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The multipath effect error (MEE) is typically not taken into account by the RTKLIB localization method, and this may lead to poor positioning accuracy. This paper proposes an expectation maximization (EM) algorithm for GPS positioning based on Volterra series, and the pseudoranges contaminated by MEE are considered as missing data. Firstly, the Volterra series is introduced to linearize the pseudorange equation. Then, the EM algorithm is used to iteratively update the user location and missing data. Compared with the RTKLIB method, the proposed algorithm has more accurate positioning accuracy. The simulation example shows the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Reduced-order identification algorithms are usually used in machine learning and big data technologies, where the large-scale systems widely exist. For large-scale system identification, traditional least squares algorithm involves high-order matrix inverse calculation, while traditional gradient descent algorithm has slow convergence rates. The reduced-order algorithm proposed in this paper has some advantages over the previous work: (1) via sequential partitioning of the parameter vector, the calculation of the inverse of a high-order matrix can be reduced to low-order matrix inverse calculations; (2) has a better conditioned information matrix than that of the gradient descent algorithm, thus has faster convergence rates; (3) its convergence rates can be increased by using the Aitken acceleration method, therefore the reduced-order based Aitken algorithm is at least quadratic convergent and has no limitation on the step-size. The properties of the reduced-order algorithm are also given. Simulation results demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The traditional least squares (LS) and gradient descent (GD) algorithms can estimate the parameters of the regression models. They can be inefficient when the models have complex structures: (1) the unknown parameters in the information vector make the algorithm be impossible to update the parameters; (2) the zigzagging nature of the gradient descent algorithm and the complex structures lead to slow convergence rates; and (3) the step-size and derivative function calculations may be unsolvable for complex nonlinear models. This paper proposes two kinds of algorithms for exponential nonlinear models. The first is the two-stage algorithm, which decomposes the complex model into a linear part and a nonlinear part, where the linear part is estimated using the LS algorithm and the nonlinear part is identified based on the GD algorithm. The second is the particle swarm optimization algorithm which can simultaneously obtain all the parameters. To increase the convergence rates, the Aitken method is also introduced. The simulation results demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This article studies agent–server system identification problems by using a varying infimum gradient descent (VI-GD) algorithm. To efficiently use the GD algorithm for the agent–server with noise, a VI-GD algorithm, which performs a preconditioning matrix before the negative direction of the GD algorithm, is developed. This algorithm can reduce the infimum of the convergence rates without full matrix inversion calculation and can be extended to the systems with ill-conditioned information matrix. Convergence analysis and the comparisons with other methods show the effectiveness of the proposed algorithm. Furthermore, the theoretical results are also verified through simulations. [ABSTRACT FROM AUTHOR]

For Hammerstein output-error autoregressive systems, a decomposition based multi-innovation stochastic gradient (D-MISG) identification algorithm and a data filtering based multi-innovation stochastic gradient (F-MISG) identification algorithm are derived by means of the key-term separation principle and the multi-innovation identification theory. The D-MISG algorithm uses the decomposition technique to transform a Hammerstein system into two subsystems and requires less computational cost, and the F-MISG algorithm uses a linear filter to filter the input-output data and has a higher estimation accuracy for larger innovation lengths. The simulation results show that the proposed two algorithm can give satisfactory parameter estimates. [ABSTRACT FROM PUBLISHER]

This paper studies the parameter estimation problems of the Hammerstein nonlinear systems using the adaptive filtering technique. A linear filter based recursive least squares (LF-RLS) identification algorithm with good convergence properties and high parameter estimation accuracy is proposed by filtering the input-output data. A linear filter based multi-innovation stochastic gradient (LF-MISG) algorithm is proposed by the innovation expansion, in order to improve the computational efficiency of the LF-RLS algorithm. Furthermore, a time-varying factor is introduced in the linear filter to improve the convergence speed of the LF-MISG algorithm. The efficiency of the proposed algorithms are shown in comparison with the conventional identification algorithms. [ABSTRACT FROM AUTHOR]

This letter focuses on the parameter estimation of block-oriented Hammerstein nonlinear systems. In order to solve the dimension disaster problem and reduce the computational complexity of the over-parametrization based methods, a parameter separation based multi-innovation stochastic gradient identification algorithm is proposed by using the filtering technique and the multi-innovation identification theory. The proposed method can avoid estimating the redundant parameters and can generate highly accurate parameter estimates. A simulation example is provided to demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]