Abstract Geometry free model for resolving GPS ambiguity is a linear model which does not take baseline components as unknown parameters. For the Geometry free model, the code observation is almost used in ambiguity resolution directly , and although the observation time span is very short, the design matrix will not have characteristics of multicollinearity,so that the geometry free model is very useful in ambiguity resolution. In this paper, the expressions for triple frequency float ambiguities and covariance matrix for the geometry free model have been deduced by use of the Kronecker product. The phenomena that the expression of covariance matrix is independent from the geometry between the receiver and satellites but only relates with code and phase noise and number of epochs , and the Ztransformation martrix Z is independent of the geometry between the receiver and satellites and number of epochs but only relates with code and phase noise is discovered by analysing the expression. Furthermore, the success rate of ambiguity resolution for single frequency, dual frequency and triple frequency is computed respectively. At last,the conclusions that only a few epochs need fixing ambiguities for dual frequency and triple frequency, and especially for triple frequency only one epoch needs fixing ambiguities are drawn.
