Equivalence between the internal observability and equation

This paper is concerned with a third order in time linear Moore-Gibson-Thompson equation which describes the acoustic velocity potential in ultrasound wave program.Influenced by the work of Kaltenbacher,Lasiecka and Marchand(Control Cybernet.2011,40:971-988),we establish an observability inequality of the conservative problem,and then discuss the equivalence between the exponential stabilization of a dissipative system and the internal observational inequality of the corresponding conservative system.

Optimal maneuver strategy to improve the observability of angles-only rendezvous

This paper proposes an optimal maneuver strategy to improve the observability of angles-only rendezvous from the perspective of relative navigation.A set of dimensionless relative orbital elements(ROEs)is used to parameterize the relative motion,and the objective function of the observability of anglesonly navigation is established.An analytical solution of the optimal maneuver strategy to improve the observability of anglesonly navigation is obtained by means of numerical analysis.A set of dedicated semi-physical simulation system is built to test the performances of the proposed optimal maneuver strategy.Finally,the effectiveness of the method proposed in this paper is verified through the comparative analysis of the objective function of the observability of angles-only navigation and the performances of the angles-only navigation filter under different maneuver schemes.Compared with the cases without orbital maneuver,it is concluded that the tangential filtering accuracy with the optimal orbital maneuver at the terminal time is increased by 35%on average,and the radial and normal filtering accuracy is increased by 30%on average.

Optimal maneuvering strategy of spacecraft evasion based on angles-only measurement and observability analysis

Spacecraft orbit evasion is an effective method to ensure space safety. In the spacecraft’s orbital plane, the space non-cooperate target with autonomous approaching to the spacecraft may have a dangerous rendezvous. To deal with this problem, an optimal maneuvering strategy based on the relative navigation observability degree is proposed with angles-only measurements. A maneuver evasion relative navigation model in the spacecraft’s orbital plane is constructed and the observability measurement criteria with process noise and measurement noise are defined based on the posterior Cramer-Rao lower bound. Further, the optimal maneuver evasion strategy in spacecraft’s orbital plane based on the observability is proposed. The strategy provides a new idea for spacecraft to evade safety threats autonomously. Compared with the spacecraft evasion problem based on the absolute navigation, more accurate evasion results can be obtained. The simulation indicates that this optimal strategy can weaken the system’s observability and reduce the state estimation accuracy of the non-cooperative target, making it impossible for the non-cooperative target to accurately approach the spacecraft.

Sectorial Approach of the Gradient Observability of the Hyperbolic Semilinear Systems Intern and Boundary Cases

The aim of this paper is to study the notion of the gradient observability on a subregion w of the evolution domain W and also we consider the case where the subregion of interest is a boundary part of the system evolution domain for the class of semilinear hyperbolic systems. We show, under some hypotheses, that the flux reconstruction is guaranteed by means of the sectorial approach combined with fixed point techniques. This leads to several interesting results which are performed through numerical examples and simulations.

Controllability and observability of networked control systems with time-varying delays

The controllability and observability of networked control systems are studied. Aiming at the networked control system with time-varying delay, the sufficient and necessary conditions for complete controllability and complete observability of the system are presented, respectively. Because of Markov characteristic of the network-induced delay, in terms of stochastic theory, a sufficient and necessary condition for completely mean value controllability of networked control systems is obtained. Further, the conditions that the controllability and observability of networked control systems are equivalent to the initial time-invariant system are given. Controllability and observability realization indexes are also discussed, respectively. The numerical example demonstrates the effectiveness of the proposed theory.

