The GNSS integer ambiguities: estimation and validation

with the weight function
wz(â) =
1 exp{− 2â − z2Qâ }
exp{− 1
2â − z2 z ∈ Zn
}, Qâ
z∈Z n
and conditional posterior
1
pb|a(b|a, y) =
|Qˆb|â |(2π) p
2
(3.99)
exp{− 1
2 ˆ b(a) − b 2 Qˆ b|â } (3.100)
The Bayes baseline estimate can now be determined with equations (3.93) and (3.98)
as
ˆbBayes =
(â − zwz(â)) (3.101)
bp(b|y)db = ˆ b − Qˆ bâ Q −1
â
z∈Z n
So, with the Bayesian approach the ambiguities are not resolved as integers. Instead a
weighted sum over all possible ambiguities is used with proper weights derived from the
likelihood function. A discussion on the corresponding confidence regions can be found
in Gundlich and Koch (2002) and Gundlich (2002).
66 Integer ambiguity resolution