The unscented Kalman filter (UKF) proposed in [12,13] uses a minimal set of deterministically chosen sample points to capture the mean and covariance of a Gaussian density. following website When propagated through a nonlinear function, these points capture the true mean and covariance up to a second-order of the nonlinear function. However, the parameters used in the UKF are required to tune finely in order to prevent the propagation of non-positive definite covariance matrix for a state vector’s dimension higher than three. Another Gaussian filter, named the divided difference filter (DDF) was introduced in Inhibitors,Modulators,Libraries [14] using multidimensional Stirling’s interpolation formula. It is shown in [15] that the UKF and DDF algorithms are commonly referred to as sigma point filters due to the properties of deterministic sampling and weighted statistical estimation [16], but the covariance obtained in the DDF is more accurate than that in the UKF.
The iterated UKF with the variable step (IUKF-VS) in [10] proposed improved the accuracy of state estimation but its runtime was large due to its computation of the sigma points. Lastly, a relatively Inhibitors,Modulators,Libraries new technique called the particle filter (PF) uses a set of randomly chosen samples with associated weights to approximate the posterior density [17] and its variants are presented in [18]. The large number of samples required often makes the use of PF computationally expensive, and the performance of PF is crucially dependent on the selection of the proposal distribution. Table 1 lists the pro and cons of the above filters.Table 1.Pro and cons for various filters.
The DDF also shows its weakness in the state estimation due to the large initial error and high nonlinearity in the application for state estimation of maneuvering target in the air-traffic Inhibitors,Modulators,Libraries control and ballistic re-entry target. Emboldened by the superiority of DDF, the basic idea of the IEKF and the iteration termination condition based on maximum likelihood, we propose a new filter named the maximum likelihood based iterated divided difference Kalman filter (MLIDDF). The performance of the state estimation for MLIDDF is greatly improved when involving the use of the iteration measurement update in the MLIDDF and the use of the current measurement. The remainder of this paper is organized as follows: in Section 2, we develop the maximum likelihood surface based iterated divided difference Kalman filter (MLIDDF).
Section 3 presents the applications of the MLIDDF to state estimation for maneuvering targets in air-traffic control and ballistic target re-entry applications and discuss the simulation results. Finally, Section 4 concludes the Inhibitors,Modulators,Libraries paper and presents our outlook on future work.2.?Development Carfilzomib of Likelihood Surface Based Iterated Divided Difference Filter2.1. Divided Difference FilterConsider the nonlinear function:y=f(x)(1)Assuming that the random selleck products variable x nx has Gaussian density with mean and covariance Px.