LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION

In this article, we study a least squares estimator （LSE） of θ for the Ornstein- Uhlenbeck process X0=0,dXt=θXtdt＋dBt^ab, t ≥ 0 driven by weighted fractional Brownian motion B^a,b with parameters a, b. We obtain the consistency and the asymptotic distribution of the LSE based on the observation {Xs, s∈[0,t]} as t tends to infinity.

ERRATUM TO： LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION （ACTA MATHEMATICA SCIENTIA 2016,36B （2） ：394-408）

We give a correction of Theorem 2.2 of Shen, Yin and Yan （2016）.

Recursive weighted least squares estimation algorithm based on minimum model error principle

Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.

A new method of weighted choice in InSAR Least Squares unwrapping

The decorelation phenomena such as Low-SNR radar signal, shadows and layover caused by topography etc, causes phase data discontinuous and makes the result of unwrapping phase inaccurate or completely wrong. Based on the analysis of influencing factors to the weight selection, this paper develops a new method to choose the weights based on the measurement of confidence in frequency domain. Results show that it is more precise and robust than other methods, and can make up for the defect of sub-estimate to the slope of least squares method.

Hybrid Architecture and Beamforming Optimization for Millimeter Wave Systems

Hybrid beamforming(HBF)has become an attractive and important technology in massive multiple-input multiple-output(MIMO)millimeter-wave(mmWave)systems.There are different hybrid architectures in HBF depending on different connection strategies of the phase shifter network between antennas and radio frequency chains.This paper investigates HBF optimization with different hybrid architectures in broadband point-to-point mmWave MIMO systems.The joint hybrid architecture and beamforming optimization problem is divided into two sub-problems.First,we transform the spectral efficiency maximization problem into an equivalent weighted mean squared error minimization problem,and propose an algorithm based on the manifold optimization method for the hybrid beamformer with a fixed hybrid architecture.The overlapped subarray architecture which balances well between hardware costs and system performance is investigated.We further propose an algorithm to dynamically partition antenna subarrays and combine it with the HBF optimization algorithm.Simulation results are presented to demonstrate the performance improvement of our proposed algorithms.

A new method of weight choice in InSAR least squares unwrapping

The de-coherence phenomena such as Low-SNR radar signal, shadows and layover caused by topography, etc. , causing phase data discontinuity, makes the result of unwrapping phase inaccuracy or even completely wrong. Based on the analysis of influencing factors to weight choice, this thesis develops a new method to choose the weights based on the measure of the confidence in the frequency domain. Experiments show that it could overcome the defect of sub-estimate to the slope of least squares method very well, which has a better rationale, stability and performance.

ADJUSTMENT OF LEVELING NETWORK BY INFORMATION SPREAD ESTIMATION

In practical parameter estimation,we have always chosen either Least Squares Estimation(LSE) or Robust Estimation.Since the distribution of observations is unknown,to select a correct estimation method is very difficult.It is well known that if observations include gross errors,the result of LSE will be badly containinated.On the other hand,if observations do not include any gross errors,the result of robust estimation is not as good as that of LSE.To solve this problem,Wang (1999) developed an estimation method called Information Spread Estimation (ISE) based on the information spread principle.The ISE is a very good method for estimating one parameter which is very robust.However, most of instances in surveying data processing are multi_parameters’ estimation,owing to the inherent restrictions of ISE,it can not be applied to the surveying data processing directly.To apply the good method to the field of surveying data processing widely,the author has done the research deeply.This paper applies ISE successfully to the adjustment of leveling network by using the specialties of leveling.

A weighted averaging method for signal probability of logic circuit combined with reconvergent fan-out structures

By analyzing the structures of circuits,a novel approach for signal probability estimation of very large-scale integration(VLSI)based on the improved weighted averaging algorithm(IWAA)is proposed.Considering the failure probability of the gate,first,the first reconvergent fan-ins corresponding to the reconvergent fan-outs were identified to locate the important signal correlation nodes based on the principle of homologous signal convergence.Secondly,the reconvergent fan-in nodes of the multiple reconverging structure in the circuit were identified by the sensitization path to determine the interference sources to the signal probability calculation.Then,the weighted signal probability was calculated by combining the weighted average approach to correct the signal probability.Finally,the reconvergent fan-out was quantified by the mixed-calculation strategy of signal probability to reduce the impact of multiple reconvergent fan-outs on the accuracy.Simulation results on ISCAS85 benchmarks circuits show that the proposed method has approximate linear time-space consumption with the increase in the number of the gate,and its accuracy is 4.2%higher than that of the IWAA.

