Evolutionary programming Kalman ®lter Zhiqian Weng a , Guanrong Chen b , Leang S. Shieh b, * , Johan Larsson b a College of Astronautics, Northwestern Polytechnical University, Xi'an 710072, People's Republic of China b Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77204-4793, USA Received 1 January 2000; received in revised form 5 May 2000; accepted 28 July 2000 Abstract A robust Kalman ®ltering (KF) algorithm based on the evolutionary programming (EP) technique is proposed in this paper, for uncertain systems with unknown-but- bounded uncertain parameters which are described by interval systems. This algorithm takes advantage of the global optima-searching capability of EP to ®nd the optimal KF results at every iteration, which include both the upper±lower boundaries and the nominal trajectory of the optimal estimates of the system state vectors. One prominent feature of this EP ®ltering algorithm is that it assumes the same statistical conditions and provides the same optimal estimates as the conventional KF scheme. Both linear and nonlinear systems are studied. Two typical computer simulation examples are given with comparison, which verify the merits of the new method ± it yields more accurate estimation results and is less conservative as compared to the existing interval Kalman ®ltering (IKF). Ó 2000 Elsevier Science Inc. All rights reserved. Keywords: Evolutionary programming; Kalman ®lter; Interval systems; Uncertain systems Information Sciences 129 (2000) 197±210 www.elsevier.com/locate/ins * Corresponding author. Tel.: +1-713-743-4439; fax: +1-713-743-4444. E-mail address: lshieh@uh.edu (L.S. Shieh). 0020-0255/00/$ - see front matter Ó 2000 Elsevier Science Inc. All rights reserved. PII: S 0 0 2 0 - 0 2 5 5 ( 0 0 ) 0 0 0 6 4 - 5