ESTIMATION OF IONOSPHERIC DELAY FOR SINGLE AND DUAL FREQUENCY GPS RECEIVERS: A COMPARISON

Transcription

1 ESTMATON OF ONOSPHERC DELAY FOR SNGLE AND DUAL FREQUENCY GPS RECEVERS: A COMPARSON K. Durga Rao, Dr. V B S Srilatha ndira Dutt Dept. of ECE, GTAM UNVERSTY Abstract: Global Positioning System is the emerging technology for Navigation especially in Civil Aviation and Defense sector. The accuracy of GPS navigation solution can be effects by several error sources and one such error source is atmosphere in which the refraction of GPS signal causes an error of -50meters. This atmospheric error is due to refraction of the GPS signal in ionosphere and troposphere. n this paper, an attempt is made to estimate the error due to ionosphere, which causes the delay of GPS signal in atmosphere. This delay of the GPS signal in ionosphere causes an error in ranging measurement, which reduces the accuracy of Navigation Solution. n this paper, ionospheric delay is estimated using two popular algorithms called the linear free combination algorithm and Klubochar algorithm for dual frequency receivers and single frequency receivers respectively. The delay estimated using the data provided by Scripps Orbit And Permanent Array Center (SOPAC) for one of the nternational GNSS Service (GS) station i.e. NGR,(NGR:Lat/Long:7 4'39"N/78 33'4"E) located in Hyderabad, Andhra Pradesh, ndia for one typical day i.e. August st 0. Keywords: Global Positioning System, Total Electron Content, Refraction. NTRODUCTON Among all other GNSS systems GPS is the most widely used service it was originally developed by the US army and is still monitored by the U.S. Department of Defense (DOD). However, today, GPS is managed by the National Space-Based Positioning, Navigation, and Timing (PNT) Executive Committee to provide user with his position, velocity and time. GPS comprises of three functional segments they are Space segment, Control segment and User segment. GPS Space segment constellation consists of 3 operational satellites placed in 6 orbital planes in the medium earth orbit (MEO) which is at a height of 0,00km above the surface of the earth that provides users with continuous worldwide positioning capability using the data transmitted in the GPS navigation message. GPS Provides service to unlimited number of users since the user receivers operate passively. The system utilizes the concept of one-way time of arrival (TOA) of the GPS signal []. GPS signal consists of 3 components they are PRN ranging codes, navigation message and carrier frequencies. The satellites broadcast PRN ranging codes and navigation data on two carrier frequencies i.e. L (575.4MHz) and L (7.6MHz) using Code Division Multiple Access (CDMA). Each Satellite generates a unique PRN sequence which is randomly generated binary sequence which is different from other satellites which allows all the satellites to share the same frequency signals. The PRN codes are selected in such a way that they have low crosscorrelation properties with respect to each one another. Each satellite generates a short code called as Coarse/Acquisition or C/A code which has a bit rate of.03 Mbps and a long code denoted as Precision or P code with a bit rate of 0.3Mbps. The navigation data provides the means for the receiver to determine the location of the satellite at the time of signal transmission 30

2 and the ranging codes enable the receiver to determine the transit time. Based on the satellite position and the transit time, Receiver location can be computed at any instant of Time. GPS OBSERVABLES They are two types of observables in GPS measurements..e. code range measurements and carrier phase measurements. As the code range measurements are less prone to noise, in this paper we are considering the code range measurements for TEC estimation.. Carrier phase measurements The carrier phase measurement is the difference in phase between the carrier wave from the satellite and the receiver oscillator signal at a specified epoch. The range is simply the sum of the total number of full carrier cycles between the receiver and the satellite multiplied by the carrier wavelength. The ranges determined by the carriers are more accurate than those obtained by the codes, but in carrier phase measurements the carrier signals are highly influenced by noise as compared to the pseudo random codes. So, we are estimating the range using code range measurements other than carrier phase measurements.. Code range measurements The PRN codes transmitted by a satellite are used to determine the pseudo range or distance between the satellite antenna and the antenna of the GPS receiver the receiver can make this measurement by replicating the code being generated by the satellite and determine the time offset between the arrival of a particular transition in the code and the same transmission in the code replica []. The ranging equation of the arrived GPS signal can be given as p c( dt dt ) d ion d tro () Where p is measured pseudo range is geometric or true range c represents speed of light dt and dt are offsets of satellite and receiver clocks ' d ion ',' dtro ' Are delays due to ionosphere and troposphere represent effects of multipath and receiver measurement noise Navigation solution accuracy of the GPS system is dependent on the accuracy of the measured GPS ranging signals []. But, the GPS signals are degraded due to several factors such as atmospheric refraction, multipath, receiver clock bias, satellite clock bias and satellite-receiver geometry [3]. Table represents the typical error value for each of the error source. Error Type Error Segment (meters) Ephemeris 3.0 Signal-n- Space Clock 3.0 Signal-n- 3

3 Space onosphere 4.0 Atmosphere Troposphere.0 Atmosphere Multipath.4 Receiver Receiver 0.8 Receiver Table of GPS ERROR BUDGET From Table (), it can be observed that the error due to ionospheric delay is around (-0m) meters and it is necessary to estimate this delay for precise positioning applications. n this paper, ionospheric delay is estimated for single frequency receiver and dual frequency receiver using klubochar algorithm and linear free combination algorithm respectively. 3 Estimation of onosphere delay After the turning off of the Selective Availability, ionosphere is the largest source of error for GPS positioning and navigation. Hence to improve the accuracy of GPS, it is necessary to estimate the error due to ionosphere. Propagation of the GPS signal is effected by the free electrons present in the ionosphere. At some point of ionosphere, the speed of the GPS signal is affected by density of electrons. The net effect on GPS signal is determined by integrating it along the whole path of its travel from satellite to receiver, which is called Total Electron Content (TEC). 3. Total Electron Content The important parameter causing the ionosphere time delay is the Total Electron Content (TEC) which is encountered by the radio waves on its path from satellite to the GPS receiver. The TEC is defined as the total number of electrons present in an area of m cross section along the propagation path of the satellite signal to receiver. TEC is defined as the integral of the electron density along the propagation path of the signal or the numbers of free electrons in a column of unit cross sectional. TEC = p N (s) ds () Where, N(s) is the electron content per unit volume and p is the propagation path between the source and the receiver. TEC is measured in TEC units i.e.tecu, which indicates 0 6 electrons in an area of m. TEC of TECU causes a ranging error of 0.63m. The ionosphere delay is estimated for single frequency receiver as well as dual frequency receiver using Klubochar algorithm and Linear Fee combination algorithm respectively. 3. Klubochar Algorithm This model is exclusively meant for ionospheric delay estimation of the single frequency GPS receivers. n this model, ionospheric delay is estimated by considering the TEC between the satellite and the receiver, and 50 to 60% of the error can be eliminated based on the solar activity of the region. n this, it is assumed that the electron density is more at an altitude of 350Km on an imaginary line of thickness zero and is maximum at 4:00Hrs of the local time. The klubochar 3

4 model makes use of geomagnetic latitude on onospheric Pierce Point(PP),which is defined as the point where the line of sight connecting the satellite and receiver meets the single layer at an altitude of 350Km[4].n order to estimate delay due to klubochar model, klubochar coefficients n and n are required. The GPS master control station broadcast these coefficients in GPS navigation message. The and are collected from the navigation data of the GS station NGR, Hyderabad, on the typical day i.e. August st 0. Fig. onospheric geometry Steps to calculate the delay using klubochar algorithm are: a. Calculate the Earth-centered angle using the Elevation angle of the satellites w.r.t ground station using Eq () ( E 0.) is the Earth-centered angle units in semicircles E is the Elevation Angle (convert degrees in to semicircles) b. Compute the sub-ionospheric latitude using Eq.3 i u cos A (3) where U 7, which is the geodetic latitude of NGR A is the azimuth angle c. Compute the sub-ionospheric longitude using Geodetic longitude etc U sin A cos( 3.4) (4) where is geodetic longitude of NGR U d. compute geomagnetic latitude of the subionospheric location looking toward each GPS satellite using Eq cos[(.67) 3.4] (5) m is the geomagnetic latitude units in semicircles m e. compute local time, at the sub-ionospheric point usingeq.6 t 4.3 *0 4 Time GPS (6) Time is the GPS time value in seconds. GPS f. Compute the slant factor SF using Eq.7 SF 3 6 (0.53 E ) (7) 33

5 g. Compute Phase of the model x ( t ) PER (8) x is the phase of the model which is (max at 4hours =50400sec) local time. h. Compute Amplitude of the model is (9) 9 i. if x. 57 then use T iono SF (50 ) (0) 4 9 x x Otherwise T iono SF [(5 0 ) AMP ( )] 4 () T iono is the ionospheric time delay. From this ionospheric time delay range delay on any one of the two carriers can be calculated. 3.3 Linear Free Combination Algorithm Linear Free Combination Algorithm (LFCA), is the algorithm is based on the ranging measurements of Dual frequency GPS receivers [3]. The ranging measurements on L and L carrier frequencies of GPS receiver are represented as Eq. By considering the ranging measurements on both frequencies, TEC can be estimated in Eq. TEC 40.3 f f = MHz f = 7.60 MHz f ( pr pr ) ' pr' And ' pr ' are ranging measurements on L and L frequency respectively. Once the TEC is estimated which is independent of frequency, onospheric delay which is dependent on frequency can be estimated as using Eq.3 (3) Where f is the carrier frequency i.e. it can be L(575.4MHz) or L(7.60MHz). () 5 Results The Results are based on the data due to the dual frequency GPS Receiver located at National Geophysical Research nstitute, Hyderabad (Hyde: Long/Lat: 78 33'4"E 7 4'39"N). The data of a typical day i.e August st 0 is collected and sampled at an interval of 30 seconds, in order to carry out the thesis work. Visibility of the satellites for complete 4 hours of the typical day is tabulated below. Table Satellite Visibility at NGR GPS Receiver 34

