arXiv subjects

Maria Kulikova

Publications and source records attributed to Maria Kulikova.

4 recordsLinked to original sources

arXiv2023

Chandrasekhar-based maximum correntropy Kalman filtering with the adaptive kernel size selection

This technical note is aimed to derive the Chandrasekhar-type recursion for the maximum correntropy criterion (MCC) Kalman filtering (KF). For the classical KF, the first Chandrasekhar difference equation was proposed at the beginning of 1970s. This is the alternative to the traditionally used Riccati recursion and it yields the so-called fast implementations known as the Morf-Sidhu-Kailath-Sayed KF algorithms. They are proved to be computationally cheap because of propagating the matrices of a smaller size than $n \times n$ error covariance matrix in the Riccati recursion. The problem of deriving the Chandrasekhar-type recursion within the MCC estimation methodology has never been raised yet in engineering literature. In this technical note, we do the first step and derive the Chandrasekhar MCC-KF estimators for the case of adaptive kernel size selection strategy, which implies a constant scalar adjusting weight. Numerical examples substantiate a practical feasibility of the newly suggested MCC-KF implementations and correctness of the presented theoretical derivations.

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arXiv2023

One-step condensed forms for square-root maximum correntropy criterion Kalman filtering

This paper suggests a few novel Cholesky-based square-root algorithms for the maximum correntropy criterion Kalman filtering. In contrast to the previously obtained results, new algorithms are developed in the so-called {\it condensed} form that corresponds to the {\it a priori} filtering. Square-root filter implementations are known to possess a better conditioning and improved numerical robustness when solving ill-conditioned estimation problems. Additionally, the new algorithms permit easier propagation of the state estimate and do not require a back-substitution for computing the estimate. Performance of novel filtering methods is examined by using a fourth order benchmark navigation system example.

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arXiv2023

Continuous-discrete unscented Kalman filtering framework by MATLAB ODE solvers and square-root methods

This paper addresses the problem of designing the {\it continuous-discrete} unscented Kalman filter (UKF) implementation methods. More precisely, the aim is to propose the MATLAB-based UKF algorithms for {\it accurate} and {\it robust} state estimation of stochastic dynamic systems. The accuracy of the {\it continuous-discrete} nonlinear filters heavily depends on how the implementation method manages the discretization error arisen at the filter prediction step. We suggest the elegant and accurate implementation framework for tracking the hidden states by utilizing the MATLAB built-in numerical integration schemes developed for solving ordinary differential equations (ODEs). The accuracy is boosted by the discretization error control involved in all MATLAB ODE solvers. This keeps the discretization error below the tolerance value provided by users, automatically. Meanwhile, the robustness of the UKF filtering methods is examined in terms of the stability to roundoff. In contrast to the pseudo-square-root UKF implementations established in engineering literature, which are based on the one-rank Cholesky updates, we derive the stable square-root methods by utilizing the $J$-orthogonal transformations for calculating the Cholesky square-root factors.

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arXiv2023

Estimation of market efficiency process within time-varying autoregressive models by extended Kalman filtering approach

This paper explores a time-varying version of weak-form market efficiency that is a key component of the so-called Adaptive Market Hypothesis (AMH). One of the most common methodologies used for modeling and estimating a degree of market efficiency lies in an analysis of the serial autocorrelation in observed return series. Under the AMH, a time-varying market efficiency level is modeled by time-varying autoregressive (AR) process and traditionally estimated by the Kalman filter (KF). Being a linear estimator, the KF is hardly capable to track the hidden nonlinear dynamics that is an essential feature of the models under investigation. The contribution of this paper is threefold. We first provide a brief overview of time-varying AR models and estimation methods utilized for testing a weak-form market efficiency in econometrics literature. Secondly, we propose novel accurate estimation approach for recovering the hidden process of evolving market efficiency level by the extended Kalman filter (EKF). Thirdly, our empirical study concerns an examination of the Standard and Poor's 500 Composite stock index and the Dow Jones Industrial Average index. Monthly data covers the period from November 1927 to June 2020, which includes the U.S. Great Depression, the 2008-2009 global financial crisis and the first wave of recent COVID-19 recession. The results reveal that the U.S. market was affected during all these periods, but generally remained weak-form efficient since the mid of 1946 as detected by the estimator.

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