quadratic collocation

The solution was proposed for the problem of geodetic data processing by least squares collocation with additional conditions. Corresponding expressions were derived for the disturbance potential. They may be transformed easily tor any derivative of the potential. Results of numerical testing of the proposed method are discussed for the construction of altimeter-gravimetric geoid in the Black Sea area from satellite altimeter data and absolute gravity.

Three different principles were considered for the determination of the regulanzation parameter in the variational problem of data processing. These principles are based exclusively on properties of the covariance matrixes and they are treated as analogies of traditional principles of misclosure, quasisolution and smoothing functional, respectively. It is remarkable, that the classical case of the least squares collocation (with the regulanzation parameter equal to 1) was obtained as one of the roots of the equation corresponding to the misclosure principle.