Impact of Coastal Radar Observability on the Forecast of the Track and Rainfall of Typhoon Morakot(2009)Using WRF-based Ensemble Kalman Filter Data Assimilation

This study explored the impact of coastal radar observability on the forecast of the track and rainfall of Typhoon Morakot （2009） using a WRF-based ensemble Kalman filter （EnKF） data assimilation （DA） system. The results showed that the performance of radar EnKF DA was quite sensitive to the number of radars being assimilated and the DA timing relative to the landfall of the tropical cyclone （TC）. It was found that assimilating radial velocity （Vr） data from all the four operational radars during the 6 h immediately before TC landfall was quite important for the track and rainfall forecasts after the TC made landfall. The TC track forecast error could be decreased by about 43% and the 24-h rainfall forecast skill could be almost tripled. Assimilating Vr data from a single radar outperformed the experiment without DA, though with less improvement compared to the multiple-radar DA experiment. Different forecast performances were obtained by assimilating different radars, which was closely related to the first-time wind analysis increment, the location of moisture transport, the quasi-stationary rainband, and the local convergence line. However, only assimilating Vr data when the TC was farther away from making landfall might worsen TC track and rainfall forecasts. Besides, this work also demonstrated that Vr data from multiple radars, instead of a single radar, should be used for verification to obtain a more reliable assessment of the EnKF performance.

The Controllability, Observability, and Stability Analysis of a Class of Composite Systems with Fractional Degree Generalized Frequency Variables

This paper is concerned with fundamental properties of a class of composite systems with fractional degree generalized frequency variables, including controllability, observability and stability. Firstly, some necessary and sufficient conditions are given to guarantee controllability and observability of such composite systems. Then we prove that the stability problem of such composite systems can be reduced to judging whether a fractional degree polynomial is stable. Finally, the stability analysis result is applied in the supervisory control of fractional-order multi-agent systems, and an example is provided to illustrate the effectiveness of the proposed methods.

Self-alignment of full skewed RSINS: observability analysis and full-observable Kalman filter

Traditional orthogonal strapdown inertial navigation sys-tem （SINS） cannot achieve satisfactory self-alignment accuracy in the stationary base： taking more than 5 minutes and al the iner-tial sensors biases cannot get ful observability except the up-axis accelerometer. However, the ful skewed redundant SINS （RSINS） can not only enhance the reliability of the system, but also improve the accuracy of the system, such as the initial alignment. Firstly, the observability of the system state includes attitude errors and al the inertial sensors biases are analyzed with the global perspective method： any three gyroscopes and three accelerometers can be assembled into an independent subordinate SINS （sub-SINS）;the system state can be uniquely confirmed by the coupling connec-tions of al the sub-SINSs;the attitude errors and random constant biases of al the inertial sensors are observable. However, the ran-dom noises of the inertial sensors are not taken into account in the above analyzing process. Secondly, the ful-observable Kalman filter which can be applied to the actual RSINS containing random noises is established; the system state includes the position, ve-locity, attitude errors of al the sub-SINSs and the random constant biases of the redundant inertial sensors. At last, the initial self-alignment process of a typical four-redundancy ful skewed RSINS is simulated： the horizontal attitudes （pitch, rol ） errors and yaw error can be exactly evaluated within 80 s and 100 s respectively, while the random constant biases of gyroscopes and accelero-meters can be precisely evaluated within 120 s. For the ful skewed RSINS, the self-alignment accuracy is greatly improved, mean-while the self-alignment time is widely shortened.

Online Detection of State Estimator Performance Degradation via Efficient Numerical Observability Analysis

An efficient observability analysis method is proposed to enable online detection of performance degradation of an optimization-based sliding window visual-inertial state estimation framework.The proposed methodology leverages numerical techniques in nonlinear observability analysis to enable online evaluation of the system observability and indication of the state estimation performance.Specifically,an empirical observability Gramian based approach is introduced to efficiently measure the observability condition of the windowed nonlinear system,and a scalar index is proposed to quantify the average system observability.The proposed approach is specialized to a challenging optimizationbased sliding window monocular visual-inertial state estimation formulation and evaluated through simulation and experiments to assess the efficacy of the methodology.The analysis result shows that the proposed approach can correctly indicate degradation of the state estimation accuracy with real-time performance.

