Abstract




 
   

IJE TRANSACTIONS B: Applications Vol. 28, No. 2 (February 2015) 172-179   

downloaded Downloaded: 363   viewed Viewed: 2895

  ESTIMATION OF LOS RATES FOR TARGET TRACKING PROBLEMS USING EKF AND UKF ALGORITHMS- A COMPARATIVE STUDY
 
A.R. Toloei and S. Niazi
 
( Received: July 08, 2014 – Accepted: November 13, 2014 )
 
 

Abstract    One of the most important problem in target tracking is Line Of Sight (LOS) rate estimation for using from PN (proportional navigation) guidance law. This paper deals on estimation of position and LOS rates of target with respect to the pursuer from available noisy RF seeker and tracker measurements. Due to many important for exact estimation on tracking problems must target position and Line Of Sight rates estimated with least error rather than actual values. In this paper extended Kalman filter (EKF) and unscented Kalman filter (UKF) algorithms are used for estimation of target position in three-dimensional (3-D) and LOS rates in elevation and azimuth for seekers and trackers. For comparison of algorithms, model of the system simulated using MATLAB and many tests were carried out. Simulation experiments show that the efficiency of EKF due to least RMSE has better performance. However, the performance of EKF algorithm has been dramatically decreased when initializations (initial state assumption) are not near to real values, which in this condition UKF method provides a more accurate approximation. Numerical results from simulations show that the UKF is robust against uncertainties and has better state estimation accuracy. Therefore, UKF algorithm is appropriate, and it can run on target tracking systems

 

Keywords    Estimation, gimbal seeker, line of sight rate, optimal filtering, extended Kalman filter, unscented Kalman filter

 

چکیده    یکی از مهمترین مسائل در تعقیب هدف، تخمین نرخ خط دید برای استفاده در قانون هدایت ناوبری متناسب می‌باشد. این مقاله بر روی تخمین موقعیت یک هدف متحرک و نرخ‌های خط دید مابین تعقیب کننده و هدف بر اساس اندازه گیری‌های همراه با نویز در جستجوگرهای فرکانس رادیوییوردیاب‌ها تمرکز نموده است. بعلت اهیمت فراوان تخمین دقیق در مسائل ردیابی می‌بایست موقعیت و نرخ‌های خط دید هدف با خطای کمتری نسبت به مقادیر واقعی تخمین زده شوند. در این مقاله الگوریتم‌های فیلتر کالمن توسعه یافته (EKF) و فیلتر کالمن خنثی (UKF) برای تخمین موقعیت هدف در سه بعد ونرخ های خط دید در سمت و فراز برای جستجوگرها و ردیاب‌ها استفاده شده است. برای مقایسه الگوریتم‌ها، مدل سیستم با استفاده از نرم‌افزار MATLAB شبیه سازی شده و تعدادی سناریو اجرا گردیده است. نتایج آزمایش‌های شبیه‌سازی نشان می‌دهد کهدر ابتدا، کارایی EKF به علت خطای مربع میانگین ریشه (RMSE) کمتر،عملکرد بهتری داشته اما زمانی که مقادیر اولیه (فرض حالت اولیه) به مقدار واقعی نزدیک نباشد عملکرد EKF بصورت فزاینده‌ای کاهش می‌یابد که در این شرایط روش UKFدقت تقریب حالت بهتری دارد. نتایج عددی از شبیه سازی‌هانشان می‌دهد که UKFدقت تخمین حالت بهتری داشته و در برابر نامعینی‌ها مقاوم‌تر است. بنابراین الگوریتمUKFمناسب بوده و می‌تواند در سیستم‌های ردیابی هدف بکار گرفته شود.

References   

1.     Sadhu, S., Mondal, S., Srinivasan, M. and Ghoshal, T.K., "Sigma point kalman filter for bearing only tracking", Signal Processing,  Vol. 86, No. 12, (2006), 3769-3777.

2.     F. Khakpour and G. Ardeshir, "Use of a novel concept of potential pixel energy for object tracking", International Journal of Engineering Transactions A: Basics,  Vol. 27, No. 7, (2014), 1023-1032.

3.     Abdo, M., Toloei, A., Vali, A. and Arvan, M., "Modeling, control and simulation of cascade control servo system for one axis gimbal mechanism", International Journal of Engineering-Transactions A: Basics,  Vol. 27, No. 1, (2013), 157-170.

