On the probability density function of the GNSS ambiguity residuals

where y is the random vector with m double difference code and phase observations, a the n-vector with unknown integer carrier phase ambiguities, i.e. a2Z, b is a p-vector with the unknown real-valued parameters, and e is the noise vector. The real-valued parameters are referred to as the baseline unknowns, although b may also contain for example atmospheric delays. The covariance matrix of the observation vector is given by Qy. Taking into account the integer nature of the ambiguity parameters in an optimal way, cf. (Teunissen 1999), involves that a non-standard least-squares problem has to be solved, referred to as integer leastsquares (ILS), (Teunissen 1993). The solution of model (1) is then obtained by the following minimization problem: