Skip to main content

Maria Adam

UNIVERSITY OF THESSALY, GREECE, Computer Science and Biomedical Informatics, Faculty Member

Followers

22

Following

34

Co-authors

7

Mentions

1

Public Views

Address: Greece

less

InterestsView All (7)

Uploads

Papers by Maria Adam

Proceedings of the Workshop on Parallel and Distributed Systems: Testing, Analysis, and Debugging

Nonrecursive solution for the discrete algebraic Riccati equation and X + A*X-1A=L

Open Mathematics, 2015

In this paper, we present two new algebraic algorithms for the solution of the discrete algebraic... more In this paper, we present two new algebraic algorithms for the solution of the discrete algebraic Riccati equation. The first algorithm requires the nonsingularity of the transition matrix and is based on the solution of a standard eigenvalue problem for a new symplectic matrix; the proposed algorithm computes the extreme solutions of the discrete algebraic Riccati equation. The second algorithm solves the Riccati equation without the assumption of the nonsingularity of the transition matrix; the proposed algorithm is based on the solution of the matrix equation X C A X 1 A D L; where A is a singular matrix and L a positive definite matrix.

Iterative and Algebraic Algorithms for the Computation of the Steady State Kalman Filter Gain

ISRN Applied Mathematics (Print), May 4, 2014

The Kalman filter gain arises in linear estimation and is associated with linear systems. The gai... more The Kalman filter gain arises in linear estimation and is associated with linear systems. The gain is a matrix through which the estimation and the prediction of the state as well as the corresponding estimation and prediction error covariance matrices are computed. For time invariant and asymptotically stable systems, there exists a steady state value of the Kalman filter gain. The steady state Kalman filter gain is usually derived via the steady state prediction error covariance by first solving the corresponding Riccati equation. In this paper, we present iterative per-step and doubling algorithms as well as an algebraic algorithm for the steady state Kalman filter gain computation. These algorithms hold under conditions concerning the system parameters. The advantage of these algorithms is the autonomous computation of the steady state Kalman filter gain.

Discrete Time Kalman and Lainiotis 1 Filters Comparison

A comparison study between the discrete time Kalman filter and the Lainiotis filter is presented.... more A comparison study between the discrete time Kalman filter and the Lainiotis filter is presented. It is pointed out that the two filters calculate the same estimates, thus the filters are equivalent with respect to their behavior. The calculation burdens of the filtering algorithms are determined. A method is proposed to a-priori (before the filters' implementation) decide which filter is the faster one.

Fast Doubling Algorithm for the Solution of the Riccati Equation Using Cyclic Reduction Method

A new iterative doubling algorithm for the solution of the discrete time Riccati equation is prop... more A new iterative doubling algorithm for the solution of the discrete time Riccati equation is proposed. The algorithm is based on the Cyclic Reduction Method (CRM). The proposed doubling algorithm does not require non-singularity of the transition matrix and is faster than the classical doubling algorithm. The method can be applied to infinite measurement noise case, where the Riccati equation takes the form of the Lyapunov equation. In this case, the classical doubling algorithm is faster.

Global Systems for Mobile Position Tracking Using Kalman and Lainiotis Filters

The Scientific World Journal, 2014

We present two time invariant models for Global Systems for Mobile (GSM) position tracking, which... more We present two time invariant models for Global Systems for Mobile (GSM) position tracking, which describe the movement in-axis and-axis simultaneously or separately. We present the time invariant filters as well as the steady state filters: the classical Kalman filter and Lainiotis Filter and the Join Kalman Lainiotis Filter, which consists of the parallel usage of the two classical filters. Various implementations are proposed and compared with respect to their behavior and to their computational burden: all time invariant and steady state filters have the same behavior using both proposed models but have different computational burden. Finally, we propose a Finite Impulse Response (FIR) implementation of the Steady State Kalman, and Lainiotis filters, which does not require previous estimations but requires a well-defined set of previous measurements.

Fast iterative solutions of Riccati and Lyapunov equations

Open Mathematics, 2022

In this article, new iterative algorithms for solving the discrete Riccati and Lyapunov equations... more In this article, new iterative algorithms for solving the discrete Riccati and Lyapunov equations are derived in the case where the transition matrix is diagonalizable with real eigenvalues. It is shown that the proposed iterative algorithms are faster than the classical ones, even for a small number of iterations.

