E.A. Kirsanov1

1 MESC AF "Air Force Academy named after prof. N.E. Zhukovsky and Yu.A. Gagarin" (Voronezh, Russia)

Statement of a problem. Results of the analysis of the existing approaches to filtration of a harmonious signal in discrete time in the presence of unknown frequency showed need of use of the linearized (quasilinear) filter of Kallman. However at a considerable interval of possible values of frequency of a signal the specified filter can disperse. In this regard it is necessary to apply a division method with use of bank of filters, each of which is adjusted on the initial value of frequency.

Purpose. Carrying out the comparative analysis of efficiency of algorithms of filtration of a harmonious signal in discrete time at inclusion in structure of a vector of a condition of two counting of a signal or counting of a signal and its derivative and also the specified algorithms synthesized according to method of division of the adaptive options with an unknown frequency of a signal providing its inclusion in structure of a vector of a state.

Results. The analysis of the received results demonstrates that with the known frequency of a signal both filters (at inclusion in structure of a vector of a condition of two counting of a signal or counting of a signal and its derivative) have identical efficiency. Use of expansion of a vector of a state with inclusion in its structure of unknown frequency of a signal and linearization of the equation of a state at a considerable interval of possible values of frequency leads to the divergence of the procedure of filtration. The adaptive expanded filter of Kallman synthesized by a division method keeps the working capacity.

Practical importance. Due to ignorance of frequency the error of estimation of a signal on the basis of the adaptive expanded filter of Kallman for 50 steps of filtration increases for 57% in comparison with the linear filter of Kallman corresponding to the known frequency of a signal.

Kirsanov E.A. Algorithms of adaptive filtration of a harmonious signal in discrete time. Radiotekhnika. 2022. V. 86. № 2. P. 29−35. DOI: https://doi.org/10.18127/j00338486-202202-04 (In Russian)

1. Borisov V.I., Zinchuk V.M., Limarev A.E., Nemchilov A.V. Ocenka momenta skachka chastoty signala s psevdosluchajnoj perestrojkoj rabochej chastoty v zadachah radiorazvedki. Teorija i tehnika radiosvjazi. 2008. № 2. S. 23-41. (In Russian).
2. Sovetov V.M., Kojokin V.A. Optimal'nyj algoritm priema pri ispol'zovanii modeli signala v prostranstve sostojanij. Jelektromagnitnye volny i jelektronnye sistemy. 2009. № 11. S. 22-28 (In Russian).
3. Kuznecov V.P., Churakov E.P. Adaptivnyj fil'tr Kalmana dlja ocenki parametrov otrazhennogo signala. Raketno-kosmicheskoe priborostroenie i informacionnye sistemy. 2015. № 3. S. 79-83. (In Russian).
4. Pugachev V.S., Sinicyn I.N. Stohasticheskie differencial'nye sistemy. Analiz i fil'tracija. Izd. 2-e. M.: Nauka. 1990. 632 s. (In Russian).
5. Zarchan P., Musoff H. Fundamentals of Kalman Filtering: A Practical Approach. Fourth Edition. Reston: American Institute of Aeronautics and Astronautics. 2015. 852 p. (In Russian).
6. Radzievskij V.G., Sirota A.A. Teoreticheskie osnovy radiojelektronnoj razvedki. M.: Radiotehnika. 2004. 432 s. (In Russian).
7. Kirsanov Je.A., Sirota A.A. Obrabotka informacii v prostranstvenno-raspredelennyh sistemah radiomonitoringa: statisticheskij i nejrosetevoj podhody. M.: FIZMATLIT. 2012. 344 s. (In Russian).