Alternating Projections Filtering Algorithm to Track Moving Objects
An interest is often present in knowing evolving variables that are not directly observable; this is the case in aerospace, engineering control, medical imaging, or data assimilation. What is at hand, though, are time-varying measured data, a model connecting them to variables of interest, and a mod...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2019/8450905 |
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| _version_ | 1832552220013363200 |
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| author | Youssef Qranfal |
| author_facet | Youssef Qranfal |
| author_sort | Youssef Qranfal |
| collection | DOAJ |
| description | An interest is often present in knowing evolving variables that are not directly observable; this is the case in aerospace, engineering control, medical imaging, or data assimilation. What is at hand, though, are time-varying measured data, a model connecting them to variables of interest, and a model of how to evolve the variables over time. However, both models are only approximation and the observed data are tainted with noise. This is an ill-posed inverse problem. Methods, such as Kalman filter (KF), have been devised to extract the time-varying quantities of interest. These methods applied to this inverse problem, nonetheless, are slow, computation wise, since they require large matrices multiplications and even matrix inversion. Furthermore, these methods are not usually suitable to impose some constraints. This article introduces a new iterative filtering algorithm based on alternating projections. Experiments were run with simulated moving projectiles and were compared with results using KF. The new optimization algorithm proves to be slightly more accurate than KF, but, more to the point, it is much faster in terms of CPU time. |
| format | Article |
| id | doaj-art-471ad05020f640889b94c3c27b173f7c |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-471ad05020f640889b94c3c27b173f7c2025-02-03T05:59:15ZengWileyJournal of Applied Mathematics1110-757X1687-00422019-01-01201910.1155/2019/84509058450905Alternating Projections Filtering Algorithm to Track Moving ObjectsYoussef Qranfal0Department of Applied Mathematics, Wentworth Institute of Technology, Boston, MA 02115, USAAn interest is often present in knowing evolving variables that are not directly observable; this is the case in aerospace, engineering control, medical imaging, or data assimilation. What is at hand, though, are time-varying measured data, a model connecting them to variables of interest, and a model of how to evolve the variables over time. However, both models are only approximation and the observed data are tainted with noise. This is an ill-posed inverse problem. Methods, such as Kalman filter (KF), have been devised to extract the time-varying quantities of interest. These methods applied to this inverse problem, nonetheless, are slow, computation wise, since they require large matrices multiplications and even matrix inversion. Furthermore, these methods are not usually suitable to impose some constraints. This article introduces a new iterative filtering algorithm based on alternating projections. Experiments were run with simulated moving projectiles and were compared with results using KF. The new optimization algorithm proves to be slightly more accurate than KF, but, more to the point, it is much faster in terms of CPU time.http://dx.doi.org/10.1155/2019/8450905 |
| spellingShingle | Youssef Qranfal Alternating Projections Filtering Algorithm to Track Moving Objects Journal of Applied Mathematics |
| title | Alternating Projections Filtering Algorithm to Track Moving Objects |
| title_full | Alternating Projections Filtering Algorithm to Track Moving Objects |
| title_fullStr | Alternating Projections Filtering Algorithm to Track Moving Objects |
| title_full_unstemmed | Alternating Projections Filtering Algorithm to Track Moving Objects |
| title_short | Alternating Projections Filtering Algorithm to Track Moving Objects |
| title_sort | alternating projections filtering algorithm to track moving objects |
| url | http://dx.doi.org/10.1155/2019/8450905 |
| work_keys_str_mv | AT youssefqranfal alternatingprojectionsfilteringalgorithmtotrackmovingobjects |