and Zhang, B.: 2018, Precise point positioning with mixed use of time-differenced and undifferenced
carrier phase from multiple GNSS.
Unrestricted constant (C) model allows for a linear trend in the undifferenced
data (t = 0 and p = 0), cointegrating equations are stationary around a nonzero mean.
Liu, "URTK: undifferenced
network RTK positioning," GPS Solutions, vol.
The model for an undifferenced
GNSS pseudorange, [rho], and carrier-phase measurement, [phi], (with units of carrier cycles) is given as 
We start with a VAR model using undifferenced
data, including 8 lagged terms, and iteratively delete insignificant lags using the Bayesian Information Criteria (BIC).
Generally, the ZTD of GNSS signals can be estimated using undifferenced
precise point positioning (PPP) or differential strategies.
We first assume that [[beta].sub.0] = [[beta].sub.1] = 0 a priori, (i.e., we do not include any regressors in the undifferenced
regression model (11)).
Variables specified as additional instruments (lagged saving) are included, undifferenced
, in the instruments matrix.
We also estimated differenced models, but the undifferenced
models produced more parsimonious results.
The lag length of the Johansen procedure was determined by the Schwarz Information Criterion (SIC) on the undifferenced
VAR (See Schwarz, 1978) while ensuring all residual series from the VAR were uncorrelated.
All these studies find that the variables in their models must be differenced to become stationary, a property that undermines the validity of traditional estimation procedures and statistical inferences in regressions involving undifferenced