Simplified equivalent representation of GPS observation equations

The single and double-differencing operation of GPS observations is effectively used to eliminate nuisance parameters of receiver- and satellite-specific biases. According to the theorem of equivalent representation, we develop the simplified equations that equivalently represent the single and double-differenced observation equations using corresponding pseudo-observations in single or multi-baseline solutions. The transformation of the covariance matrix of original observables is no longer necessary. Therefore, the algorithms are very convenient for programming and efficient in computation. The unbiased estimate of the variance of unit weight is also derived from equivalent observation equations. The simplified equations are verified by numerical examples.