6 Hour of the Day Visible Satellites G0, G03, G06, G4, G6, G0, G3, G30, G3, G3 G03, G06, G07, G6, G9, G0, G3, G30, G3 3 G03, G06, G07, G3, G6, G9, G0, G3, G30, G3 4 G03, G06, G07, G0,G, G3, G6, G9, G0, G3, G3 5 G0, G03, G06, G07, G08, G0, G, G3, G9, G0, G3 6 G0, G07, G08, G0, G, G3, G7, G9, G3, G8 7 G0, G07, G08, G, G3, G7, G6, G8 8 G0, G04, G07, G08, G, G7, G6, G8 9 G0, G0, G04, G07, G08, G7, G6, G7, G8 0 G0, G04, G08, G09, G0, G7, G6, G7, G8 G0, G04, G05, G09, G0, G7, G7, G8 G0, G04, G05, G09, G0, G, G7, G7, G8 3 G0, G04, G05, G09, G0, G, G7, G5, G7 4 G0, G05, G09, G0, G, G5, G5, G6, G9 5 G0, G05, G, G5, G8, G, G5, G6, G9 6 G0, G05, G, G5, G8, G, G5, G6, G9 7 G09, G5, G8, G, G, G5, G6, G7, G9 8 G09, G4, G5, G8, G, G,G7, G9 9 G03, G06, G09, G4, G5, G8, G, G, G7, G9 0 G03, G06, G09, G4, G8, G, G, G3 G03, G06, G4, G8, G9, G, G, G5, G3 G06, G, G4, G8, G9, G, G5, G30, G3 3 G0, G, G4, G6, G8, G, G5, G30, G3, G3 4 G0, G, G4, G6, G0, G, G30, G3, G3 t can be observed that at every epoch at least 5 GPS satellites are visible to the receiver. Algorithms, TEC is estimated using which ionospheric delay is estimated by both algorithms and is shown in Fig. 35

7 Fig. TEC estimated using both the algorithms on the typical day From Fig. it is observed that the maximum TEC is observed at 4:0Hrs of the day. The maximum TEC is 57TECU using LFCA algorithm and with klubochar algorithm it is 53TECU, Minimum TEC is observed at the starting of the day i.e. at 5:00Hrs and 3:00Hrs of the day in both the algorithms. Using TEC, ionospheric delay which is dependent on carrier frequency is calculated for Klubochar(on single Frequency) algorithm and LFCA algorithm (on dual frequencies) and is shown in Fig.3 Fig.3 onospheric time delay estimated using both the algorithms on August st 0 Maximum ionospheric time delay is observed at 4:0Hrs of the day in both the algorithms. The maximum onospheric time delay observed using Klubochar algorithm is 9ns and with LFCA algorithm maximum on L carrier frequency is 3ns and on L carrier frequency is 50ns.onospheric range delay is also estimated using both the algorithms and is shown in Fig.4. 36

8 Fig.4 onospheric range delay estimated using both the algorithms on August st 0 Maximum ionospheric range delay is observed at 4:0Hrs of the day in both the algorithms. The maximum onospheric delay observed using Klubochar algorithm is 8.5m and with LFCA algorithm maximum on L carrier frequency is 9.3m and on L carrier frequency is 5m. Hence it can be observed that the TEC as well as ionospheric delay estimation is better with LFCA algorithm, because the Klobuchar algorithm itself states that only 40% of the delay can be eliminated. 6 Conclusion onosphere Delay parameters such as onospheric Total Electron Content, onospheric Time Delay and onospheric Range Delay parameters are estimated using Klobuchar Algorithm (uses Single Frequency Receiver) and Linear Free Combination Algorithm or LFCA (uses Dual Frequency Receiver) for a complete day i.e st August 0 for National Geophysical Research nstitute (NGR) and observed that the impact of onosphere Delay on GPS signal is more in Mid Afternoon of the day as compared to pre sunrise and post sunset time of the day. Among the two onospheric Delay Estimation methods LFCA gives high accurate positioning as compared to Klobuchar model and the Klobuchar algorithm is computationally more complex and takes consuming algorithm. References [] Kaplan, E. D., ed., Understanding GPS Principles and Applications, Artech House, Norwood, MA, 996 [] Spilker JJ, Parkinson BW (Eds) Global positioning system: theory and applications, vol. AAA, pages [3] G.S.Rao, Global Navigation Satellite Systems, Tata McGraw Hill publications, 00. [4] Klobuchar, [J.A. 987] onospheric time-delay algorithm for single-frequency GPS users, EEE Trans Aerospace Electron Syst., 3 (3), pages