Discrete-time sliding mode observer for the state estimation of a manoeuvring target

Abstract

This article addresses the problem of estimating the position, velocity, and acceleration of a manoeuvring target from noisy position measurements. A discrete-time sliding mode observer is designed to handle unmeasured disturbance input and measurement noise. A first-order linear dynamics is considered for target acceleration. The acceleration input command and the pole of the first-order acceleration dynamics are considered to be unknown parameters with known upper bounds. A finite non-zero boundary layer is employed to reduce the chattering phenomenon typically associated with sliding mode observers. Analysis of estimation error dynamics is presented for the case where the discrete-time sliding mode observer is operating outside the boundary layer and also within the boundary layer. An algorithm is developed for obtaining the observer gain vector that guarantees the stability of the error dynamics. Numerical simulations and experimental results are presented to validate the stability and performance of the proposed observer.

Keywords

Discrete-time sliding mode observer error dynamics polytopic uncertainty target tracking

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References

Yanushevsky

RT.

Generalized missile guidance laws against manoeuvring targets. Proc IMechE, Part I: J Systems and Control Engineering 2007; 221(4): 645–651.

Kandath

Bera

Bardhan

et al . Autonomous navigation and sensorless obstacle avoidance for UGV with environment information from UAV. In: Second IEEE international conference on robotic computing (IRC), Laguna Hills, CA, 31 January–2 February 2018, pp.266–269. New York: IEEE.

Blair

Watson

Rice

. Interacting multiple model filter for tracking maneuvering targets in spherical coordinates. In: IEEE proceedings of SoutheastCon, Williamsburg, VA, 7–10 April 1991, pp.1055–1059. New York: IEEE.

Lan

Jilkov

et al . Second-order Markov chain based multiple-model algorithm for maneuvering target tracking. IEEE T Aero Elec Syst 2013; 49(1): 3–19.

Mazor

Averbuch

Bar-Shalom

et al . Interacting multiple model methods in target tracking: a survey. IEEE T Aero Elec Syst 1998; 34(1): 103–123.

Mehrotra

Mahapatra

PR.

A jerk model for tracking highly maneuvering targets. IEEE T Aero Elec Syst 1997; 33(4): 1094–1105.

Cao

Jiang

Wang

et al . Tracking methods of high speed strong maneuvering targets in near space. In: 12th international conference on signal processing (ICSP), Hangzhou, China, 19–23 October 2014, pp.1885–1889.

Jin

Jiu

et al . Switched Kalman filter-interacting multiple model algorithm based on optimal auto-regressive model for manoeuvring target tracking. IET Radar Sonar Nav 2015; 9(2): 199–209.

Simon

Optimal state estimation: Kalman, H infinity, and nonlinear approaches. New York: Wiley, 2006.

10.

Spurgeon

SK.

Sliding mode observers: a survey. Int J Syst Sci 2008; 39(8): 751–764.

11.

Davila

Fridman

Levant

Second-order sliding-mode observer for mechanical systems. IEEE T Automat Contr 2005; 50(11): 1785–1789.

12.

Thein

MWL

. A discrete time variable structure observer with overlapping boundary layers. In: Proceedings of the American control conference, Anchorage, AK, 8–10 May 2002, pp.2633–2638. New York: IEEE.

13.

Mihoub

Nouri

Abdennour

RB.

A second order discrete sliding mode observer for the variable structure control of a semi-batch reactor. Control Eng Pract 2011; 19(1): 1216–1222.

14.

Bernardes

Montagner

Grundling

et al . Discrete-time sliding mode observer for sensorless vector control of permanent magnet synchronous machine. IEEE T Ind Electron 2014; 61(4): 1679–1691.

15.

Pal

Seetharama Bhat

Discrete time second order sliding mode observer for uncertain linear multi-output system. J Frankl Inst 2014; 351(4): 2143–2168.

16.

Harikumar

Bera

Bardhan

et al . State estimation of an agile target using discrete sliding mode observer. In: 5th international conference on control, decision and information technologies (CoDIT), Thessaloniki, 10–13 April 2018, pp.75–79. New York: IEEE.

17.

Sun

Lin

TL.

An adjustable parameter model for tracking a manoeuvring target. Proc IMechE, Part I: J Systems and Control Engineering 2003; 217(4): 275–284.

18.

Peaucelle

Ebihara

. Robust stability analysis of discrete-time systems with parametric and switching uncertainties. In: Proceedings of 19th world congress of IFAC, Cape Town, South Africa, 24–29 August 2014, pp.724–729. Kidlington Oxford, UK: Elsevier.

19.

Bizhong

Zheng

Zizhou

et al . Strong tracking of a H-infinity filter in lithium-ion battery state of charge estimation. Energies 2018; 11(6): 1481.

20.

Harikumar

Bera

Bardhan

et al . Cooperative obstacle avoidance for heterogeneous unmanned systems during search mission. Encycl Semant Comput Robot Intell 2018; 2(1): 1850002.