Robust Least Squares Estimator Research Articles

Vertical deformation analysis based on combined adjustment for GNSS and leveling data

A method is proposed to fuse the velocity data of the global navigation satellite system (GNSS) and leveling height via combined adjustment with constraints. First, stable GNSS–leveling points are uniformly selected, and the constraints of the geodetic height change velocity and normal height change velocity are given. Then, the GNSS vertical velocities and leveling height difference are used as observations of combined adjustment, and robust least-squares estimation are used to estimate the velocities of the unknown points. Finally, a vertical movement model is established with the GNSS vertical velocities and leveling vertical velocities obtained via combined adjustment. Data from the second-order leveling network and GNSS control points in Shandong Province are taken as test data, and eight calculation schemes are used for discussion. One of the schemes, the bifactor robust combined adjustment method based on variance component estimation with two kinds of vertical velocity constraints achieves the optimal results. The method applied in the scheme can be recommended for data fusion of GNSS and leveling, further improving the reliability of vertical crustal movement in Shandong Province.

Impact of Economic and Noneconomic Factors on Inflow of Remittances into Bangladesh

Purpose: Remittance plays an important role in the economy of Bangladesh. It also contributes to the change in the social structure and standard of living. The purpose of the study is to identify the economic and non-economic determinants of the remittance inflow into Bangladesh. 
 Methodology: The study considered two types of variables as the determinants of the remittance inflow: economic and non-economic. Economic determinants of remittances inflows included exchange rate, education, economic growth rate, and market interest rate. The non-economic determinants covered control of corruption, government effectiveness, and political stability. Monthly data were used for the case of economic determinants from 2014 to 2020 and annual data were used in the case of non-economic determinants from 1996 to 2018. The marginal effect of each variable has been analyzed by using the Robust Least Squares (RLS) method. 
 Results: The estimated results of this study state that, economic determinants like capital formation and education factors have a positive and significant impact on remittances inflows in both static and dynamic cases. However, the exchange rate does not create a positive impact due to volatility. The RLS estimation shows the control of corruption has a positive impact on remittances inflows whereas government effectiveness and political stability hurt remittances inflows in Bangladesh. 
 Implications: The current study identified the significant determinates of remittances inflows in Bangladesh. The findings have implications for policy formulation as regard remittances and non-resident Bangladeshis.

Empirical study of robust estimation methods for PAR models with application to the air quality area

This paper compares three estimators for periodic autoregressive (PAR) models. The first is the classical periodic Yule-Walker estimator (YWE). The second is a robust version of YWE (RYWE) which uses the robust autocovariance function in the periodic Yule-Walker equations, and the third is the robust least squares estimator (RLSE) based on iterative least squares with robust versions of the original time series. The daily mean particulate matter concentration (PM10) data is used to illustrate the methodologies in a real application, that is, in the Air Quality area.

Combined high-order algorithms in robust least-squares estimation with harmonic regressor and strictly diagonally dominant information matrix

This article describes new high-order algorithms in the least-squares problem with harmonic regressor and strictly diagonally dominant information matrix. Estimation accuracy and the number of steps to achieve this accuracy are controllable in these algorithms. Simplified forms of the high-order matrix inversion algorithms and the high-order algorithms of direct calculation of the parameter vector are found. The algorithms are presented as recursive procedures driven by estimation errors multiplied by the gain matrices, which can be seen as preconditioners. A simple and recursive (with respect to order) algorithm for update of the gain matrix, which is associated with Neumann series, is found. It is shown that the limiting form of the algorithm (algorithm of infinite order) provides perfect estimation. A new form of the gain matrix is also a basis for unification method of high-order algorithms. New combined and fast convergent high-order algorithms of recursive matrix inversion and algorithms of direct calculation of the parameter vector are presented. The stability of algorithms is proved and explicit transient bound on estimation error is calculated. New algorithms are simple, fast and robust with respect to round-off error accumulation.

