THE ALGORITHM FOR PREDICTING THE STABILITY OF THE PIPELINED ADAPTIVE RECURSIVE FILTERS IN CONTROL SYSTEMS
Abstract
At present, adaptive filters are widely used in various fields of technology: control systems, mobile communications, radar, etc. The main property of an adaptive system is time-varying func-tioning with self-regulation. The advantage of this functioning is the ability to timely adjust the system to change both the incoming signals and the conditions of the transmission medium during the operation of the device. If recursive filters are used in the implementation of adaptive systems, these systems get additional advantages: they require less equipment, allow you to achieve performance gains relatively non-recursive, achieve filter characteristics with fairly sharp transitions, etc. However, the use of recursive adaptive filters carries a risk of loss of stability when their characteristics change as a result of adaptation. Today, real-time digital signal processing re-quires a constant increase in computation speed, which necessitates the use of parallel computing. The most efficient parallelization method is pipelining computing. The introduction of pipeline registers in recursive filters can lead to a violation of the algorithm of the filter. This problem can be solved with the help of auto-substitution and resynchronization. A method for determining the stability of a recursive adaptive pipelined filter is proposed. It consists in the fact that we deter-mine the range in which the adaptive filter parameters change, and for each value in this range we find the degree of conveyorization at which all the poles of the transfer function of this filter lie inside the unit circle. Thus, pipelining serves not only to achieve high computational performance of the filter, but also to adjust its stability. This is especially true for adaptive filters, which can lose stability as a result of changes in their parameters during adaptation.
References
2. Nikitin A.A, Petrov A.V. Teoreticheskie osnovy obrabotki geofizicheskoy informatsii: ucheb. posobie [Theoretical bases of processing of geophysical information: a textbook]. Moscow: Izd-vo, 2008, 112 p.
3. Sayed. A. Hadei. A Family of Adaptive Filter Algorithms in Noise Cancellation for Speech Enhancement, International Journal of Computer and Electrical Engineering, 2010, No. 2 (2).
4. Dzhigan V.I. Parallel'nye vychisleniya v RLS-algoritmakh adaptivnoy fil'tratsii [Parallel calcu-lations in RLS algorithms of adaptive filtering], Vestnik MGTU im. N.E. Baumana. Seriya “Priborostroenie” [Herald of the Bauman Moscow State Technical University. Series Instru-ment Engineering], 2006, No. 1.
5. Sluzhivyy M.N. Adaptivnye sistemy radiosvyazi [Adaptive radio communication systems], Vestnik UlGTU [Bulletin of the Ulyanovsk state technical University], 2000, No. 3.
6. Mitrofanov D.G., Ivanushkin S.V. Usovershenstvovannyy variant adaptivnogo metoda formirovaniya radiolokatsionnykh izobrazheniy vozdushnykh tseley dlya signalov so stupenchatoy perestroykoy nesushchey chastoty [An improved version of the adaptive method for generating radar images of air targets for signals with stepwise carrier frequency tuning], Izvestiya instituta inzhenernoy fiziki [Proceedings of the Institute of engineering physics], 2014, No. 1(31).
7. Aliev T.M. Izmeritel'naya tekhnika [Measurement technology]. Moscow: Vysshaya shkola, 1991, 384 p.
8. Furno G.N. Mikrokomp'yuternye meditsinskie sistemy [Microcomputer medical systems]. Moscow: Mir, 1983, 544 p.
9. Kougi P.M. Arkhitektura konveyernykh EVM [The architecture of pipelined computers]: transl. from engl. Moscow: Radio i svyaz', 1985, 360 p.
10. Levin I.I., Semernikov E.A. Ustoychivost' konveyernykh rekursivnykh fil'trov [Stability of conveyor recursive filters], Vestnik Yuzhnogo nauchnogo tsentra RAN» [Bulletin of the south-ern scientific center of the Russian Academy of Sciences]. Moscow: Nauka, 2005.
11. Parkhi K.K. Metody preobrazovaniya algoritmov dlya parallel'nykh protsessorov [Methods for converting algorithms for parallel processors], TIIER [TIIER], 1987, Vol. 77, No. 12, pp. 96-114.
12. Sergienko A.M. VHDL dlya proektirovaniya vychislitel'nykh ustroystv [VHDL for designing computing devices]. Kiev: Izd-vo “CHP «Korneychuk», OOO«TID «DS»»”, 2003, 208 p.
13. Gol'denberg L.M., Matyushkin B.D., Polyak M.N. TSifrovaya obrabotka signalov. Spravochnik [Digital signal processing. Guide]. Moscow: Radio i svyaz', 1985, 312 p.
14. Gadzikovskiy V.I. Teoreticheskie osnovy tsifrovoy obrabotki signalov [Theoretical foundations of digital signal processing]. Moscow: Radio i svyaz', 2004, 344 p.
15. Uidrou B., Stirnz S. Adaptivnaya obrabotka signalov [Adaptive signal processing]: transl. from engl. Moscow: Radio i svyaz', 1989, 440 p.
16. Voronin N.S., Kolyadov D.V. Realizatsiya adaptivnoy fil'tratsii meshayushchikh otrazheniy v RLS AS UVD [Implementation of adaptive filtering of interfering reflections in ATC ra-dar], Nauchnyy vestnik MGTU GA. Ceriya «Radiofizika i radiotekhnika» [Scientific Bulletin of MSTU GA. Series "Radiophysics and radio engineering"], 2010, No. 152.
17. Ayficher E., Dzhervis B. TSifrovaya obrabotka signalov: prakticheskiy podkhod [Digital signal processing: a practical approach]. 2 ed: transl. from engl. Moscow: Izdatel'skiy dom «Vil'yams», 2004, 992 p.
18. Kester U. Proektirovanie sistem tsifrovoy i smeshannoy obrabotki signalov [Design of digi-tal and mixed signal processing systems]. Moscow: Tekhnosfera, 2010, 328 p.
19. Grant P., Kouen K. Adaptivnye fil'try [Adaptive filters]: transl. from engl. Moscow: Mir, 1988, 392 p.
20. Dzhigan V.I. Adaptivnaya fil'tratsiya signalov: teoriya i algoritmy [Adaptive signal filtering: theory and algorithms]. Moscow: Tekhnosfera, 2013, 528 p.
