基于主成分分析的DEM粗差检测

Detection of Gross Errors in DEM Based on Principal Components Analysis

为探讨误差的空间分布特性对数字高程模型（DEM）粗差检测率的影响，建立了独立粗差模型和相关粗差模型，并模拟了不同粗差率（0．2％～3．0％）的数据．将随机分布的粗差加入DEM中，采用基于主成分分析的粗差检测算法进行了试验．结果表明，无论粗差是否空间相关，随粗差率增大，检测率均下降．对于独立分布的粗差，当粗差率小于1．0％时，基本可以定位所有污染数据；而对于空间相关的粗差，当粗差率等于1．0％时，检测率不足50％．可见，粗差的空间相关性及较大的粗差率均会降低基于主成分分析的粗差检测算法的检测率．

To probe into the effect of error spatial distribution on the detection rate of gross error for a digital elevation model （ DEM）, two different models, spike-like and pyramid-like gross error models, were constructed. Data with different gross error rates of 0.2% to 3.0% were simulated and added to DEM randomly. A detection algorithm based on the principal components analysis （PCA） was used for tests. The result shows that whether gross errors are spatially correlated or not, the detection rate decreases with increasing of the gross error rate. To a spike-like gross error, when the rate is below 1.0% , almost all gross errors can be found out. While to a pyramid-like gross error, the detection efficiency decreases to 50% when the rate is equal to 1.0%. It can be found that the spatial relativity and a high gross error rate will cut down the detection rate of the algorithm.