Time synchronisation for WAAS over Indian airspace using GPS

Time Synchronisation Implementation in Wadgps
In US WAAS, GPS Common-View Time Transfer Technique is used to estimate the difference between the Reference Station Clocks and the Master Clock, located at MCC. The basic equation used to estimate, the clock offset is the following pseudorange residual equation :

{(D_k,m= Dr_k.1_k,m+Db_m-DB_k+n_k,m)_k=1,K}_m=1,M            ...........(6)

In eq .(6) above, Dr_k is the vector that connects the true location of the k^th satellite, to its location according to the broadcast navigation message. In eq. (6), 1 k,m denotes the unit vector from the k th satellite to the m th reference station. Additionally, Db_m and DB_k are the offsets in the Reference Station and satellite clocks to the GPS time. The measurement noise is given by n_k,m . K is the number of satellites in view of the m th Reference station and M is the total number of Reference Stations.

The GPS Pseudoranges at the Reference Stations, can be corrected for ionospheric effects, because dual-frequency measurements can be used to estimate the ionospheric delay accurately and removed. In addition, the Reference Stations also collect meteorological parameters, Pressure, Temperature and Relative Humidity and the tropospheric delay can be estimated accurately and corrected for.

Basically there are three possible approaches to estimate, the difference between the Reference Station clocks and the Master clock located at MCC. They are discussed below in detail.

In one of the methods, Enge & Vandierendonck have discussed a methodology to be implemented in US WAAS, which is as folows.

Eq. (6) above can be rewritten as follows for an MCC.

(D_K,MCC = Dr_k.1_k,MCC + Db_MCC -DB_k + n_k,MCC)_k=1,K           ....... (7)

In equation (7) above, Dr_k is the vector that connect the true location of the k^th satellite, to its location, according to the Broadcast Navigation Message. 1_k,MCC denotes the unit vector from the k^th satellite to the MCC. Additionally, Db_MCC and DB_k are the offsets in the MCC and satellite clocks with respect to GPS Time. n_k,MCC is the measurement noise. For each satellite of common visibility between a Reference Station,m and an MCC, we can have a pair of equations (6) and (7). Substracting one from the other, we can write,

where N is the number of satellites in common view of the MCC and the m th Reference Station. This can be written as approximately as equal to

= Db_MCC- Db_m

This family of estimated clock offsets (Db_m,MCC)_m=1,M is used in US WAAS to eliminate the clock differences in the observations from the M Reference Stations. It should be made sure that the MCC clock is kept in close synchronism with GPS time. This can be done by averaging the GPS observations at MCC to steer an atomic clock or an ensemble of atomic clocks at MCC. Alternatively (which is more accurate) it could be done if there were a more direct connection from the MCC Master Clock to GPS Time as kept by US Naval Observatory, through some means like a Two Way Satellite Time & Frequency Transfer Technique. Once the Reference Station clock differences are eliminated, one can determine the satellite ephemeris correction (along track, cross track and radial error) as well as satellite clock correction, using ranging data from M (M>4) Reference Stations.

IN EGNOS, a slightly different scheme, as described below, is followed. The individual pseudorange measurements from each RIMS to each satellite can be expressed as
rⁱ_A=Rⁱ_A+Aⁱ_A+C(Dtⁱ_s-Dt^u_A) + e               ........ (9)

where
rⁱ_A is the pseudorange measured from RIMS site A to the satellite i

Rⁱ_A is the range calculated from the RIMS known position (well surveyed point) to the satellite, i, using broadcast ephemeris

Aⁱ_A is the atmospheric delay (ionospheric and tropospheric delay)

C is the velocity of light

Dtⁱ_s is the i^th satellite clock offset (relative to GPS time)

Dt^u_A is the RIMS clock offset relative to GPS time

e is the random error term

The pseudorange measurements are corrected for ionospheric and tropospheric delays by MCC using models. By applying double difference technique, requiring simultaneous tracking of two satellites, i and j, from two RIMS, A and B, we get

F^ij_AB=((rⁱ_A-r^j_A)-(rⁱ_B-r^j_B)) = ((Rⁱ_A–R^j_A) - (Rⁱ_B-R^j_B))           — (10)

This equation is used to estimate the satellite ephemeris errors as it is free from satellite clock and RIMS clock errors. After this using a common pseudorange observations for a satellite, i, between one RIMS, say and MCC, a single difference equation is formed as follows.

Fⁱ_AM=(rⁱ_A-rⁱ_M)+(Dt^u_A-Dt^u_M)           (11)

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