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a r t i c l e i n f o a b s t r a c t Keywords: Kalman filter Lainiotis filter Discrete time Decentralized algorithms Analysis of algorithms Optimization A method to implement the optimal decentralized Kalman filter and the optimal decentralized Lainiotis filter is proposed; the method is based on the a priori determination of the optimal distribution of… (More)

The relation between the discrete time Lainiotis filter on the one side and the golden section and the Fibonacci sequence on the other is established. As far as the random walk system is concerned, the relation between the Lainiotis filter and the golden section is derived through the Riccati equation since the steady state estimation error covariance is… (More)

We present two time invariant models for Global Systems for Mobile (GSM) position tracking, which describe the movement in x-axis and y-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… (More)

Keywords: Positive definite matrices Riccati equation Kalman filter Lainiotis filter Golden section Fibonacci sequence a b s t r a c t We consider the discrete time Kalman and Lainiotis filters for multidimensional stochastic dynamic systems and investigate the relation between the golden section, the Fibonacci sequence and the parameters of the filters.… (More)

- Nicholas Assimakis, Maria Adam
- 2015

In this paper we present two time invariant models mobile position tracking in three dimensions, which describe the movement in x-axis, y-axis and z-axis simultaneously or separately, provided that there exist measurements for the three axes. We present the time invariant filters as well as the steady state filters: the classical Kalman Filter and Lainiotis… (More)

- Nicholas Assimakis, Maria Adam
- 2013

An implementation of the time invariant Lainiotis filter using a Chandrasekhar type algorithm is presented and compared to the classical one. The size of model determines which algorithm is faster; a method is proposed to a-priori decide, which implementation is faster. In the infinite measurement noise case, the proposed method is always faster than the… (More)

Recursive per multiple steps algorithms for solving the discrete time Riccati and Lyapunov equations emanating from Kalman and Lainiotis filter are developed, for the case where the plant and measurement noise covariance are positive definite matrices. The resulting algorithms preserve the structure of the corresponding recursive per step algorithms and are… (More)

- X A T X, X A T X, A Q † Maria Adam, Nicholas Assimakis, Grigoris Tziallas, Francesca Sanida
- 2009

A test is developed for checking the existence of a finite number of solutions of the matrix equations X + A T X 1 A = Q and X A T X 1 A = Q, when A is a nonsingular matrix. An algebraic method for computing all the solutions of these matrix equations is proposed. The method is based on the algebraic solution of the corresponding discrete time Riccati… (More)

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