A new solution method is given for the general multiple collocation
problem formulated in terms of the covariance equations. By a
logarithmic transformation, the covariance equations reduce to ordinary
linear equations that can be handled using standard methods. Solution by
matrix inversion has the advantage that the analytical solutions can be
reconstructed. The method can be applied to each determined or
overdetermined subset of the covariance equations. It is demonstrated on
quintuple collocations of ocean surface vectors winds obtained from
buoys, three scatterometers and model forecasts, with representativeness
errors estimated from differences in spatial variances. The results are
in good agreement with those from quadruple collocation analyses
reported elsewhere. The average of the solutions from all determined
subsets of the covariance equations equals the least-squares solution of
all equations. The standard deviation of all solutions from determined
subsets agrees with the accuracy found in earlier triple and quadruple
collocation studies, but the difference between minimum and maximum
value is much larger. It is shown that this is caused by increased
statistical noise in more complex solutions. The averages of the error
covariances are close to zero, with a few exceptions that may point at
small deficiencies in the underlying error model. Precise accuracy
estimates are needed to decide to what extent statistical noise explains
the spreading in the results and what is the role of deficiencies in the
underlying error model.