STUDY ON FREQUENCY ESTIMATION BASED ON WEIGHTED LEAST SQUARE METHOD WITH THREE FOURIER COEFFICIENTS

In this paper,a sinusoidal signal frequency estimation algorithm is proposed by weighted least square method.Based on the idea of Provencher,three biggest Fourier coefficients in the maximum periodogram are considered,the Fourier coefficients can be written as three equations about the amplitude,phase,and frequency,and the frequency is estimated by solving equations.Because of the error of measurement,weighted least square method is used to solve the frequency equation and get the signal frequency.It is shown that the proposed estimator can approach the Cramer-Rao Bound(CRB)with a low Signal-to-Noise Ratio(SNR)threshold and has a higher accuracy.

2.5D induced polarization forward modeling using the adaptive finite-element method

The conventional finite-element（FE） method often uses a structured mesh, which is designed according to the user’s experience, and it is not sufficiently accurate and flexible to accommodate complex structures such as dipping interfaces and rough topography. We present an adaptive FE method for 2.5D forward modeling of induced polarization（IP）. In the presented method, an unstructured triangulation mesh that allows for local mesh refinement and flexible description of arbitrary model geometries is used. Furthermore, the mesh refinement process is guided by dual error estimate weighting to bias the refinement towards elements that affect the solution at the receiver locations. After the final mesh is generated, the Jacobian matrix is used to obtain the IP response on 2D structure models. We validate the adaptive FE algorithm using a vertical contact model. The validation shows that the elements near the receivers are highly refined and the average relative error of the potentials converges to 0.4 % and 1.2 % for the IP response. This suggests that the numerical solution of the adaptive FE algorithm converges to an accurate solution with the refined mesh. Finally, the accuracy and flexibility of the adaptive FE procedure are also validated using more complex models.

Visualising data distributions with kernel density estimation and reduced chi-squared statistic

The application of frequency distribution statistics to data provides objective means to assess the nature of the data distribution and viability of numerical models that are used to visualize and interpret data.Two commonly used tools are the kernel density estimation and reduced chi-squared statistic used in combination with a weighted mean.Due to the wide applicability of these tools,we present a Java-based computer application called KDX to facilitate the visualization of data and the utilization of these numerical tools.

Ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints

The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the mixed additive and multiplicative random error model with equality constraints and derive the weighted least squares iterative solution of the model. In addition, aiming at the ill-posed problem of the coefficient matrix, we also propose the ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints based on the principle of ridge estimation method and derive the U-curve method to determine the ridge parameter. The experimental results show that the weighted least squares iterative solution can obtain more reasonable parameter estimation and precision information than existing solutions, verifying the feasibility of applying the equality constraints to the mixed additive and multiplicative random error model. Furthermore, the ridge estimation iterative solution can obtain more accurate parameter estimation and precision information than the weighted least squares iterative solution.

CHANNEL ERROR CORRECTION FOR WIDEBAND SAR-A JOINT MULTIPLE SUBPULSES PROCESSING METHOD

A novel method,referred to as joint multiple subpulses processing,is developed to calibrate the nonideal transfer function of radio frequency front-end and I/Q imbalance in quadrature modulate/demodulate systems simultaneously,which frequently occur in wideband Synthetic Aperture Radar(SAR) systems.Based on the time-frequency relation of the chirp signal and the analyses of the channel errors in wideband SAR,joint multiple subpulses processing method is adopted to separate the image frequency component due to the I/Q channel error.Then,the complete description of the channel error is acquired for building the correction function,which is used to correct the radar raw echo in frequency domain.The validity and capability of this method are demonstrated by the experiments of the channel error correction on the high resolution SAR system with the effective bandwidth of 500 MHz.