Distributed Periodic Steady State Kalman Filter

International journal of circuits, systems and signal processing, Jan 10, 2022

Kalman filter [1]-[2] is the most well-known and widely used estimation algorithm, since it has b... more Kalman filter [1]-[2] is the most well-known and widely used estimation algorithm, since it has been used to successfully solve real time p roblems in various applications, such as in [ 2] aerospace industry, chemical process, communication systems design, control, civil engineering, filtering noise from two dimensional images, pollution prediction and power systems. The estimation problem is associated with time varying systems described by the following state space equations: x(k + 1) = F(k)x(k) + w(k) (1) z(k) = H(k)x(k) + v(k) (2) where x(k) is the n-dimensional state vector, z(k) is the m-dimensional measurement vector, F(k) is the transition matrix, H(k) is the output matrix, w(k) is the state noise and v(k) is the measurement noise at time k ≥ 0. The statistical model expresses the nature of the state and the measurements. The basic assumption is that the state noise and the measurement noise are zero mean Gaussian processes with known covariances Q(k) and R(k), respectively. The following assumptions hold: (a) the initial value of the state x(0) is a Gaussian random variable with known mean 0 and covariance P 0 ; (b) the noise processes and the initial state are independent. Periodic linear systems arise from continuous linear systems, when multi-rate sampling is performed, with many interesting and practical applications as stated in [3]. In this paper we focus on the case of periodic models and especially on the periodic steady state Kalman filter [4]-[6]. Parallel Kalman Filter implementations are mentioned in [7]. Distributed implementations for the steady state Kalman filter are proposed in [8]. The problem of distributed state estimation is addressed in [9]. The problem of distributed state estimation has been

FIR implementation of the Steady-State Kalman Filter

International Journal of Signal and Imaging Systems Engineering, 2008

... Maria Adam Department of Computer Science and Biomedical Informatics, University of Central G... more

Kalman Filter Riccati Equation for the Prediction, Estimation, and Smoothing Error Covariance Matrices

ISRN Computational Mathematics (Online), Dec 12, 2013

The classical Riccati equation for the prediction error covariance arises in linear estimation an... more The classical Riccati equation for the prediction error covariance arises in linear estimation and is derived by the discrete time Kalman filter equations. New Riccati equations for the estimation error covariance as well as for the smoothing error covariance are presented. These equations have the same structure as the classical Riccati equation. The three equations are computationally equivalent. It is pointed out that the new equations can be solved via the solution algorithms for the classical Riccati equation using other well-defined parameters instead of the original Kalman filter parameters.

Steady state Kalman filter design for cases and deaths prediction of Covid-19 in Greece

Results in Physics, 2021

In this work we study the applicability of the steady state Kalman filter in order to predict new... more In this work we study the applicability of the steady state Kalman filter in order to predict new cases and deaths of Covid-19. We use the actual observations of new cases and deaths. First, we deal with short term prediction, namely daily prediction. We propose the use of the golden steady state Kalman Filter, which is designed to have parameters related to the golden section. It was found that the proposed golden steady state Kalman Filter has a satisfactory behavior compared with the classical mean or average filter. Secondly, we deal with long term prediction, for example average prediction per quarantine period (14 days). We propose to process blocks of measurements of time window corresponding for example to the quarantine period in order to predict the average of cases and deaths using steady state Kalman Filter. It was found that the proposed golden steady state Kalman Filter produces more reliable predictions than the classical mean or average filter does. The use of steady state Kalman Filter for cases and deaths prediction of Covid-19 can be effective for resources and prevention measures planning.

