The Kalman filter for linear systems on time scales

Böhner, Martin; Wintz, Nick

doi:10.1016/j.jmaa.2013.04.075

Cited by 33 publications

(12 citation statements)

References 8 publications

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“…Taking into account the characteristics of the quantities constituting the measurement environment where the measuring instruments under consideration operate, it can be concluded that the best form of eliminating the influence of the interference sources is the Kalman filter. The characteristics of this algorithm fit very well into the solution of a number of problems emerging in the process of optimization of the accuracy characteristics of the measuring instruments defining the parameters of the above listed moving objects [8,10,13,14,17]. Therefore, a module for signal processing by means of the Kalman algorithm is included in each measurement channel of the block diagram (Fig.2.).…”

Section: A Measuring System For Determining the Heel And Trim Of A Momentioning

confidence: 94%

A Gyro-Free System for Measuring the Parameters of Moving Objects

Dichev¹,

Koev²,

Bakalová³

et al. 2014

Measurement Science Review

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The present paper considers a new measurement concept of modeling measuring instruments for gyro-free determination of the parameters of moving objects. The proposed approach eliminates the disadvantages of the existing measuring instruments since it is based, on one hand, on a considerably simplified mechanical module, and on the other hand, on the advanced achievements in the area of nanotechnologies, microprocessor and computer equipment. A specific measuring system intended for measuring the trim, heel, roll, and pitch of a ship has been developed in compliance with the basic principles of this concept. The high dynamic accuracy of this measuring system is ensured by an additional measurement channel operating in parallel with the main channel. The operating principle of the additional measurement channel is based on an appropriate correction algorithm using signals from linear MEMS accelerometers. The presented results from the tests carried out by means of stand equipment in the form of a hexapod of six degrees of freedom prove the effectiveness of the proposed measurement concept.

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Section: A Measuring System For Determining the Heel And Trim Of A Momentioning

confidence: 94%

A Gyro-Free System for Measuring the Parameters of Moving Objects

Dichev¹,

Koev²,

Bakalová³

et al. 2014

Measurement Science Review

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“…The purpose of this theory is to unify discrete and continuous analysis and to offer an extension to cases "in between". Many applications in mathematical modelling exist for this theory, e.g., to optimal control [5,18,19,20,21,29], population biology [9], calculus of variations [8,10,13], and economics [4,11,14,15,34].…”

Section: Introductionmentioning

confidence: 99%

Separated and state-constrained separated linear programming problems on time scales

Al-Salih

Böhner

2019

B Soc Paran Mat

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Separated linear programming problems can be used to model a wide range of real-world applications such as in communications, manufacturing, transportation, and so on. In this paper, we investigate novel formulations for two classes of these problems using the methodology of time scales. As a special case, we obtain the classical separated continuous-time model and the state-constrained separated continuous-time model. We establish some of the fundamental theorems such as the weak duality theorem and the optimality condition on arbitrary time scales, while the strong duality theorem is presented for isolated time scales. Examples are given to demonstrate our new results

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“…The purpose of this theory is to unify discrete and continuous analysis and to offer an extension to cases "in between". Many applications in mathematical modelling exist for this theory, e.g., to optimal control [2,[15][16][17][18]25], population biology [6], calculus of variations [5,7,10], and economics [1,8,11,12,26].…”

Section: Introductionmentioning

confidence: 99%

Linear programming problems on time scales

Al-Salih

Böhner

2018

APPL ANAL DISCRETE M

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In this work, we study linear programming problems on time scales. This approach unifies discrete and continuous linear programming models and extends them to other cases "in between." After a brief introduction to time scales, we formulate the primal as well as the dual time scales linear programming models. Next, we establish and prove the weak duality theorem and the optimality conditions theorem for arbitrary time scales, while the strong duality theorem is established for isolated time scales. Finally, examples are given in order to illustrate the effectiveness of the presented results.

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The Kalman filter for linear systems on time scales

Cited by 33 publications

References 8 publications

A Gyro-Free System for Measuring the Parameters of Moving Objects

A Gyro-Free System for Measuring the Parameters of Moving Objects

Separated and state-constrained separated linear programming problems on time scales

Linear programming problems on time scales

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