Study On The Method Of Robust Biased Estimation In The Baseline Solution

The data processing problems in measurement systems,such as control network adjustment,calculation of the internal and external azimuth elements in the photogrammetry,had been weighting with ill-posed model problems.The traditional LS estimate solution for this kind of ill-condition equation caused unstable parameter value,and the research on adjust method more reliable than the least squares method became very important.In this paper,on the basis of calculation of double difference model in GPS data processing,we tried to improve the method of pathological linear model and based on this basis differential biased estimation was researched.The GPS double difference observation model,the biased estimation and resistance estimation theory,the Helmert variance estimation theory,and also the singular value theory of the direct solution were studied in this paper.On this basis,the pathological GPS double difference observation model was analyzed and processed via the above methods.The results showed that these methods can improve the precision and stability of the parameters estimation of pathological GPS double difference observation model.The methods of the ridge estimation and partial ridge estimation were adopted when the application of biased estimation was used to process data.The ridge trace method,the L-curve method and the Helmert variance method were used respectively on the selection of ridge parameters for each method.It was found that the valuation accuracy of parameters by using these methods to process data could be obviously much higher than that of least squares,and the accurate ridge parameter values could be confirmed by the Helmert method,and maked sure that the ridge parameter possessing physical significance.In this paper,the pathological model were handled with Biased estimation could also get parameter value with high precision,but the truncated singular value method,ridge estimation method of singular value and the partial ridge estimation modified singular value method were the most suitable for the equation in the text.The morbid equation could be improved greatly by robust-biased estimation as well,and the influence of gross error could be eliminated,the precision of the valuation was enhanced obviously when the robust-biased estimation was used to deal with data with gross error.The methods within the accuracy problem of the biased estimation were also studied in this paper.For the purpose of this research,not only could solve the problems such as model ill-condition and containing gross error of GPS double difference observation,also could be applied to observation data obtained from other measurement techniques,and also had a certain reference value for data processing questions in other areas.