Geo-location for Ground Target with Multiple Observations Using Unmanned Aerial Vehicle

In order to improve the target location accuracy of unmanned aerial vehicle(UAV),a novel target location method using multiple observations is proposed.Firstly,the camera intrinsic parameters are calibrated.Then,the weighted least squares estimation is used to improve the localization precision because the traditional crossover method is vulnerable to noise and has low precision.By repeatedly measuring the same target point,a nonlinear observation equation is established and then covered to linear equations using Taylor expansion.The weighted matrix is obtained according to the height of the measurement point and the camera optic axis pointing angle,and then the weighted least squares estimation is used to calculate the target position iteratively.Finally,the effectiveness and robustness of this method is verified by numerical simulation and flight test.The results show that this method can effectively improve the precision of target location.

Deep Unfolding for Cooperative Rate Splitting Multiple Access in Hybrid Satellite Terrestrial Networks

Rate splitting multiple access(RSMA)has shown great potentials for the next generation communication systems.In this work,we consider a two-user system in hybrid satellite terrestrial network(HSTN)where one of them is heavily shadowed and the other uses cooperative RSMA to improve the transmission quality.The non-convex weighted sum rate(WSR)problem formulated based on this model is usually optimized by computational burdened weighted minimum mean square error(WMMSE)algorithm.We propose to apply deep unfolding to solve the optimization problem,which maps WMMSE iterations into a layer-wise network and could achieve better performance within limited iterations.We also incorporate momentum accelerated projection gradient descent(PGD)algorithm to circumvent the complicated operations in WMMSE that are not amenable for unfolding and mapping.The momentum and step size in deep unfolding network are selected as trainable parameters for training.As shown in the simulation results,deep unfolding scheme has WSR and convergence speed advantages over original WMMSE algorithm.

Total least-squares EIO model,algorithms and applications

A functional model named EIO(Errors-In-Observations) is proposed for general TLS(total least-squares)adjustment. The EIO model only considers the correction of the observation vector, but doesn't consider to correct all elements in the design matrix as the EIV(Errors-In-Variables) model does, furthermore, the dimension of cofactor matrix is much smaller. Iterative algorithms for the parameter estimation and their precise covariance matrix are derived rigorously, and the computation steps are also presented. The proposed approach considers the correction of the observations in the coefficient matrix, and ensures their agreements in every matrix elements. Parameters and corrections can be solved at the same time.An approximate solution and a precise solution of the covariance matrix can be achieved by corresponding algorithms. Applications of EIO model and the proposed algorithms are demonstrated with several examples. The results and comparative studies show that the proposed EIO model and algorithms are feasible and reliable for general adjustment problems.

A Robust Algorithm for Estimating Motion Parameters Based on the Modified LMedS

We put forward a robust method for estimating motion parameters from the 3-D space position vectors of feature points on the basis of the modified least median of squares (LMedS) regression estimator. First, initial values of motion parameters are estimated by the primary LMedS, then the motion parameters with an iterative reweighted estimator are re-estimated, in which a hybrid weight function of Huber weight and Tukey weight takes place of the dichotomy weight in the primary LMedS, The algorithm alleviates the difficulty of deleting some outliers while SNR is too low, so we can get a more accurate estimation. Computer simulations show that its performance is satisfactory.

Estimating the Parameters Geographically Weighted Regression (GWR) with Measurement Error

Geographically weighted regression models with the measurement error are a modeling method that combines the global regression models with the measurement error and the weighted regression model. The assumptions used in this model are a normally distributed error with that the expectation value is zero and the variance is constant. The purpose of this study is to estimate the parameters of the model and find the properties of these estimators. Estimation is done by using the Weighted Least Squares (WLS) which gives different weighting to each location. The variance of the measurement error is known. Estimators obtained are . The properties of the estimator are unbiased and have a minimum variance.

ON ANALYSIS METHOD FOR INFRARED MULTI-SITES SYSTEM PERFORMANCE

The calculation method about infrared multi-sites passive system location is introduced based on the principle of the weighted least square method, and the variance matrix of estimated error is offered. Through deduction, it can be found out that treated appraise precision can be directly analyzed and deduced without carrying out real measure and reaching estimation value. The simulation result shows that the system performance based on the weighted least square method is much better than the traditional passive location method, and it can be also used for reference to the research of the location algorithm of similar system.

Parameter Estimation for the NEAR(p) Model

As to the acronym NEAR（p）, it means “New Exponential Autoregressive Process of order p”. The NEAR（p） model is defined by