广义岭估计的直接解法

提出了广义岭估计的直接解法。该解法不需计算岭参数,可直接求得具有最小均方误差的解。并举例证实了该解法的优越性

Direct Solution to Generalized Ridge Estimate

Generally,under the Gauss-Markov model L = BX +Δ,the least square estimators of the parameters X = N ^-1 B^TL possess some nice characters.In surveying,especially in dynamic GPS surveying,ill-conditioned problems may be encountered.When the surveying system is morbid and then the characters of the least square estimators become bad.Adding a diagonally matrix K to N will improve the state of N and then decrease the total variance of the estimates.Recent investigations of ill-conditioned problems have demonstrated that ridge-type estimation methods provide increased solution accuracy over conventional estimation techniques.That the generalized ridge estimate has less mean square error than the least square estimation.Naturally,the gotten estimators is expected to reach the minimum of mean square error.Because the mean square error of estimators is the function of K ,we should fix K depending on the minimum of the mean square error.On the basis of this idea,this paper brings about a method to solve the above problem,which is called direct solution to generalized ridge estimate(DSGRE).With DSGRE,we can obtain the optimal solution(that possesses the minimum of MSE) to the generalized ridge estimate directly and the ridge parameters K needn't to be calculated.