矿区GPS高程异常相关向量机拟合模型

为提高GPS高程异常拟合的精度及可靠性,基于相关向量机模型(Relevance vector machine,RVM),提出了一种稀疏化概率式的GPS高程异常SVM拟合模型。以柯西核函数与交叉验证法构建相关向量机,并推导了置信区间的估计公式。以某矿区GPS高程控制网为例,构建了基于相关向量机的高程异常拟合模型,并与多项式拟合、BP神经网络和遗传最小二乘支持向量机进行精度对比,通过置信区间估计,评价拟合结果的可靠性。试验结果表明:1相关向量机的平均绝对误差(Mean absolute error,MAE)、平均绝对百分误差(Mean absolute percentage error,MAPE)、均方根误差(Root mean square error,RMSE)等精度指标均较大幅度优于多项式、BP神经网络和遗传最小二乘支持向量机;2测试数据集的实测高程异常均在相关向量机估计的置信区间内。上述试验结果进一步表明:相关向量机是一种精度及可靠性高的矿区GPS高程异常拟合方法,对于快速测定矿区正常高有一定的参考价值。

GPS Height Anomaly Fitting Model in Mining Area Based on the Relevant Vector Machine

In order to improve the accuracy and reliability of GPS height anomaly fitting,the GPS height anomaly fitting method based on the relevant vector machine (RVM) is established.The new model has the characteristics of sparse and probability.The relevance vector machine is established based on cauchy kernel function and the cross validation method,and the formula of confidence interval estimation is established.Taking the GPS height control network in a mining area as an example,the GPS height anomaly fitting model based on the relevant vector machine is put forward，the height anomaly fitting accuracy of the polynomial,BP neural network,genetic algorithm least squares support vector machine and the relevant vector machine are analyzed in depth.The reliability of the above methods are evaluated by means of confidence interval estimation.Indicators of mean absolute error(MAE),mean absolute percentage error(MAPE) and root mean square error(RMSE)are adopted to conducted evaluation of the accuracy of the above methods.The research results show that:①values of MAE,MAPE,RMSE of the new method proposed in this paper is superior than polynomial,BP neural network and genetic algorithm least squares support vector machine;②GPS height anomaly values of test data set are all within the estimated confidence intervals.The above research results further indicated that the fitting precision and reliability of the GPS height anomaly based on the relevant vector machine are good,it is very suitable for the GPS height anomaly fitting,therefore，the normal height in mining area can be measured quickly with high precision by this model.