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Linear Quadratic Recursive Estimation Scheme Using Bayesian Inference for Navigation Systems

A. Jawahar


In the ocean environment, two dimensional Range & Bearings Target Motion Analysis (TMA) is generally used. In the underwater scenario, the active sonar, positioned on a observer, is capable of sensing the sound waves reflected from the target in water. The sonar sensors in the water pick up the target reflected signal in the active mode. The observer is assumed to be moving in straight line and the target is assumed to be moving mostly in straight line with maneuver occasionally. The observer processes the measurements and estimates the target motion parameters, viz., Range, Bearing, Course and Speed of the target. It also generates the validity of each of these parameters. Here we try to apply Kalman Filter for the sea scenario using the input estimation technique to detect target maneuver, estimate target acceleration and correct the target state vector accordingly.     There are mainly two versions of Kalman Filter – a Linearised Kalman Filter (LKF) in which polar measurements are converted into Cartesian coordinates and the well-known Extended Kalman Filter (EKF). Recently S. T. Pork and L. E. Lee presented a detailed theoretical comparative study of the above two methods and stated that both the methods perform well. Here, EKF is used throughout.


Estimator, Fire Control System, Helicopter, Initial Turn Angle, Weapon Control Algorithm, Kalman Filter, Splash Point Algorithm.

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V.J. Aidala, S.E.Hammel, “Utilization of modified polar coordinates for for bearings only tracking”,IEEE trans. Automatic control,Vol AC-28,No.3, pp. 283-294, March 1983.

E.A.Wan and R.Van Der Merwe,” The unscented Kalman filter for non linear estimation”, in Proceedings of Symposiums 2000 on Adaptive System for Signal Processing, Communication and Control, Canada, Oct.2000.S.Blackman and R.Popolli, “Design and analysis of modern tracking systems”,Norwood, MA, Artech House, 1999.

Y.Bar -shalom and Fortman, “Tracking and Data association” , Academic Press, Inc., San Diego, USA,1991.

Y.Bar-shalmon and X.R.Lee. “Estimation and tracking principles, Techniques and Software”, Artech House, Boston, London, 1993.

Branko Ristic, Sanjeev Arulampalam and Neil Gordon, “Beyond the Kalman Filter: Particle Filters for Tracking Applications”, Artech House, 2004.

Dan Simon, “Optimal State Estimation: Kalman, and Nonlinear Approaches”, John Wiley & Sons, Inc. 2006.

Yu Liu and X. Rong Li, “Measure of nonlinearity for estimation”, IEEE Transactions on Signal Processing, Vol.63, No.9, May 1.2015.

Kumari, B. Leela, S. Koteswara Rao, and K.Padma Raju. "Simplified target location estimation for underwater vehicles", 2013 Ocean Electronics, 2013.

S.Koteswara Rao,”Algorithm for detection of maneuvering targets in bearings only passive target tracking”, IEE proc.-sonar Navig., vol.146, No.3, june 1999,pp141-146.

S.Koteswara Rao,”Modified gain extended Kalman filter with application to bearings only passive maneuvering target tracking”, IEE proc.-Radar Sonar navig., vol 152,No.4,August 2005,pp239-244..

A.Jawahar, S. Koteswara Rao, A.Sampath Dakshina Murthy, K.S. Srikanth, Rudra Pratap Das “Multi-sensor Submarine Surveillance System using MGBEKF”, Indian Journal of Science and Technology, Vol 8(35), DOI: 10.17485/ijst/2015/v8i35/82088

M. Morgado, P. Oliveira, C. Silvestre, and J. F. Vasconcelos,

“Embedded vehicle dynamics aiding for USBL/INS underwater

navigation system,” IEEE Transactions on Control Systems Technology, vol. 22, no. 1, pp. 322–330, 2014.

A. Jayasiri, R. G. Gosine, G. K. I. Mann, and P. McGuire, “AUVbased plume tracking: a simulation study,” Journal of Control

Science and Engineering, vol. 2016, Article ID 1764527, 15 pages,

G. E. Packard, A. Kukulya, T. Austin et al., “Continuous

autonomous tracking and imaging of white sharks and basking

sharks using a remus-100 auv,” in Proceedings of the IEEE

OCEANS, pp. 1–5, San Diego, Calif, USA, September 2013.

N. Stilinovic, D. Nad, and N. Miskovic, “Auv for diver assistance

and safety—design and implementation,” in Proceedings of the

OCEANS, pp. 1–4, Geneva, Switzerland, May 2015.

T. Zhang, W. Zeng, L. Wan, and S. Ma, “Underwater target

tracking based on Gaussian particle filter in looking forward

sonar images,” Journal of Computational Information Systems,

vol. 6, no. 14, pp. 4801–4810, 2010.

D. W. Krout, W. Kooiman, G. Okopal, and E. Hanusa, “Object

tracking with imaging sonar,” in Proceedings of the 15th International Conference on Information Fusion (FUSION ’12), pp.

–2405, IEEE, Singapore, September 2012.

K. M. Han and H. T. Choi, “Shape context based object recognition and tracking in structured underwater environment,” in Proceedings of the IEEE International Conference on Geoscience and Remote

Sensing Symposium, pp. 617–620, 2011.