The Joint Numerical Range of Bordered and Tridiagonal Matrices

30 Maria Adam and John Maroulas Recently a connection of Co {JNR [^ m]^= 1} with the numerical ra... more

On compressions of normal matrices

Linear Algebra and its Applications, 2002

Let A be a normal matrix and consider the polygon NR[A] = {x * Ax: x = 1}. If υ * Aυ ∈ int NR[A],... more

Sequences of lower and upper bounds for the spectral radius of a nonnegative matrix

Linear Algebra and its Applications, Jun 1, 2023

Enumeration of the roots of Boolean matrices

Nucleation and Atmospheric Aerosols, 2018

The number of the roots of certain Boolean matrices is calculated in this paper. In particular, t... more

Inversion Free Algorithms for Computing the Principal Square Root of a Matrix

International Journal of Mathematics and Mathematical Sciences, 2014

New algorithms are presented about the principal square root of an × matrix. In particular, all t... more New algorithms are presented about the principal square root of an × matrix. In particular, all the classical iterative algorithms require matrix inversion at every iteration. The proposed inversion free iterative algorithms are based on the Schulz iteration or the Bernoulli substitution as a special case of the continuous time Riccati equation. It is certified that the proposed algorithms are equivalent to the classical Newton method. An inversion free algebraic method, which is based on applying the Bernoulli substitution to a special case of the continuous time Riccati equation, is also proposed.

Bounds on the Spectral Radius of Nonnegative Matrices

In this paper, we determine some new bounds for the spectral radius of a nonnegative matrix with ... more In this paper, we determine some new bounds for the spectral radius of a nonnegative matrix with respect to the upper and the lower bounds for the spectral radius given by Frobenius’ bounds, by using similarity transformations. We also provide illustrative examples in order to compare the new bounds with the existing ones.

On the Positive Definite Solutions of the Matrix Equation XS + A*X-S A = Q

The Open Applied Mathematics Journal, Nov 30, 2011

In this paper, necessary and sufficient conditions for the existence of the positive definite sol... more In this paper, necessary and sufficient conditions for the existence of the positive definite solutions of the nonlinear matrix equation X s + A * X ! s A = Q are presented, when A is nonsingular and s an integer, as well as some new properties and bounds for the eigenvalues of matrices related to A,Q are discussed. An algebraic method for the computation of the solutions is proposed, based on the algebraic solution of the corresponding discrete time Riccati equation. The exact number of the positive definite solutions is also computed.

k-Step Sum and m-Step Gap Fibonacci Sequence

ISRN Discrete Mathematics (Online), Apr 9, 2014

For two given integers k, m, we introduce the k-step sum and m-step gap Fibonacci sequence by pre... more For two given integers k, m, we introduce the k-step sum and m-step gap Fibonacci sequence by presenting a recurrence formula that generates the nth term as the sum of k successive previous terms starting the sum at the mth previous term. Known sequences, like Fibonacci, tribonacci, tetranacci, and Padovan sequences, are derived for specific values of k, m. Two limiting properties concerning the terms of the sequence are presented. The limits are related to the spectral radius of the associated {0, 1}-matrix.

On the Covariance of Regression Coefficients

Open Journal of Statistics, 2015

In many applications, such as in multivariate meta-analysis or in the construction of multivariat... more In many applications, such as in multivariate meta-analysis or in the construction of multivariate models from summary statistics, the covariance of regression coefficients needs to be calculated without having access to individual patients' data. In this work, we derive an alternative analytic expression for the covariance matrix of the regression coefficients in a multiple linear regression model. In contrast to the well-known expressions which make use of the cross-product matrix and hence require access to individual data, we express the covariance matrix of the regression coefficients directly in terms of covariance matrix of the explanatory variables. In particular, we show that the covariance matrix of the regression coefficients can be calculated using the matrix of the partial correlation coefficients of the explanatory variables, which in turn can be calculated easily from the correlation matrix of the explanatory variables. This is very important since the covariance matrix of the explanatory variables can be easily obtained or imputed using data from the literature, without requiring access to individual data. Two important applications of the method are discussed, namely the multivariate meta-analysis of regression coefficients and the so-called synthesis analysis, and the aim of which is to combine in a single predictive model, information from different variables. The estimator proposed in this work can increase the usefulness of these methods providing better results, as seen by application in a publicly available dataset. Source code is provided in the Appendix and in http://www.compgen.org/tools/regression.

