delay. The ionospheric delay obtained from the code measurements is unambiguous, but coarse in nature. On the other hand, that obtained from the carrier phase measurements is precise, but ambiguous. The measurement error (rms) due to receiver noise and multipath in code is about 0.5-1.0m and that due to carrier phase measurement is of the order of 0.5-1cm . The algorithms presented in this paper make use of the relative merits of both code and carrier phase measurements for reducing the effect of receiver measurement noise and multipath.
2. THEORETICAL BACKGROUND
In this section, three prominent ionospheric delay smoothing algorithms are briefly discussed. The first algorithm named as combined code and carrier smoothing filter (CCCSF) uses the variances of the code and carrier phase data to minimize the receiver measurement noise and multipath, where as the second algorithm is an averaging technique based on the Hatch filter. The third algorithm is provided within the Bernese software, which is used for validation purpose. The first two techniques are recursive in nature, whereas the third technique is non-recursive.
2.1 Combined Code and Carrier Smoothing
The combined code and carrier smoothing filter (CCCSF) is a recursive technique for minimizing the effect of receiver measurement noise and multipath. The ionospheric delay () at time tk is estimated from the code and carrier phase measurements of the current epoch, the previous estimate (), and two weighting functions (and) that are derived from the variances of the code and carrier measurements. The smoothed ionospheric delay at time tk is computed as follows ,
P1, P2 are the code measurements,,are the corresponding carrier phase measurements and represents the change in the carrier ionospheric delay at time tk from tk-1.
2.2 Hatch Smoothing Filter
The Hatch smoothing filter (HSF) developed by Mr. Ron Hatch during eighties is based on the concept that the change in code range between observations at different time epochs equals the change in carrier range. Using this condition, 'N' equations (for 'N' observations) can be formulated for the code ionospheric delay, (P2-P1)N at Nth epoch. The expression for the smoothed ionospheric delay is obtained by taking the average of these 'N' equations. The Hatch filter for estimation of smoothed ionospheric delay can be represented in recursive form as ,
where is the smoothed differential ionospheric delay at Nth epoch. is the smoothed differential ionospheric delay at (N-1)th epoch. is the code differential ionospheric delay at Nth epoch. is the carrier differential ionospheric delay at Nth epoch. The precision of the smoothed ionospheric delay estimate is a direct function of the number of epochs N.
2.3 Bernese Smoothing Algorithm
The Bernese GPS Software is developed at the Astronomical Institute University of Berne (AIUB), Switzerland, in the late 1980s and is widely used around the world. The Bernese GPS software (version 4.2) provides many algorithms for processing GPS data including one for smoothing . The smoothed code on L1 (f1) frequency is given by,
The smoothed code on L2 (f2) frequency is given by,
whereis the smoothed code measurement at epoch N (on frequency fk , k =1,2). is the carrier phase measurement at epoch N (on frequency fk ). is the mean difference between all the code and phase measurements (on frequency fk). is the mean ionospheric delay over all the phase measurements.
By subtracting equation (7) from (6), the differential ionospheric delay is obtained.
3. RESULTS AND DISCUSSION
In this investigation, dual frequency GPS data in Receiver Independent Exchange (RINEX) observation format is considered. The data corresponds to the Hyderabad GAGAN station (4th March 2005) and is provided by the Space Applications Centre (SAC), ISRO, Ahmedabad. The sampling rate of the data is 60s. The raw code ionospheric delay and the corresponding carrier phase ionospheric delay for PRN 30 are shown in Fig. 1. It can be observed that the code ionospheric delay is more noisy than the carrier ionospheric delay. However, carrier phase provides only relative delay due to integer ambiguity problem. The smoothed ionospheric delay (PRN 30) obtained due to CCCSF and HSF are compared with corresponding Bernese software output in Fig. 2. It can be observed that there is significant reduction in
the noise after smoothing. It is found that the CCCSF algorithm is taking comparatively more time for convergence. The smoothing results due to
both the algorithms closely follow Bernese output, with Hatch filter performing slightly better for most
of the observation period.
The mean, standard deviation (S.D.) and RMS values of the noise suppressed due to the CCCSF, Hatch filter and Bernese are statistically compared in Table 1 for four satellites (PRN 30, 2, 6 and 29) visible during the observation period. For PRN 30, PRN 2 and PRN 29, S.D. and RMS values obtained from HSF algorithm are closer to the corresponding values obtained from Bernese software, whereas for PRN 6, CCCSF algorithm values are closer to the Bernese results.
Local Time (hours)
Code ionospheric delay
Carrier ionospheric delay
04 Mar 2005
Ionospheric delay (meters)
Fig. 1. Ionospheric delay using code and carrier measurements
Local Time (hours)
Raw code ionospheric delay
04 Mar 2005
Ionospheric delay (meters)
Fig. 2. Comparison of ionospheric delay due to raw code, Hatch, CCCSF and Bernese
Table 1 Mean, standard deviation (S.D.) and RMS value of the suppressed noise
Hatch Smoothing Filter (HSF)
Combined code and carrier Smoothing Filter (CCCSF)
In this paper, two prominent ionospheric delay smoothing algorithms are compared for improving the accuracy of ionospheric delay estimation using the dual frequency GPS data. The smoothing results are validated with the Bernese GPS data processing software. Both CCCSF and HSF algorithms closely follow Bernese output, but the advantage of the Hatch filter technique is that it is simple to implement and requires less time for convergence as compared to CCCSF. The two proposed algorithms can be used for real-time ionospheric modeling keeping in view of their recursive form. The work presented here would be useful for enhancing the performance of the present and proposed CNS systems including GAGAN.
The research work presented in this paper has been carried out under the Department of Science and Technology (DST), Govt. of India sponsored Project No. SR / S4 / AS-230 / 03. The authors are also thankful to Shri Kalyan Bandyopadhyay and Dr. M R Sivaraman, Space Applications Centre, Indian Space Research Organisation (ISRO),Ahmedabad, India for providing the GPS
data. Thanks are due to Mr. D. Venkata Ratnam, SRF, NERTU for his help in implementing some of the algorithms.