A CONSTRAINED LEAST SQUARES FITTING TECHNIQUE FOR ARMA MODELING

Several ARMA modeling approaches are addressed. In these methods only part of a correlation sequence is employed for estimating parameters. It is satisfying, if the given correlation sequence is of real ARMA, since an ARMA process can be completely determined by part of its correlation se -quence. But for the case of a measured correlation sequence the whole sequence may be used to reduce the effect of error on model parameter estimation. In addition, these methods now do not guarantee a nonnegative spectral estimate. In view of the above-mentioned fact, a constrained least squares fitting technique is proposed which utilizes the whole measured correlation sequence and guarantees a nonnegative spectral estimate.

Large Scattered Data Fitting Based on Radial Basis Functions

Solving large radial basis function （RBF） interpolation problem with non-customized methods is computationally expensive and the matrices that occur are typically badly conditioned. In order to avoid these difficulties, we present a fitting based on radial basis functions satisfying side conditions by least squares, although compared with interpolation the method loses some accuracy, it reduces the computational cost largely. Since the fitting accuracy and the non-singularity of coefficient matrix in normal equation are relevant to the uniformity of chosen centers of the fitted RBE we present a choice method of uniform centers. Numerical results confirm the fitting efficiency.

Overlapped peaks resolution for linear sweep polarography using Gaussian-like distribution

A resolution method based on Gaussian-like distribution for overlapped linear sweep polarographic peaks was proposed to simultaneously detect the polymetallic components, such as Zn（Ⅱ） and Co（Ⅱ）, coexisting in the leaching solution of zinc hydrometallurgy. A Gaussian-like distribution was constructed as the sub-model of overlapped peaks by analyzing the characteristics of linear sweep polarographic curve. Then, the abscissas of each peak and trough were pinpointed through multi-resolution wavelet decomposition, the curve and its derivative curves were fitted by using nonlinear weighted least squares （NWLS）. Finally, overlapped peaks were resolved into independent sub-peaks based on fitted reconstruction parameters. The experimental results show that the relative error of half-wave potential pinpointed by multi-resolution wavelet decomposition is less than 1% and the accuracy of Ip fitted by NWLS is higher than 96%. The proposed resolution method is effective for overlapped linear sweep polarographic peaks of Zn（Ⅱ） and Co（Ⅱ）.

Human motion prediction using optimized sliding window polynomial fitting and recursive least squares

Human motion prediction is a critical issue in human-robot collaboration(HRC)tasks.In order to reduce the local error caused by the limitation of the capture range and sampling frequency of the depth sensor,a hybrid human motion prediction algorithm,optimized sliding window polynomial fitting and recursive least squares(OSWPF-RLS)was proposed.The OSWPF-RLS algorithm uses the human body joint data obtained under the HRC task as input,and uses recursive least squares(RLS)to predict the human movement trajectories within the time window.Then,the optimized sliding window polynomial fitting(OSWPF)is used to calculate the multi-step prediction value,and the increment of multi-step prediction value was appropriately constrained.Experimental results show that compared with the existing benchmark algorithms,the OSWPF-RLS algorithm improved the multi-step prediction accuracy of human motion and enhanced the ability to respond to different human movements.

Robust inversion analysis of local gravity anomalies caused by geological dislocation model of faults

Theoretical analysis and practical observations show that fault dislocations can change the gravity field around the fault. Gravity changes which were caused by the repeated dislocations over a long period of time were superimposed on the Bougeur gravity anomalies. These anomalies became the evidence of historical movement of fault as well as provide a way for the study of paleo earthquakes. This paper investigates inversion methods for the geological dislocation modeling of faults using the local Bouguer's gravity anomalies. To remove the effects of the irrelevant part of gravity anomalies to fault movements, we propose the robust nonlinear inversion method and set up the corresponding algorithm. Modeling examples indicate that the Marquardt's and Baye's least squares solutions depart from the true solution due to the attraction of gross errors in the data. The more seriously the data is contaminated, the more seriously the solutions are biased. In contrast, the proposed robust Marquardt's and Baye's inversion solutions can still maintain consistency with the solution without gross errors, even though 50 percent of the data is contaminated. This indicates that the proposed robust methods are effective. Using the proposed methods, we invert the geological dislocation models of the faults around the Erhai Lake in West Yunnan. The results show that the Northern Cangdong fault and the Erhai fault are normal dip slip faults with about 4 to 5 km dislocations; and that the Southern Cangdong fault has a less dip slip compared with the former two. A satisfactory fitting between the theoretical values of the inversion solution and the actual local gravity field is achievable.

Development of Precise Geoid Model for the Establishment of Consistent Height System in Geoga Grand Bridge Construction Area

The national benchmarks on islands were mostly established by trigonometric leveling in Korea. This method results in inaccuracy, which is a serious problem in Geoga Grand Bridge construction work that tried to link the mainland and the islands. The Geoga Grand Bridge （Pusan-Geoje fixed link project） was selected as the study area, a huge construction work in Korea that will connect the mainland （Pnsan） and an island （Gecje island）. However, the orthometric heights issued at benchmarks （JINH and GOFJ） were not consistent, because they did not refer to the same zero point, which would make the linking of the sections problematic. This paper introduces the precise local geoidas a vertical datum for the construction area in order to establish a consistent height system. To determine the precise local geoid for the construction area, we firstly developed a precise gravimetric geoid for Korea and its adjoining seas as a whole. This gravimetric geoid was developed by use of all available gravity data, including surface and satellite data on land and on the ocean. The gravimetrie gecid was computed by spherical fast fourier transform with modified Stokes＇ kernels. The remove-restore technique was used to eliminate the terrain effects by use of the RTM reduction and to determine the residual geoid by combining the GGM02S/EGM96 geopotential model, free-air gravity anomalies and high-resolutinn DEM data. Finally, the gravimetric model was fitted to the geoid heights obtained from GPS and tide observations （Ncps/Tiae） by least square coUocatian, to provide the final GPS-consistent local precise geoid model. The post-fit error （std. dev. ） of the final geoid to the NetS/Tide derived from GPS and tide observations was ± 2.2 cm for the construction area. We solved the height inconsistency problem by calculating the orthometric height of the benchmarks and the cnntrol points using the final geoid model. Also, the highly accurate orthometric height was estimated through the GPS/leveling technique by applying the developed local precise geoid. Therefore, the precise local geoid is expected to improve the quality of the construction procedure of the Geoga Grand Bridge.

Numerical partitioning of components for four-modal sedimentary grain-size distribution based on gradient descent method

The gradient descent(GD)method is used to fit the measured data(i.e.,the laser grain-size distribution of the sediments)with a sum of four weighted lognormal functions.The method is calibrated by a series of ideal numerical experiments.The numerical results indicate that the GD method not only is easy to operate but also could effectively optimize the parameters of the fitting function with the error decreasing steadily.The method is applied to numerical partitioning of laser grain-size components of a series of Garzêloess samples and three bottom sedimentary samples of submarine turbidity currents modeled in an open channel laboratory flume.The overall fitting results are satisfactory.As a new approach of data fitting,the GD method could also be adapted to solve other optimization problems.