Study Of Least Squares And Its Improved Algorithm In Data Fitting Of Absolute Gravimeter

Gravity measurement aims at research on the gravity field of the earth,which helps people understand the shape of the earth,the internal material distribution,internal structure etc.,and is of great significance in navigation,military,earthquake research and resource exploration.To obtain the absolute gravity value is the key to gravity measurement systems.At present,the accurate measurement of gravitational acceleration in the field is achieved with the falling body laser interferometer absolute gravimeter,whose method is generally to produced laser interference fringes by free fall in the vacuum cavity,which is transformed into electrical signals by a photoelectric converter and then converted into digital signals by a high speed digitizer.The recombination of track-time distance coordinates of the falling body is gained through digital signal processing,and the gravitational acceleration in high precision is calculated by fitting algorithm.An appropriate fitting algorithm is of great importance to obtain the high-precision gravity field information.The least squares method,one of the most commonly used method of curve fitting and parameter estimation,is widely used in the fitting of absolute gravimeter data because of its simplicity,small amount of computation as well good convergence performance.But for the new problems in the practical measurement,algorithm is still needed to be explored and improved based on the conventional least squares method.In this paper,partial least squares regression is proposed considering the frequency variation characteristics of the absolute gravity interference signal.But the estimation by conventional least-squares method and partial least squares regression will be distorted seriously and can be even unacceptable for the abnormal point in the absolute gravimeter data segment.Therefore,the robust least squares method,involving the product of multidimensional matrix and inverse matrix,is put forward to solve this problem.In order to further improve the reliability,based on the matrix form of parameter estimation and features of the absolute gravity data,the weighted recursive least squares method is deduced,which transforms the complicated computing process into the repetition of a simple process,avoiding the multidimensional inverse matrix multiplication and inverse matrix solution,with advantages of simple code and less programming.Based on simulation data generated with MATLAB,parameters estimation is implemented by the conventional least squares method,the partial least squares regression,the robust least squares method and the weighted recursive least squares method respectively,whose result is compared and analyzed by the deviation between the calculated value and the set value,the standard error and the corresponding processing time.The result shows that the weighted recursive method gains a better effect in the absolute gravimeter data fitting,with a high stability and good fitting precision as well as a unique advantage in the inhibition of abnormal data.Then the actual absolute gravimeter data is processed using the four algorithms,and the result is analyzed by the average value,standard error and processing time.The result shows that the weighted recursive method gains an advantage over other three methods in anti-jamming ability to the uncertainty in the actual data,which is consistent with the case of simulation data.When applied to absolute gravimeter data processing of the free fall,the weighted recursive least squares method greatly inhibited the effects of abnormal points on the gravitational acceleration,whose accuracy and stability are improved.And better result is gained comparing to the conventional least squares method,partial least squares regression and robust least squares method.So the weighted recursive least squares method,with a good robust performance,is more suitable for data processing in absolute gravimeter.