Compensated robust least‐squares estimator for target localisation in sensor network using time difference of arrival measurements

A target localisation estimator based on time difference of arrival (TDOA) measurement is proposed. The localisation estimator is designed in the framework of the recently developed robust least-squares (RoLS) estimator, which provides an unbiased estimation result and can be implemented with a recursive filtering structure. However, when the RoLS estimator is applied to the localisation problem, its localisation performance depends on the knowledge of the stochastic information of the TDOA measurement. This dependency means that incorrectly given information causes localisation error. Therefore to complement the dependency of the given stochastic information of the TDOA measurement, we design a compensation procedure based on the constraints on the state variables of the estimator. The performance of the proposition under several cases of incorrectly given stochastic information is verified through computer simulation, and its filtering structure is compared with other existing localisation algorithms mathematically. In addition, the entire process of the proposed localisation estimator is derived as a recursive form for real-time applications.

Robust State Space Filtering Under Incremental Model Perturbations Subject to a Relative Entropy Tolerance

This paper considers robust filtering for a nominal Gaussian state-space model, when a relative entropy tolerance is applied to each time increment of a dynamical model. The problem is formulated as a dynamic minimax game where the maximizer adopts a myopic strategy. This game is shown to admit a saddle point whose structure is characterized by applying and extending results presented earlier in “Robust least-squares estimation with a relative entropy constraint” (B. C. Levy and R. Nikoukhah, IEEE Trans. Inf. Theory, vol. 50, no. 1, 89-104, Jan. 2004) for static least-squares estimation. The resulting minimax filter takes the form of a risk-sensitive filter with a time varying risk sensitivity parameter, which depends on the tolerance bound applied to the model dynamics and observations at the corresponding time index. The least-favorable model is constructed and used to evaluate the performance of alternative filters. Simulations comparing the proposed risk-sensitive filter to a standard Kalman filter show a significant performance advantage when applied to the least-favorable model, and only a small performance loss for the nominal model.

Recursive robust least squares estimator for time-varying linear systems with a noise corrupted measurement matrix

A recursive robust least-squares (RLS) estimator is newly proposed for time-varying linear systems with a noise-corrupted measurement matrix. Analysing the properties of the conventional least-squares (LS) estimator for uncertain systems reaches an inspirational result that the LS estimates contains both scale-factor and bias errors. The scale-factor error is caused by the auto-correlation of the stochastic parametric uncertainties in the measurement matrix, and the bias error comes from the correlation between the uncertain stochastic parameters and measurement noises. On the basis of this observation, the RLS estimation problem is reformulated as finding a compensation strategy of these errors. It is shown that the magnitudes of weighted errors in nominal LS estimates can be approximated using the known statistical information on the stochastic parametric uncertainty. Therefore if the existence condition is satisfied, a recursive RLS solution is readily derived by introducing the proper error compensation method to the nominal LS estimator. The suboptimality of the proposed approach is assessed in the sense of unbiasedness. Furthermore, it is pointed out that the proposed estimator can be reduced to the existing robust Kalman filter under certain conditions. A direct frequency estimation problem is provided to show that the proposed estimator can be an excellent choice for the actual estimator design problem in the presence of stochastic parametric uncertainties.

Robust motion estimation using spatial Gabor-like filters

This paper presents a new algorithm for motion estimation. It combines Gabor-like filter decomposition and robust least-squares estimation in a multiresolution framework. The spatial Gabor-like filter bank, based on recursive implementation, provides a fast multichannel decomposition of frame sequence. Then, applying the brightness constancy constraint on each channel between two consecutive frames, an over-determined system of velocity equations at each pixel is obtained. In order to be robust to outliers, this over-determined system is solved using a robust least-squares technique. A multiresolution framework is used in order to manage large and small displacements. Two kinds of recursive filter implementation have been tested: whereas third order filtering is very similar to a real Gabor filter, first order recursive filters are fastest and can be implemented with very large scale integration (VLSI) analog circuit. Performances of our algorithm for the two filter implementations are tested on synthetic and real sequences, and are compared with other techniques.