Reduced-order Kalman filtering for state constrained linear systems

This paper aims at solving the state filtering problem for linear systems with state constraints. Three classes of typical state constraints, i.e., linear equality, quadratic equality and inequality, are discussed. By using the linear relationships among different state variables, a reduced-order Kalman filter is derived for the system with linear equality constraints. Afterwards, such a solution is applied to the cases of the quadratic equality constraint and inequality constraints and the two constrained state filtering problems are transformed into two relative constrained optimization problems. Then they are solved by the Lagrangian multiplier and linear matrix inequality techniques, respectively. Finally, two simple tracking examples are provided to illustrate the effectiveness of the reduced-order filters.

ESTIMATE ACCURACY OF NONLINEAR COEFFICIENTS OF SQUEEZEFILM DAMPER USING STATE VARIABLE FILTER METHOD

The estimate model for a nonlinear system of squeeze film damper (SFD) is described.The method of state variable filter (SVF) is used to estimate the coefficients of SFD.The factors which are critical to the estimate accuracy are discussed

On extended state Kalman filter-based identification algorithm for aerodynamic parameters

In this paper, the problem of time-varying aerodynamic parameters identification under measurement noises is studied. By analyzing the key aerodynamic parameters that affect the aircraft control system, a system model with extended states for identifying equivalent aerodynamic parameters is established, and error parameters are extended to the system state, avoiding the difficulty caused by the unknown dynamic in the system. Furthermore, an identification algorithm based on extended state Kalman filter is designed, and it is proved that the algorithm has quasi-consistency, thus, the estimation error can be evaluated in real time. Finally, the simulation results under typical flight scenarios show that the designed algorithm can accurately identify aerodynamic parameters, and has desired convergence speed and convergence precision.

Cubature Kalman filters: Derivation and extension

This paper focuses on the cubature Kalman filters （CKFs） for the nonlinear dynamic systems with additive process and measurement noise. As is well known, the heart of the CKF is the third-degree spherical–radial cubature rule which makes it possible to compute the integrals encountered in nonlinear filtering problems. However, the rule not only requires computing the integration over an n-dimensional spherical region, but also combines the spherical cubature rule with the radial rule, thereby making it difficult to construct higher-degree CKFs. Moreover, the cubature formula used to construct the CKF has some drawbacks in computation. To address these issues, we present a more general class of the CKFs, which completely abandons the spherical–radial cubature rule. It can be shown that the conventional CKF is a special case of the proposed algorithm. The paper also includes a fifth-degree extension of the CKF. Two target tracking problems are used to verify the proposed algorithm. The results of both experiments demonstrate that the higher-degree CKF outperforms the conventional nonlinear filters in terms of accuracy.

Adaptive Gaussian sum squared-root cubature Kalman filter with split-merge scheme for state estimation

The paper deals with state estimation problem of nonlinear non-Gaussian discrete dynamic systems for improvement of accuracy and consistency. An efficient new algorithm called the adaptive Gaussian-sum square-root cubature Kalman filter（AGSSCKF） with a split-merge scheme is proposed. It is developed based on the squared-root extension of newly introduced cubature Kalman filter（SCKF） and is built within a Gaussian-sum framework. Based on the condition that the probability density functions of process noises and initial state are denoted by a Gaussian sum using optimization method, a bank of SCKF are used as the sub-filters to estimate state of system with the corresponding weights respectively, which is adaptively updated. The new algorithm consists of an adaptive splitting and merging procedure according to a proposed split-decision model based on the nonlinearity degree of measurement. The results of two simulation scenarios（one-dimensional state estimation and bearings-only tracking） show that the proposed filter demonstrates comparable performance to the particle filter with significantly reduced computational cost.

Event-based Control and Filtering of Networked Systems:A Survey

In recent years, theoretical and practical research on event-based communication strategies has gained considerable research attention due primarily to their irreplaceable superiority in resource-constrained systems（especially networked systems）. For networked systems, event-based transmission scheme is capable of improving the efficiency in resource utilization and prolonging the lifetime of the network components compared with the widely adopted periodic transmission scheme. As such, it would be interesting to 1） examining how the event-triggering mechanisms affect the control or filtering performance for networked systems, and 2） developing some suitable approaches for the controller and filter design problems. In this paper, a bibliographical review is presented on event-based control and filtering problems for various networked systems. First, the event-driven communication scheme is introduced in detail according to its engineering background, characteristic, and representative research frameworks. Then, different event-based control and filtering（or state estimation） problems are categorized and then discussed. Finally, we conclude the paper by outlining future research challenges for event-based networked systems.

A principal consideration on general Bayes'filters for a state estimation of environmental sound and vibration systems

This paper describes a fundamental consideration on our works on the design of general Bayes' filters for the state estimation of non-stationary, non-linear, and non-Gaussian environmental sound and vibration systems. We have discussed an essential point of several Bayes' filters proposed by using the orthogonal or non-orthogonal expansion form of Bayes' theorem. They can estimate any kinds of statistics of arbitrary function type of state variables including the lower and the higher order statistics connected with the Lx evaluation index in the environmental sound and vibration systems. Here, we have mainly focussed on giving the fundamental viewpoints of their design policies. Some new estimation methods and new results not yet published are included.

Recursive Filter with Partial Knowledge on Inputs and Outputs

This paper investigates the problem of state estimation for discrete-time stochastic linear systems, where additional knowledge on the unknown inputs is available at an aggregate level and the knowledge on the missing measurements can be described by a known stochastic distribution. Firstly, the available knowledge on the unknown inputs and the state equation is used to form the prior distribution of the state vector at each time step. Secondly, to obtain an analytically tractable likelihood function, the effect of missing measurements is broken down into a systematic part and a random part, and the latter is modeled as part of the observation noise. Then, a recursive filter is obtained based on Bayesian inference. Finally, a numerical example is provided to evaluate the performance of the proposed methods.