Proceedings of the Workshop on Parallel and Distributed Systems: Testing, Analysis, and Debugging

Nonrecursive solution for the discrete algebraic Riccati equation and X + A*X-1A=L

Open Mathematics, 2015

In this paper, we present two new algebraic algorithms for the solution of the discrete algebraic... more In this paper, we present two new algebraic algorithms for the solution of the discrete algebraic Riccati equation. The first algorithm requires the nonsingularity of the transition matrix and is based on the solution of a standard eigenvalue problem for a new symplectic matrix; the proposed algorithm computes the extreme solutions of the discrete algebraic Riccati equation. The second algorithm solves the Riccati equation without the assumption of the nonsingularity of the transition matrix; the proposed algorithm is based on the solution of the matrix equation X C A X 1 A D L; where A is a singular matrix and L a positive definite matrix.

Iterative and Algebraic Algorithms for the Computation of the Steady State Kalman Filter Gain

ISRN Applied Mathematics (Print), May 4, 2014

The Kalman filter gain arises in linear estimation and is associated with linear systems. The gai... more The Kalman filter gain arises in linear estimation and is associated with linear systems. The gain is a matrix through which the estimation and the prediction of the state as well as the corresponding estimation and prediction error covariance matrices are computed. For time invariant and asymptotically stable systems, there exists a steady state value of the Kalman filter gain. The steady state Kalman filter gain is usually derived via the steady state prediction error covariance by first solving the corresponding Riccati equation. In this paper, we present iterative per-step and doubling algorithms as well as an algebraic algorithm for the steady state Kalman filter gain computation. These algorithms hold under conditions concerning the system parameters. The advantage of these algorithms is the autonomous computation of the steady state Kalman filter gain.

Discrete Time Kalman and Lainiotis 1 Filters Comparison

A comparison study between the discrete time Kalman filter and the Lainiotis filter is presented.... more A comparison study between the discrete time Kalman filter and the Lainiotis filter is presented. It is pointed out that the two filters calculate the same estimates, thus the filters are equivalent with respect to their behavior. The calculation burdens of the filtering algorithms are determined. A method is proposed to a-priori (before the filters' implementation) decide which filter is the faster one.

Fast Doubling Algorithm for the Solution of the Riccati Equation Using Cyclic Reduction Method

A new iterative doubling algorithm for the solution of the discrete time Riccati equation is prop... more A new iterative doubling algorithm for the solution of the discrete time Riccati equation is proposed. The algorithm is based on the Cyclic Reduction Method (CRM). The proposed doubling algorithm does not require non-singularity of the transition matrix and is faster than the classical doubling algorithm. The method can be applied to infinite measurement noise case, where the Riccati equation takes the form of the Lyapunov equation. In this case, the classical doubling algorithm is faster.

Global Systems for Mobile Position Tracking Using Kalman and Lainiotis Filters

The Scientific World Journal, 2014

We present two time invariant models for Global Systems for Mobile (GSM) position tracking, which... more We present two time invariant models for Global Systems for Mobile (GSM) position tracking, which describe the movement in-axis and-axis simultaneously or separately. We present the time invariant filters as well as the steady state filters: the classical Kalman filter and Lainiotis Filter and the Join Kalman Lainiotis Filter, which consists of the parallel usage of the two classical filters. Various implementations are proposed and compared with respect to their behavior and to their computational burden: all time invariant and steady state filters have the same behavior using both proposed models but have different computational burden. Finally, we propose a Finite Impulse Response (FIR) implementation of the Steady State Kalman, and Lainiotis filters, which does not require previous estimations but requires a well-defined set of previous measurements.

Fast iterative solutions of Riccati and Lyapunov equations

Open Mathematics, 2022

In this article, new iterative algorithms for solving the discrete Riccati and Lyapunov equations... more In this article, new iterative algorithms for solving the discrete Riccati and Lyapunov equations are derived in the case where the transition matrix is diagonalizable with real eigenvalues. It is shown that the proposed iterative algorithms are faster than the classical ones, even for a small number of iterations.

