The GNSS integer ambiguities: estimation and validation

d, δ instrumental delay for code and phase observations respectively
da, δa atmospheric delay for code and phase observations respectively
T tropospheric delay
I ionospheric delay
µj
= λ2 j /λ21 dm, δm multipath effect for code and phase observations respectively
M real-valued carrier phase ambiguity parameter
N integer-valued carrier phase ambiguity parameter
ρ satellite-receiver range
r position vector
u unit line-of-sight vector
ψ mapping function for tropospheric delays
P, Φ vector with code and phase observation respectively
ρ vector with satellite-receiver ranges
T vector with tropospheric delays
I vector with ionospheric delays
dt vector with lumped instrumental delays and clock errors
a vector with carrier phase ambiguities
Λ diagonal matrix with wavelengths as diagonal elements
G matrix with line-of-sight vectors
Ψ vector with mapping functions for tropospheric delays
D double difference operator
σp, σφ
σI
Estimation
standard deviation of code and phase observation respectively
standard deviation of ionospheric pseudo-observation
E{·} expectation operator
D{·} dispersion operator
y m-vector of observations
a n-vector with ambiguity parameters
b p-vector with real-valued parameters: baseline, atmospheric delays, etc.
e, ε noise parameters
A, B design matrices: E{y} = Aa + Bb + e
Qx
variance-covariance matrix of x
Qx|v conditional variance-covariance matrix: Qx|v = Qx − QxvQ−1 σ
v Qvx
2 variance factor
Gx
cofactor matrix of x: Qx = σ2 Q = LDL
Gx
T LDLT -decomposition of Q with lower triangular matrix L,
diagonal matrix D
σi|I conditional standard deviation of ith entry of a parameter vector
conditioned on the I = 1, . . . , i − 1 entries
xvi Notation and symbols