In this paper, a recursive state estimator is developed to handle the problem of state estimation of nonlinear discrete-time dynamical systems when some of the states of these systems are subject to equality or inequality constraints which are due to physical or practical considerations. The paper is concluded by a preliminary assessment of the performance of the proposed procedures with the help of applications regarding manned rotorcraft vehicles. In the case of the batch optimization methods, we present a formulation based on a new single-multiple shooting approach specifically designed for vehicle models with slow and fast solution components. An important highlight of the proposed approach is that it does not require a reduced-order model of the system. In the recursive approach, we formulate a novel version of the Extended Kalman Filter which specifically accounts for the presence of unobservable states in the model. Both classes of methods are formulated so as to be applicable to complex first-principle models of rotorcraft vehicles. We describe two alternative parameter estimation classes of methods in the time domain, namely the recursive filtering and the batch optimization methods. In this paper, we consider the problem of parameter estimation from flight test data for rotorcraft vehicle models.

Finally, the validity of the filtering scheme is verified by a numerical example. By comparing the filtering results, it shows that the addition of equality constraints can not only enhance the filtering effect, but also can estimate the loss points more effectively.

In the case where there is a loss of data, that is, the feature points are lost partly, and the predicted values of the lost points are estimated as the true value. Then, the equality constraints of the feature points are added to the filter scheme to increase the measurement information. Firstly, the acceleration model of the feature points in the image plane is established as the motion equation, and the motion information of the feature points is extracted by filter. In this paper, the extended Kalman filter (EKF) is used to estimate the position of the feature points when data missing occurs, taking the feature extraction of plane moving robot ceiling-based positioning as background and the coordinates of the feature points in the image plane as objects. The estimation performance is illustrated in numerical target tracking examples. Furthermore, an algorithm comparison, a performance analysis, and a convergence analysis are presented. For nonlinear systems and nonвЂђGaussian complex noise, an algorithm is proposed based on variational Bayesian inference to address this general problem. Therefore, linear systems with complex noise include additive noise and multiplicative noise, which are taken into account, and an optimal algorithm is deduced. Considering the additional prior information about the state with constraint increase, the estimate quality is compared to classical state estimation methods, which cannot utilize the prior information. Thus, this paper focuses on the state estimation problem with prior information for systems with complex noise pollution. Much a priori information and complex noise pollution exist in real systems and impact the accuracy of system descriptions. This paper derives several interesting properties of the constrained Kalman ВЇlters.ДЄccurate system description is important to obtain accurate state estimation for many application areas. This results in a family of constrained ВЇlters with each member parameterized by a weighting matrix. That is, given a linear system such that the expected values of the state variables satisfy some linear equality, we can constrain the Kalman ВЇlter estimates to sat-1 isfy those constraints. This paper extends that work to develop the properties of Kalman ВЇlters in the presence of statistical state constraints. Previous work by the authors demonstrated an analytic method of incorporating deterministic state equality constraints in the Kalman ВЇlter.

For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not ВЇt easily into the structure of the optimal ВЇlter. However, in the appli-cation of Kalman ВЇlters known signal information is often either ignored or dealt with heuristically. In the case that the random quantities are Gaussian, then the Kalman ВЇlter is the minimim variance state estimator.

For linear dynamic systems with white process and measurement noise, the Kalman ВЇlter is known to be the minimum variance linear state estimator.

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