S. Y. Chen, “Kalman filter for robot vision: a survey,” IEEE Transactions on Industrial Electronics, vol. 59, no. 11, pp. 4409–4420, 2012.

D. Eickstedt, M. Benjamin, H. Schmidt et al., “Adaptive tracking of underwater targets with autonomous sensor networks,” Journal of Underwater Acoustics, vol. 56, pp. 465–495, 2006.

H. Shi, W. Wang, N. M. Kwok, and S. Y. Chen, “Game theory for wireless sensor networks: a survey,” Sensors, vol. 12, no. 7, pp. 9055–9097, 2012.

S. Chen, W. Huang, C. Cattani, and G. Altieri, “Traffic dynamics on complex networks: a survey,”Mathematical Problems in Engineering, vol. 2012, Article ID 732698, 23 pages, 2012.

J. Xue, M. Li, W. Zhao, and S. Chen, “Bound maxima as a traffic feature under DDOS flood attacks,”Mathematical Problems in Engineering, vol. 2012, Article ID 419319, 20 pages, 2012.

L. Z. Xu, X. F. Li, and S. X. Yang, “Wireless network and communication signal processing,” Intelligent Automation & Soft Computing, vol. 17, no. 8, article 1019, 2011.

I. F. Akyildiz, D. Pompili, and T. Melodia, “Underwater acoustic sensor networks: research challenges,” Ad Hoc Networks, vol. 3, no. 3, pp. 257–279, 2005.

C. H. Yu, K. H. Lee, J. W. Choi, and Y. B. Seo, “Distributed single target tracking in underwater wireless sensor networks,” in Proceedings of the SICE Annual Conference, pp. 1351–1356, Japan, August 2008.

G. Isbitiren and O. B. Akan, “Three-dimensional underwater target tracking with acoustic sensor networks,” IEEE Transactions on Vehicular Technology, vol. 60, no. 8, pp. 3897–3906, 2011.

E. Kim, S. Lee, C. Kim, and K. Kim, “Bearings-only tracking systems with distributed floating beacons in underwater sensor networks,” in Proceedings of the IEEE/IFIP 8th International Conference

on Embedded and Ubiquitous Computing, (EUC ’10), pp. 311–315, December 2010.

L. Z. Xu, X. F. Ding, X. Wang, G. F. Lv, and F. C. Huang, “Trust region based sequential quasi-Monte Carlo filter,” Acta Electronica Sinica, vol. 39, no. 3 A, pp. 24–30, 2011.

S. Y. Chen and Z. J. Wang, “Acceleration strategies in generalized belief propagation,” IEEE Transactions on Industrial Informatics, vol. 8, no. 1, pp. 41–48, 2012.

X. F. Ding, L. Z. Xu, X. Wang et al., “Robust visual object tracking using covariance features in QuasiMonte Carlo filter,” Intelligent Automation and Soft Computing, vol. 17, no. 5, pp. 571–582, 2011.

X. Wang and Z. Tang, “Modified particle filter-based infrared pedestrian tracking,” Infrared Physics and Technology, vol. 53, no. 4, pp. 280–287, 2010.

S. Y. Chen, H. Tong, Z. Wang, S. Liu, M. Li, and B. Zhang, “Improved generalized belief propagation for vision processing,” Mathematical Problems in Engineering, vol. 2011, Article ID 416963, 12 pages, 2011.

C. Cattani, “Shannon wavelets for the solution of integrodifferential equations,” Mathematical Problems in Engineering, vol. 2010, Article ID 408418, 22 pages, 2010.

Jawahar A, Vishnu Chakravarthi Ch “Comparative Analysis Of Non Linear Estimation Schemes Used For Undersea Sonar Applications”, Innovare Journal of Engineering and Technology, Volume 4, Issue 4, 2016,pp.14-19.

Jawahar A, Vishnu Chakravarthi Ch “Improved Nonlinear Signal Estimation Technique For Undersea Sonar-Based Naval Applications”, Innovare Journal of Engineering and Technology, Volume 4, Issue 4, 2016,pp.20-25.

A.Jawahar, “Feasible course trajectories for Undersea sonar target tracking systems”, Indian Journal of Automation and Artificial Intelligence, Vol 3 (1), October 2016, pp.1-5.

A.Jawahar, S.Koteswara Rao, Sk.B.Karishma “Target Estimation Analysis Using Data Association And Fusion”, International Journal of Oceans and Oceanography, Volume 9, Number 2 (2015), pp. 203-210.

K.Lakshmi Prasanna, S.Koteswara Rao, A.Jawahar, Sk.B.Karishma “Modern Estimation technique for Undersea Active Target tracking”, International Journal of Engineering and Technology, Vol 8 No 2 Apr-May 2016,pp 791-803.

K.Lakshmi Prasanna, S.Koteswara Rao, A.Jawahar, Sk.B.Karishma “Ownship Strategies during Hostile Torpedo Attack”, Indian Journal of Science and Technology, Vol 9 (16), DOI:10.17485/ijst/2016/v9i16/85556, April 2016.


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