Efficiency analysis of polynomial filtering algorithms in navigation data processing for a class of nonlinear discrete dynamical systems
Abstract A polynomial filtering algorithm is designed for estimating a Markov sequence based on linear measurements. The feature of the estimation problem is that the Markov sequence is described by a nonlinear shaping filter, which is a second‐order polynomial with respect to the state vector compo...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | IET Control Theory & Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1049/cth2.12036 |
| _version_ | 1818017714131697664 |
|---|---|
| author | O. A. Stepanov V. A. Vasiliev M. V. Basin V. A. Tupysev Y. A. Litvinenko |
| author_facet | O. A. Stepanov V. A. Vasiliev M. V. Basin V. A. Tupysev Y. A. Litvinenko |
| author_sort | O. A. Stepanov |
| collection | DOAJ |
| description | Abstract A polynomial filtering algorithm is designed for estimating a Markov sequence based on linear measurements. The feature of the estimation problem is that the Markov sequence is described by a nonlinear shaping filter, which is a second‐order polynomial with respect to the state vector components. The algorithm efficiency is illustrated by three examples of navigation data processing. It is shown that the polynomial filter provides accuracy close to the best potential one calculated using the particle filter. At the same time, the amount of computation required to implement this algorithm is much smaller than that for the particle filter. In addition, the polynomial filter provides a consistent calculated accuracy characteristic. |
| first_indexed | 2024-04-14T07:30:30Z |
| format | Article |
| id | doaj.art-b3dfea75a1b74ae5864014a01212d4f5 |
| institution | Directory Open Access Journal |
| issn | 1751-8644 1751-8652 |
| language | English |
| last_indexed | 2024-04-14T07:30:30Z |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | IET Control Theory & Applications |
| spelling | doaj.art-b3dfea75a1b74ae5864014a01212d4f52022-12-22T02:05:53ZengWileyIET Control Theory & Applications1751-86441751-86522021-01-0115224825910.1049/cth2.12036Efficiency analysis of polynomial filtering algorithms in navigation data processing for a class of nonlinear discrete dynamical systemsO. A. Stepanov0V. A. Vasiliev1M. V. Basin2V. A. Tupysev3Y. A. Litvinenko4Concern CSRI Elektropribor JSC Saint Petersburg RussiaConcern CSRI Elektropribor JSC Saint Petersburg RussiaITMO University Saint Petersburg RussiaConcern CSRI Elektropribor JSC Saint Petersburg RussiaConcern CSRI Elektropribor JSC Saint Petersburg RussiaAbstract A polynomial filtering algorithm is designed for estimating a Markov sequence based on linear measurements. The feature of the estimation problem is that the Markov sequence is described by a nonlinear shaping filter, which is a second‐order polynomial with respect to the state vector components. The algorithm efficiency is illustrated by three examples of navigation data processing. It is shown that the polynomial filter provides accuracy close to the best potential one calculated using the particle filter. At the same time, the amount of computation required to implement this algorithm is much smaller than that for the particle filter. In addition, the polynomial filter provides a consistent calculated accuracy characteristic.https://doi.org/10.1049/cth2.12036Filtering methods in signal processingSignal processing theoryInterpolation and function approximation (numerical analysis)Markov processesInterpolation and function approximation (numerical analysis)Markov processes |
| spellingShingle | O. A. Stepanov V. A. Vasiliev M. V. Basin V. A. Tupysev Y. A. Litvinenko Efficiency analysis of polynomial filtering algorithms in navigation data processing for a class of nonlinear discrete dynamical systems IET Control Theory & Applications Filtering methods in signal processing Signal processing theory Interpolation and function approximation (numerical analysis) Markov processes Interpolation and function approximation (numerical analysis) Markov processes |
| title | Efficiency analysis of polynomial filtering algorithms in navigation data processing for a class of nonlinear discrete dynamical systems |
| title_full | Efficiency analysis of polynomial filtering algorithms in navigation data processing for a class of nonlinear discrete dynamical systems |
| title_fullStr | Efficiency analysis of polynomial filtering algorithms in navigation data processing for a class of nonlinear discrete dynamical systems |
| title_full_unstemmed | Efficiency analysis of polynomial filtering algorithms in navigation data processing for a class of nonlinear discrete dynamical systems |
| title_short | Efficiency analysis of polynomial filtering algorithms in navigation data processing for a class of nonlinear discrete dynamical systems |
| title_sort | efficiency analysis of polynomial filtering algorithms in navigation data processing for a class of nonlinear discrete dynamical systems |
| topic | Filtering methods in signal processing Signal processing theory Interpolation and function approximation (numerical analysis) Markov processes Interpolation and function approximation (numerical analysis) Markov processes |
| url | https://doi.org/10.1049/cth2.12036 |
| work_keys_str_mv | AT oastepanov efficiencyanalysisofpolynomialfilteringalgorithmsinnavigationdataprocessingforaclassofnonlineardiscretedynamicalsystems AT vavasiliev efficiencyanalysisofpolynomialfilteringalgorithmsinnavigationdataprocessingforaclassofnonlineardiscretedynamicalsystems AT mvbasin efficiencyanalysisofpolynomialfilteringalgorithmsinnavigationdataprocessingforaclassofnonlineardiscretedynamicalsystems AT vatupysev efficiencyanalysisofpolynomialfilteringalgorithmsinnavigationdataprocessingforaclassofnonlineardiscretedynamicalsystems AT yalitvinenko efficiencyanalysisofpolynomialfilteringalgorithmsinnavigationdataprocessingforaclassofnonlineardiscretedynamicalsystems |