Algorithms and statistical analysis for linear structured weighted total least squares problem

Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.

The structured total least squares algorithm research for passive location based on angle information

Based on the constrained total least squares （CTLS） passive location algorithm with bearing-only measurements, in this paper, the same passive location problem is transformed into the structured total least squares （STLS） problem.The solution of the STLS problem for passive location can be obtained using the inverse iteration method.It also expatiates that both the STLS algorithm and the CTLS algorithm have the same location mean squares error under certain condition.Finally, the article presents a kind of location and tracking algorithm for moving target by combining STLS location algorithm with Kalman filter （KF）.The efficiency and superiority of the proposed algorithms can be confirmed by computer simulation results.

A SUCCESSIVE LEAST SQUARES METHOD FOR STRUCTURED TOTAL LEAST SQUARES

A new method for Total Least Squares (TLS) problems is presented. It differs from previous approaches and is based on the solution of successive Least Squares problems. The method is quite suitable for Structured TLS (STLS) problems. We study mostly the case of Toeplitz matrices in this paper. The numerical tests illustrate that the method converges to the solution fast for Toeplitz STLS problems. Since the method is designed for general TLS problems, other structured problems can be treated similarly.

Robust structured total least squares algorithm for passive location

A new approach called the robust structured total least squares(RSTLS) algorithm is described for solving location inaccuracy caused by outliers in the single-observer passive location. It is built within the weighted structured total least squares(WSTLS)framework and improved based on the robust estimation theory.Moreover, the improved Danish weight function is proposed according to the robust extremal function of the WSTLS, so that the new algorithm can detect outliers based on residuals and reduce the weights of outliers automatically. Finally, the inverse iteration method is discussed to deal with the RSTLS problem. Simulations show that when outliers appear, the result of the proposed algorithm is still accurate and robust, whereas that of the conventional algorithms is distorted seriously.

Structural total least squares algorithm for locating multiple disjoint sources based on AOA/TOA/FOA in the presence of system error

Single-station passive localization technology avoids the complex time synchronization and information exchange between multiple observatories, and is increasingly important in electronic warfare. Based on a single moving station localization system, a new method with high localization precision and numerical stability is proposed when the measurements from multiple disjoint sources are subject to the same station position and velocity displacement. According to the available measurements including the angle-of-arrival(AOA), time-of-arrival(TOA), and frequency-of-arrival(FOA), the corresponding pseudo linear equations are deduced. Based on this, a structural total least squares(STLS) optimization model is developed and the inverse iteration algorithm is used to obtain the stationary target location. The localization performance of the STLS localization algorithm is derived, and it is strictly proved that the theoretical performance of the STLS method is consistent with that of the constrained total least squares method under first-order error analysis, both of which can achieve the Cramér-Rao lower bound accuracy. Simulation results show the validity of the theoretical derivation and superiority of the new algorithm.

Doping and alloying in atomically precise gold nanoparticles

The recent success in the synthesis and total structure determination of atomically precise gold nanoparticles has provided exciting opportunities for fundamental studies as well as the development of new applications. These unique nanoparticles are of molecular purity and possess well defined formulas （i.e., specific numbers of metal atoms and ligands）, resembling organic compounds. Crystallization of such molecularly pure nanoparticles into macroscopic single crystals allows for the determination of total structures of nanoparticles （i.e., the arrangement of metal core atoms and surface ligands） by X-ray crystallography. In this perspective article, we summarize recent efforts in doping and alloying gold nanoparticles with other metals, including Pd, Pt, Ag and Cu. With atomically precise gold nanoparticles, a specific number of foreign atoms （e.g., Pd, Pt） can be incorporated into the gold core, whereas a range of Ag and Cu substitutions is observed but, interestingly, the total number of metal atoms in the homogold nanoparticle is preserved. The heteroatom substitution of gold nanoparticles allows one to probe the optical, structural, and electronic properties truly at the single-atom level, and thus provides a wealth of information for understanding the intriguing properties of this new class of nanomaterials.