Least trace extended set-membership filter

To improve the consistency of estimation result, a least-trace extended set-membership filter （LTESMF） is presented for a class of nonlinear stochastic systems, which has linear output and unknown- but-bounded noise. Feedback technique is used instead of the intersection of ellipsoid-sets in the measurement update. The feedback parameter is optimized in order to minimize the trace of error bounded ellipsoid＇s envelop matrix. A new stability analysis method was developed to prove the stochastic system＇s stability by using the convergence of some measurement of the error bounded ellipsoid. Analysis result shows that the estimation error of LTESMF will converge to a bounded area. A simulation of SINS/GPS integrated alignment with large misalignment angles is conducted. The results demonstrate that the convergence speed and the consistency of LTESMF are much better than those of extended Kalman filter （EKF）, in addition the steady estimation precision and computational complexity are close to that of EKF.