Lainiotis Filters Research Articles

Estimation-free Prediction Algorithms

For Time-varying, Time-invariant, and steady-state systems, Kalman Filter can be implemented as a prediction algorithm, since it produces the state prediction and the corresponding prediction error covariance matrix via the state estimation and the corresponding estimation error covariance matrix. Lainiotis Filter is equivalent to Kalman Filter and can be used to compute the prediction. In this paper, for Time-varying, Time-invariant and steady state systems, estimation-free Prediction Algorithms are derived via Kalman and Lainiotis filters; they are equivalent and compute iteratively the prediction and the corresponding prediction error covariance matrix. The estimation and the corresponding estimation error covariance matrix are not needed and are not computed. The proposed estimation-free prediction algorithms are faster than the Kalman filter.

Speedup of Kalman and Lainiotis filters for partitionable models

Speedup of Kalman and Lainiotis filters for partitionable models

Golden section, Fibonacci sequence and the time invariant Kalman and Lainiotis filters

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. Necessary and sufficient conditions for the existence of this relation are obtained through the associated Riccati equations. A conditional relation between the golden section and the steady state Kalman and Lainiotis filters is derived. A Finite Impulse Response (FIR) implementation of the steady state filters is proposed, where the coefficients of the steady state filter are related to the golden section. Finally, the relation between the Fibonacci numbers and the discrete time Lainiotis filter for multidimensional models is investigated.

Global systems for mobile position tracking using Kalman and Lainiotis filters.

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 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.

Lainiotis filter, golden section and Fibonacci sequence

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 related to the golden section. The relation between the closed form of the Lainiotis filter and the Fibonacci sequence is also derived. It is shown that the steady state Lainiotis filter computes the state estimate using a linear combination of the previous estimate and of the current measurement with coefficients related to the golden section. A Finite Impulse Response (FIR) implementation of the steady state Lainiotis filter is also proposed, where the filter computes the state estimate as a linear combination of a well-defined set of the last measurements with coefficients which are powers of the golden section. Finally, the scalar generic stochastic dynamic system is considered and the relation between its parameters and the golden section is investigated.

Optimal decentralized Kalman filter and Lainiotis filter

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 measurements into parallel processors, minimizing the computation time. The resulting optimal Kalman filter and optimal Lainiotis filter require uniform distribution or near to uniform distribution of measurements into parallel processors. The optimal uniform distribution has the advantages of elimination of idle time for the local processors and of low hardware cost, but it is not always applicable. The optimal filters present high parallelism speedup; this is verified through simulation results and is very important due to the fact that, in most real-time applications, it is essential to obtain the estimate in the shortest possible time.

Receding horizon filtering for discrete-time linear systems with state and observation delays

In this study, the authors consider the receding horizon filtering problem for discrete-time linear systems with state and observation time delays. Novel filtering algorithm is proposed based on the receding horizon strategy in order to achieve high estimation accuracy and stability under parametric uncertainties. New receding horizon filter uses a set of recent observations with appropriately chosen initial horizon conditions. The key contribution is the derivation of Lyapunov-like equations for receding horizon mean and covariance of system state with an arbitrary number of time delays. The authors demonstrate how the proposed algorithm robust against dynamic model uncertainties comparing with Kalman and Lainiotis filters with time delays. Superior performance of the proposed filter is illustrated through two numerical examples when the system modelling uncertainties appear.

Adaptive Estimation of FCG Using Nonlinear State-Space Models

In this paper, an efficient adaptive nonlinear algorithm for estimation and identification, the so-called adaptive Lainiotis filter (ALF), is applied to the problem of fatigue crack growth (FCG) estimation, identification, and prediction of the final crack (failure). A suitable nonlinear state-space FCG model is introduced for both ALF and extended Kalman filter (EKF). Both algorithms are tested in order to compare their efficiency. Through extensive analysis and simulation, it is demonstrated that the ALF has superior performance both in FCG estimation, as well as in predicting the remaining lifetime to failure. Furthermore, it is shown that the ALF is faster and easier to implement in a parallel/distributed processing mode, and much more robust than the classic EKF.

Lainiotis filters applications in seismic signal processing

Lainiotis filters applications in seismic signal processing

On the parallel implementations of the linear Kalman and Lainiotis filters and their efficiency

In this paper, the parallel implementations of two well-known linear state-space filtering algorithms, namely the Kalman and the Lainiotis filters, in MIMD machines are studied from a computational standpoint. The analysis assumes both time invariant and time varying system models and uses precedence graphs and critical paths. The parallelism efficiency of the implementations is also defined and studied. Results indicate that these algorithms can be implemented in parallel using a comparatively small number of processors. Furthermore, the efficiency of the parallel implementations can be very high or very low, depending on the state and measurement vector dimensions. In dieser Arbeit werden parallele Realisierungen zweier bekannter Zustandsraum-Filteralgorithmen, nämlich der Kalman- und der Lainiotis-Filter, mit MIMD Prozessoren vom rechentechnischen Standpunkt aus untersucht. Die Analyse setzt sowohl zeitinvariante als auch zeitvariante Systemmodelle voraus und benutzt Präzedenzgraphen und kritische Pfade. Der Parallelitätswirkungsgrad der Realisierungen wird definiert und untersucht. Die Ergebnisse zeigen daβ diese Algorithmen parallel mit Hilfe einer vergleichsweise kleinen Anzahl von Prozessoren realisiert werden können. Weiterhin kann der Wirkungsgrad der Parallelrealisierungen sehr hoch oder sehr niedrig sein, abhängig von den Dimensionen des Zustands- und des Beobachtungsvektors. Nous étudions dans cet article, d'un point de vue calculatoire, les implantations paralléles sur des machines MIMD de deux algorithmes de filtrage linéaire dans l'espace d'état bien connus, à savoir les filtres de Kalman et de Lainiotis. Cette analyse est valable à la fois pour des modèles invariants et variants dans le temps, et utilise des graphes de priorité et des chemins critiques. L'efficacité des implantations en parallèle est également définie et étudiée. Les résultats indiquent que ces algorithmes peuvent être implantés en parrallèle à l'aide d'un nombre comparativement petit de processeurs. De plus, l'efficacité de ces implantations en parallèle peut être très grande ou très petite selon les dimensions des vecteurs d'état et de mesure.

AR model identification with unknown process order

A method for simultaneous autoregressive (AR) model order selection and identification is proposed, which is based on the adaptive Lainiotis filter (ALF). The method is not restricted to the Gaussian case, is applicable to online/adaptive operation, and is computationally efficient. It can be realized in a parallel processing fashion. The AR model order selection and identification problem is reformulated so that it can be fitted into the framework of a state space under uncertainty estimation problem framework. The ALF is briefly presented and its application to the specific problem is discussed. Simulation examples are presented to demonstrate the superior performance of the method in comparison with previously reported ones.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>