Strong Tracking Filtering Algorithm of Randomly Delayed Measurements for Nonlinear Systems

Abstract

This paper focuses on the filtering problems of nonlinear discrete-time stochastic dynamic systems, such as the model simplification, noise characteristics uncertainty, initial conditions uncertainty, or system parametric variation. Under these circumstances, the measurements of system have one sampling time random delay. A new method, that is, strong tracking filtering algorithm of randomly delayed measurements (STF/RDM) for nonlinear systems based on recursive operating by analytical computation and first-order linear approximations, is proposed; a principle of extended orthogonality is presented as a criterion of designing the STF/RDM, and through the residuals between available and predicted measurements, the formula of fading factor is obtained. Under the premise of using the extended orthogonality principle, STF/RDM proposed in this paper can adjust the fading factor online via calculating the covariance of residuals, and then the gain matrices of the STF/RDM adjust in real time to enhance the performance of the proposed method. Lastly, in order to prove that the performance of STF/RDM precedes existing EKF method, the experiment of tracking maneuvering aircraft is carried out.

Strong Tracking Filter for Nonlinear Systems with Randomly Delayed Measurements and Correlated Noises

“…Equation (40) is the performance index of the proposed EKF, and the corresponding derivation process can refer to [22]. Equation (41) means that the discretionarily chosen pairs of residuals which are calculated based on (9) and (19) are mutually orthogonal.…”

“…Similar to the idea of the literature [22], for obtaining the suboptimal fading factor +1 , the trace operation is introduced into both sides of (63) as follows:…”

“…where (0 < ≤ 1) is a forgetting factor which is often selected as = 0.95 according to [22]. For +1 ≥ 1, the suboptimal fading factor +1 can take effect, so +1 can be ultimately calculated via…”

“…But the following cases may occur in practical situations; that is, the measurements received may be affected by the random delay, or the process noise may be correlated with the measurement noise. For the first case, literatures [21,22] have, respectively, proposed the networked STF and STF with randomly delayed measurements (STF/RDM). For the second case, a novel nonlinear filter derived from square-root CKF and the idea of STF was proposed in [23].…”

“…For the second case, a novel nonlinear filter derived from square-root CKF and the idea of STF was proposed in [23]. However, when the above two cases exist simultaneously, these existing STFs [17][18][19][20][21][22][23] are not suitable for dealing with the filtering problem in the above two coupled cases, and little attention has been paid to the study of deriving the corresponding STF. Consequently, there is a great demand to further improve the STF for the nonlinear discrete-time stochastic dynamic systems with randomly delayed measurements and correlated noises, which motivate this study.…”