Distributed Periodic Steady State Kalman Filter

International journal of circuits, systems and signal processing, Jan 10, 2022

Kalman filter [1]-[2] is the most well-known and widely used estimation algorithm, since it has b... more Kalman filter [1]-[2] is the most well-known and widely used estimation algorithm, since it has been used to successfully solve real time p roblems in various applications, such as in [ 2] aerospace industry, chemical process, communication systems design, control, civil engineering, filtering noise from two dimensional images, pollution prediction and power systems. The estimation problem is associated with time varying systems described by the following state space equations: x(k + 1) = F(k)x(k) + w(k) (1) z(k) = H(k)x(k) + v(k) (2) where x(k) is the n-dimensional state vector, z(k) is the m-dimensional measurement vector, F(k) is the transition matrix, H(k) is the output matrix, w(k) is the state noise and v(k) is the measurement noise at time k ≥ 0. The statistical model expresses the nature of the state and the measurements. The basic assumption is that the state noise and the measurement noise are zero mean Gaussian processes with known covariances Q(k) and R(k), respectively. The following assumptions hold: (a) the initial value of the state x(0) is a Gaussian random variable with known mean 0 and covariance P 0 ; (b) the noise processes and the initial state are independent. Periodic linear systems arise from continuous linear systems, when multi-rate sampling is performed, with many interesting and practical applications as stated in [3]. In this paper we focus on the case of periodic models and especially on the periodic steady state Kalman filter [4]-[6]. Parallel Kalman Filter implementations are mentioned in [7]. Distributed implementations for the steady state Kalman filter are proposed in [8]. The problem of distributed state estimation is addressed in [9]. The problem of distributed state estimation has been

FIR implementation of the Steady-State Kalman Filter

International Journal of Signal and Imaging Systems Engineering, 2008

... Maria Adam Department of Computer Science and Biomedical Informatics, University of Central G... more

Kalman Filter Riccati Equation for the Prediction, Estimation, and Smoothing Error Covariance Matrices

ISRN Computational Mathematics (Online), Dec 12, 2013

The classical Riccati equation for the prediction error covariance arises in linear estimation an... more The classical Riccati equation for the prediction error covariance arises in linear estimation and is derived by the discrete time Kalman filter equations. New Riccati equations for the estimation error covariance as well as for the smoothing error covariance are presented. These equations have the same structure as the classical Riccati equation. The three equations are computationally equivalent. It is pointed out that the new equations can be solved via the solution algorithms for the classical Riccati equation using other well-defined parameters instead of the original Kalman filter parameters.

Steady state Kalman filter design for cases and deaths prediction of Covid-19 in Greece

Results in Physics, 2021

In this work we study the applicability of the steady state Kalman filter in order to predict new... more In this work we study the applicability of the steady state Kalman filter in order to predict new cases and deaths of Covid-19. We use the actual observations of new cases and deaths. First, we deal with short term prediction, namely daily prediction. We propose the use of the golden steady state Kalman Filter, which is designed to have parameters related to the golden section. It was found that the proposed golden steady state Kalman Filter has a satisfactory behavior compared with the classical mean or average filter. Secondly, we deal with long term prediction, for example average prediction per quarantine period (14 days). We propose to process blocks of measurements of time window corresponding for example to the quarantine period in order to predict the average of cases and deaths using steady state Kalman Filter. It was found that the proposed golden steady state Kalman Filter produces more reliable predictions than the classical mean or average filter does. The use of steady state Kalman Filter for cases and deaths prediction of Covid-19 can be effective for resources and prevention measures planning.

The Joint Numerical Range of Bordered and Tridiagonal Matrices

30 Maria Adam and John Maroulas Recently a connection of Co {JNR [^ m]^= 1} with the numerical ra... more

On compressions of normal matrices

Linear Algebra and its Applications, 2002

Let A be a normal matrix and consider the polygon NR[A] = {x * Ax: x = 1}. If υ * Aυ ∈ int NR[A],... more

Sequences of lower and upper bounds for the spectral radius of a nonnegative matrix

Linear Algebra and its Applications, Jun 1, 2023

Enumeration of the roots of Boolean matrices

Nucleation and Atmospheric Aerosols, 2018

The number of the roots of certain Boolean matrices is calculated in this paper. In particular, t... more

Inversion Free Algorithms for Computing the Principal Square Root of a Matrix

International Journal of Mathematics and Mathematical Sciences, 2014

New algorithms are presented about the principal square root of an × matrix. In particular, all t... more New algorithms are presented about the principal square root of an × matrix. In particular, all the classical iterative algorithms require matrix inversion at every iteration. The proposed inversion free iterative algorithms are based on the Schulz iteration or the Bernoulli substitution as a special case of the continuous time Riccati equation. It is certified that the proposed algorithms are equivalent to the classical Newton method. An inversion free algebraic method, which is based on applying the Bernoulli substitution to a special case of the continuous time Riccati equation, is also proposed.

