Ionospheric Propagation Effects on GNSS Signals and New Correction Approaches - Global Navigation Satellite Systems: Signal,Theory and Applications - page 387

Assuming the same measurement noise on each signal, it can be shown that the carrier-
phase or code noise will be amplified by a factor of 2.98 for the GPS L1-L2 combination,
whereas for the L1-L5 and L2-L3 combinations amplification factors are 2.59 and 16.64,
respectively (see Hoque & Jakowski, 2010a). The amplification factor is inversely
proportional to the separation of combination frequencies. Since the frequency separation is
relatively large for the L1-L5 combination, the amplification factor is the smallest.

Since the first order ionospheric effect on carrier-phase and code pseudoranges (see Eq. 12
and 13) is the same in magnitude but opposite in sign, computing the sum of carrier-phase
and code pseudoranges would theoretically eliminate the first order ionospheric term in
single frequency measurements. However, the resulting observable would inherit the high
code noise and the carrier-phase ambiguity and is therefore, practically not suitable.

2.4.2 Second order ionosphere-free combination

Receiving signals on three coherent frequencies will allow triple-frequency combinations to
eliminate the first and the second order ionospheric terms. The third order ionospheric term
and errors due to ray path bending are not fully removed in this approach. Such a triple-
frequency combination can be written as (combining code / carrier-phase pseudoranges Eq.
(12) / Eq. (13) measured on f 1 , f 2 and f 3 frequencies and substituting ρ by Eq. (7), for details
see Hoque & jakowski, 2010a).

1

( ) ( )

⎡

2 2 2 2

⎤

( ) ( ) ( )

(21)

Af ΨΨ ΨΨ ρ − f − Bf − f = + Δ s + 3 Δ Δ s + s

11 22 11 33 TEC 3 len

⎣ ⎦

tr tr tr

C

( )

RRE

gr

tr

1

( ) ( )

⎡

2 2 2 2

⎤

( ) ( ) ( )

(22)

Af ΦΦ ΦΦ ρ − f − Bf − f = − Δ s − Δ Δ s + s

⎣

11 22 11 33

⎦

TEC 3 len

tr tr tr

C

( )

RRE

tr

In which

K

( ) ( ) ( )

Δ s = ⎡ B Δ TEC − Δ TEC − A Δ TEC − Δ TEC ⎤

⎦

(23)

⎣

TEC bend 3 bend 1 bend 2 bend 1

tr

C

( )

f − f

u

( )

2 3

Δ s = (24)

3

tr

3 Cf f

23

1

( ) ( )

⎡ ⎤

( )

2 len 2 len 2 len 2 len

Δ s = Bfd − fd − Afd − fd

⎦

(25)

len 33 11 22 11

⎣

tr

C

ff

⎫

12

A =

⎪

f f

ff

−

1 2

13

⎪

B = (26)

⎬

f − f

⎪

1 3

( )( )

Cf = f − f f + f + f

12 3 1 2 3

⎭