Abstract: On the basis of the research of least squares collocation and multi-quadric equations interpolation,a new estimation method is presented.Penalised least squares technique is proposed to estimate parameters and the multi-quadric equation is chosen as R matrix.At the same time,the relationship of the observed points and non-observed points is also expressed as multi-quadric equation.The formulas of this method are deduced.Without the covariance equation of sign,the result obtained by the new method corresponds with that by the collocation method.It is also the expand of multi-quadric equations interpolation.So the new method can enlarge the use of collocation model.