  This arXiv upload is to clarify that the now well-known sorted QR MIMO
decoder was first presented in the 1995 IUGG General Assembly. We clearly go
much further in the sense that we directly incorporated reduction into this one
step, non-exact suboptimal integer solution. Except for these first few lines
up to this point, this paper is an unaltered version of the paper presented at
the IUGG1995 Assembly in Boulder.
  Ambiguity resolution of GPS carrier phase observables is crucial in high
precision geodetic positioning and navigation applications. It consists of two
aspects: estimating the integer ambiguities in the mixed integer observation
model and examining whether they are sufficiently accurate to be fixed as known
nonrandom integers. We shall discuss the first point in this paper from the
point of view of integer programming. A one-step nonexact approach is proposed
by employing minimum diagonal pivoting Gaussian decompositions, which may be
thought of as an improvement of the simple rounding-off method, since the
weights and correlations of the floating-estimated ambiguities are fully taken
into account. The second approach is to reformulate the mixed integer least
squares problem into the standard 0-1 linear integer programming model, which
can then be solved by using, for instance, the practically robust and efficient
simplex algorithm for linear integer programming. It is exact, if proper bounds
for the ambiguities are given. Theoretical results on decorrelation by
unimodular transformation are given in the form of a theorem.