Bounds on the Spectral Radius of Nonnegative Matrices

In this paper, we determine some new bounds for the spectral radius of a nonnegative matrix with ... more In this paper, we determine some new bounds for the spectral radius of a nonnegative matrix with respect to the upper and the lower bounds for the spectral radius given by Frobenius’ bounds, by using similarity transformations. We also provide illustrative examples in order to compare the new bounds with the existing ones.

On the Positive Definite Solutions of the Matrix Equation XS + A*X-S A = Q

The Open Applied Mathematics Journal, Nov 30, 2011

In this paper, necessary and sufficient conditions for the existence of the positive definite sol... more In this paper, necessary and sufficient conditions for the existence of the positive definite solutions of the nonlinear matrix equation X s + A * X ! s A = Q are presented, when A is nonsingular and s an integer, as well as some new properties and bounds for the eigenvalues of matrices related to A,Q are discussed. An algebraic method for the computation of the solutions is proposed, based on the algebraic solution of the corresponding discrete time Riccati equation. The exact number of the positive definite solutions is also computed.

k-Step Sum and m-Step Gap Fibonacci Sequence

ISRN Discrete Mathematics (Online), Apr 9, 2014

For two given integers k, m, we introduce the k-step sum and m-step gap Fibonacci sequence by pre... more For two given integers k, m, we introduce the k-step sum and m-step gap Fibonacci sequence by presenting a recurrence formula that generates the nth term as the sum of k successive previous terms starting the sum at the mth previous term. Known sequences, like Fibonacci, tribonacci, tetranacci, and Padovan sequences, are derived for specific values of k, m. Two limiting properties concerning the terms of the sequence are presented. The limits are related to the spectral radius of the associated {0, 1}-matrix.

On the Covariance of Regression Coefficients

Open Journal of Statistics, 2015

In many applications, such as in multivariate meta-analysis or in the construction of multivariat... more In many applications, such as in multivariate meta-analysis or in the construction of multivariate models from summary statistics, the covariance of regression coefficients needs to be calculated without having access to individual patients' data. In this work, we derive an alternative analytic expression for the covariance matrix of the regression coefficients in a multiple linear regression model. In contrast to the well-known expressions which make use of the cross-product matrix and hence require access to individual data, we express the covariance matrix of the regression coefficients directly in terms of covariance matrix of the explanatory variables. In particular, we show that the covariance matrix of the regression coefficients can be calculated using the matrix of the partial correlation coefficients of the explanatory variables, which in turn can be calculated easily from the correlation matrix of the explanatory variables. This is very important since the covariance matrix of the explanatory variables can be easily obtained or imputed using data from the literature, without requiring access to individual data. Two important applications of the method are discussed, namely the multivariate meta-analysis of regression coefficients and the so-called synthesis analysis, and the aim of which is to combine in a single predictive model, information from different variables. The estimator proposed in this work can increase the usefulness of these methods providing better results, as seen by application in a publicly available dataset. Source code is provided in the Appendix and in http://www.compgen.org/tools/regression.

Generalized k, m-step Fibonacci sequences and matrices

by Maria Adam and ΝΙΚΟΛΑΟΣ ΑΣΗΜΑΚΗΣ

For two given integers k, m and the nonnegative real constants c i , i = 1, 2,. .. , k, we introd... more For two given integers k, m and the nonnegative real constants c i , i = 1, 2,. .. , k, we introduce the generalized k, m-step Fibonacci sequence by presenting a recursive formula that generates the n-th term as the sum of k successive previous terms starting the sum at the m-th previous term. The generalized k, m-Fibonacci matrices are defined, their characteristic polynomials are presented and some bounds for the spectral radius and the modulus of the remaining eigenvalues of the matrices are discussed. A closed formula of the n-th term of generalized k, m-step Fibonacci sequence is given generalizing the Binet' s formula. Two limiting properties of the sequence are presented. The limits are related to the spectral radius of the generalized k, m-Fibonacci matrices .