4.     Ekstrand, B., "Tracking filters and models for seeker applications", Aerospace and Electronic Systems, IEEE Transactions on,  Vol. 37, No. 3, (2001), 965-977.

5.     Ananthasayanam, M., Sarkar, A., Vorha, P., Bhattacharya, A. and Srivastava, R., "Estimation of los rates and angles using EKF from seeker measurements", in Proceedings of International Conference on Signal Processing and Communications, (2004).

6.     Kalman, R.E., "A new approach to linear filtering and prediction problems", Journal of Fluids Engineering,  Vol. 82, No. 1, (1960), 35-45.

7.     Anderson, B.D. and Moore, J.B., "Optimal filtering, Courier Dover Publications,  (2012).

8.     Julier, S.J. and Uhlmann, J.K., "Unscented filtering and nonlinear estimation", Proceedings of the IEEE,  Vol. 92, No. 3, (2004), 401-422.

9.     La Scala, B. and Morelande, M., "An analysis of the single sensor bearings-only tracking problem", in Information Fusion, 2008 11th International Conference on, (2008), 1-6.

10.   Hartikainen, J., Solin, A. and Sarkka, S., "Optimal filtering with kalman filters and smoothers", Department of Biomedica Engineering and Computational Sciences, Aalto University School of Science, 16th August, (2011).

 11.   Karlsson, R. and Gustafsson, F., "Range estimation using angle-only target tracking with particle filters", in American Control Conference, 2001. Proceedings of the 2001, IEEE. Vol. 5, (2001), 3743-3748.

12.   Mallick, M., Morelande, M., Mihaylova, L., Arulampalam, S. and Yan, Y., "Comparison of angle-only filtering algorithms in 3d using cartesian and modified spherical coordinates", in Information Fusion (FUSION), 2012 15th International Conference on, IEEE, (2012), 1392-1399.

13.   Tamhane, B. and Kurode, M.S., "Estimation of states of seeker system of a missile using sliding mode observer and kalman filter approaches-a comparative study".

14.   Kashyap, S., Shantha Kumar, N., Naidu, V. and Girija, G., "Interacting multiple model seeker filter for homing guidance",  (2009).

15.   Karami, F., Salarieh, H. and Shabani, R., "Tracking and shape control of a micro-cantilever using electrostatic actuation", International Journal of Engineering-Transactions C: Aspects,  Vol. 27, No. 9, (2014), 1439-1448.

16.   Yang, R., Huang, J.H.a., Ng, G.W. and Bar-Shalom, Y., "Interacting multiple model unscented gauss-helmert filter for bearings-only tracking with state-dependent propagation delay", in Information Fusion (FUSION), 2014 17th International Conference on, IEEE, (2014), 1-8.

17.   Leong, P., Arulampalam, S., Lamahewa, T.A. and Abhayapala, T.D., "Gaussian-sum cubature kalman filter with improved robustness for bearings-only tracking", (2014).

18.   Radhakrishnan, K., Unnikrishnan, A. and Balakrishnan, K., "Bearing only tracking of maneuvering targets using a single coordinated turn model", International Journal of Computer Applications,  Vol. 1, No. 1, (2010), 25-33.

19.   Yaakov, B.-S., Thiagalingam, K. and Rong, L., Estimation with applications to tracking and navigation, John Wiley & Sons, Inc.: New York, NY, USA, (2002).

20.   Nardone, S.C., Lindgren, A.G. and Gong, K.F., "Fundamental properties and performance of conventional bearings-only target motion analysis", Automatic Control, IEEE Transactions on,  Vol. 29, No. 9, (1984), 775-787.

21.   Julier, S.J. and Uhlmann, J.K., "A new extension of the kalman filter to nonlinear systems", in Int. symp. aerospace/defense sensing, simul. and controls, Orlando, FL. Vol. 3, (1997).

22.   Daum, F., "Nonlinear filters: Beyond the kalman filter", Aerospace and Electronic Systems Magazine, IEEE,  Vol. 20, No. 8, (2005), 57-69.

23.   Karlsson, R. and Gustafsson, F., "Recursive bayesian estimation: Bearings-only applications", in Radar, Sonar and Navigation, IEE Proceedings-, IET. Vol. 152, (2005), 305-313.





International Journal of Engineering
E-mail: office@ije.ir
Web Site: http://www.ije.ir