TRAYECTORIA

Undoubtedly ionospheric effects on very short baseline GPS can be neglected after the differential process. However it is known that the ionosphere is a problem for longer baselines. But how long is long? In fact the ionosphere can sometimes cause severe problems even over quite short baselines. A related problem is what will happen during the coming solar maximum cycle? Hence the study of ionospheric effects on GPS is necessary not only for the ionospheric modelling over longer baselines but also for the exploration of these general problems.

4.3.1 IONOSPHERIC EFFECTS ON CODE AND PHASE MEASUREMENTS

Usually the measurement errors caused by either the code ionospheric refraction or the phase ionospheric refraction are called ionospheric delays. However the propagation characteristics of GPS signals for code and for phase along the path of the ionosphere are different, and can be characterised as the delay of the PI (or C/A) and P2 code (called group delays) and the advance of the LI and L2 carrier phase (called phase advances) mainly because the phase velocity based on binary phase modulation is larger than vacuum speed and the group (code) velocity based on the modulation or the energy is smaller than vacuum speed by the same amount but opposite sign (see measurement expressions (2.4a) and (2.4b)). The integral effect of the ionosphere on GPS code and phase observables (Sc and Sp), is related to the velocity which depends on the frequency and the number of free electrons (referred to as the electron density) along the path and can be respectively formulated as follows (Tsedillina et. al., 1994, Stewart, 1997).

Chapter 4: Ionospheric D elay and Modelling = i u , [ l + 4 0 . 3 N / f ^ ] ( i i ...(4.3.b) = S + 40.3 TEC / f ^... (4.3.C) Sp — Jfiü, Np ds...(4.4.a) = 40.3 (4.4.b) = S - 40.3 TEC / f ^... (4.4.C) where S is the true range, TEC is the total electron content integrated along the signal path, N is the electron density in el/m^, and f is the operating frequency in hertz.

The corresponding ionospheric time delay or time advance of the ionospheric delay follows as

TECns = 40.3 TEC / (c f ) ...(4.4.d) where TECns is the ionospheric time delay in unit of nanoseconds (ns).

The conversion between the TEC in el/m^ and the Li and L2 frequency ionospheric

delay in metres, Ii and I2 in (2.1) and (2.2) can be written as the following expressions.

I, =40.3 T E C / f i ^ ...(4.5.a) = Ti I...(4.5.b) I2 = 40.3 T E C / f2^... (4.6.a) = T : I ...(4.6.b) where fi = 1575.42 MHz and = 1227.60 MHz, Ï 1 = f2^ / (fiZ-fz?) 5 1.5457 andÏ 2 = f i ^ / ( f i 5 2.5457,

I = [(fi ^-fz^) / (fi ^ fz^)] (40.3 TEC) in units of meters.

The conversion of the ionospheric delay I between meters and TECU or nanosecond can be written as

TEC = I [(f 1 ^ f2 ^) / (fi ^-f2 2)]/ 40.3 in unit of TECU... (4.7)

TEC = I (1/ c) 10^ in unit of ns (nanosecond)... (4.8) Where c is the light speed, and 1 TECU = 10^^ el/m^.

Therefore the ionospheric delay in meters can be converted into TECU and ns as 0.9 m = 3 ns = 8.5676789 TECU

Ionospheric effects on GPS measurements depend on the signal characteristic and frequency, and the total number of electrons along the path. The total number of electrons per square meter (or say the electron density) vary with location and time, and the ionospheric delay is proportional to the inverse of the frequency squared. From many investigation results on the ionospheric behaviour (Klobuchar, 1986 and 1991,

Knight et. al., 1996 and 1998, and Doherty et. al., 1997), it can however be summarized as follows.

• The ionospheric effects introduced into the GPS observations can vary from less than 1 meter to more than 100 meters. In particular, as the satellites remain at a low elevation mask, the ionospheric delays cannot be ignored. At nighttime, the ionosphere has shown a static characteristic of less effect.

• The ionosphere changes with time of day, season, location of the survey, viewing direction (azimuth), solar activity, and the magnetic state.

• The higher the frequency, the smaller the ionospheric effect.

4.3.2 IMPACTS OF THE IONOSPHERE ON GPS OPERATIONS

As described previously the ionospheric effects vary with time and location, but during GPS operations would these effects cause problems even over short baselines? If yes, when? or where? Many studies on this have been made. (Klobuchar, 1991, Aarons, 1994, Clynch, 1994, Bishop, 1996, Skone and Cannon, 1997-8, Skone, 1998, Pullen et. al., 1998, Stewart et. al., 1998, and Conway, 1998). These results can be summarised as follows.

• Severe scintillation may occur for several hours after sunset during the solar maximum periods.

• Seasonal variation follows the Sun’s 27-day rotational period and the roughly 11- year cycle of solar activity.

• Scintillation may fade the signal low and long enough and even cause loss of signal lock.

• The worst source of scintillation is the equatorial anomaly region — approximately 15° north and 15 south of the magnetic equator. Ascension island in the Atlantic, Diego Garcia in the Indian Ocean, Hong Kong, and Taiwan in the Pacific are some of stations that fall directly under the anomaly region.

• The other potentially active regions are at Auroral and polar cap latitude.

• Intense magnetic storms may occur even during periods of low solar flux. When severe magnetic storms occur, the ionospheric effect may last up to one or two days and the auroral effect can move down into the mid-latitudes.

Chapter 4: Ionospheric D elay and Modelling

• Depending on the model used, the grid modelling accuracy can vary from couples of tens of centimeters to meters.

Overall the ionospheric effect changes with the time of the day, season, location of the receiver, viewing direction, solar activity, the state of the earth’s magnetic field and severe scintillation can occur during the solar maximum or strong magnetic storm periods and cause severe problems such as loss of signal lock. Therefore monitoring and broadcasting the ionosphere by an accurate, reliable, and practical ionospheric model is necessary for many GPS operations possibly even over short baselines. Particularly, the monitoring of the occurrence of ionospheric irregularities for a wide and even global area can hence be implemented with the ionospheric model through the establishment of PGA (Wanninger, 1992 and 1995, Engler et. al., 1995, Mannucci et. al., 1995, Darin et. al., 1997).