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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 139503, 10 pages
Research Article

Support Vector Regression-Based Adaptive Divided Difference Filter for Nonlinear State Estimation Problems

College of Automation, Harbin Engineering University, Harbin 150001, China

Received 2 March 2014; Accepted 4 May 2014; Published 25 May 2014

Academic Editor: Weichao Sun

Copyright © 2014 Hongjian Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a support vector regression-based adaptive divided difference filter (SVRADDF) algorithm for improving the low state estimation accuracy of nonlinear systems, which are typically affected by large initial estimation errors and imprecise prior knowledge of process and measurement noises. The derivative-free SVRADDF algorithm is significantly simpler to compute than other methods and is implemented using only functional evaluations. The SVRADDF algorithm involves the use of the theoretical and actual covariance of the innovation sequence. Support vector regression (SVR) is employed to generate the adaptive factor to tune the noise covariance at each sampling instant when the measurement update step executes, which improves the algorithm’s robustness. The performance of the proposed algorithm is evaluated by estimating states for (i) an underwater nonmaneuvering target bearing-only tracking system and (ii) maneuvering target bearing-only tracking in an air-traffic control system. The simulation results show that the proposed SVRADDF algorithm exhibits better performance when compared with a traditional DDF algorithm.