Observability Analysis in Parameters Estimation of an Uncooperative Space Target

To study the parameter estimating effects of a free-floating tumbling space target,the extended Kalman filter(EKF)scheme is utilized with different high-nonlinear translational and rotational coupled kinematic&dynamic models on the LIDAR measurements.Applying the aforementioned models and measurements results in the situation where one single state can be estimated differently with varying accuracies since the EKFs based on different models have different observabilities.In the proposed EKFs,the traditional quaternions based kinematics and dynamics and the dual vector quaternions(DVQ)based kinematics and dynamics are used for the modeling of the relative motions between a chaser satellite and an uncooperative target.In the non-contact estimating scenarios,only highly nonlinear relative attitude and range measurements:the grapple fixture on the target measured from the chaser satellite via vision-based sensors,can be used.By evaluating the results of the EKFs,the observability properties of each EKF are studied analytically and numerically with the the Observability Gramian matrices(OG)and the standard deviations for every estimated parameters.The analysis of observability perform intensive studies and reveal the intrinsic factors that affect the accuracy and stability of the parameters estimation of an uncooperative space target.Finally,the analytical and numerical results show the optimal composition of the kinematic&dynamic models and measurements.

Observability and estimability of passive radar with unknown illuminator states using different observations

Most existing studies about passive radar systems are based on the already known illuminator of opportunity(IO)states.However,in practice,the receiver generally has little knowledge about the IO states.Little research has studied this problem.This paper analyzes the observability and estimability for passive radar systems with unknown IO states under three typical scenarios.Besides,the directions of high and low estimability with respect to various states are given.Moreover,two types of observations are taken into account.The effects of different observations on both observability and estimability are well analyzed.For the observability test,linear and nonlinear methods are considered,which proves that both tests are applicable to the system.Numerical simulations confirm the correctness of the theoretical analysis.

Observability analysis of feature aided terminal guidance systems

Feature aided design of estimators and guidance laws can significantly improve the interception performance of the terminal guidance system. The achieved enhancement can be effectively assessed by observability analysis methods. This paper first analyzes and discusses the existing assessment methods in a typical endgame scenario with target orientation observations. To get over their deficiencies, a novel singular value decomposition（SVD） method is proposed. Employing both theoretical analysis and numerical simulation, the proposed method can represent the degree of state observability which is enhanced by integrating target features more completely and quantitatively.

An identity concerning controllability observability and coprimeness of linear systems and its applications

It is shown in this paper that any state space realization （A, b, c） of a given transfer function T（s） =β（s）/α（s）with α（s）monic and dim（A）=deg（α（s））,satisfies the identity β（A）=Qe（A,b）Sα Qo（A,c）where Qc （A,b）and Qo（A, c） are the controllability matrix and observability matrix of the matrix triple （A, b, c）, respectively, and S,~ is a nonsingular symmetric matrix. Such an identity gives a deep relationship between the state space description and the transfer function description of single-input single-output （SISO） linear systems. As a direct conclusion, we arrive at the well-known result that a realization of any transfer function is minimal if and only if the numerator and the denominator of the transfer function is coprime. Such a result is also extended to the SISO descriptor linear system case. As an applications, a complete solution to the commuting matrix equation AX --- XA is proposed and the minimal realization of multi-input multi-output （MIMO） linear system is considered.

Observability of Inertial Navigation System

To improve the observability of strapdown inertial navigation system and the effectiveness of Kalman filter in the navigation system, the method of estimating the observability is analyzed based on eigenvalues and eigenvectors which are proved to be availabe, on this basis two-position alignment technigue is applied. The simulation shows that two-position alignment really makes the system＇s observability change from being incomplete to being complete, and the test method based on eigenvalues and eigenvectors is available to determine the observability of every state vector.

Observability conditions of switched linear singular systems

The observability problem of switched linear singular（SLS） systems is studied in this paper. Based on the observability definition, the unobservable subspaces of given switching laws are investigated under the condition that all subsystems are regular. A necessary condition and a sufficient condition for observability of SLS systems are given. It is shown that the observability and controllability are dual for some special SLS systems with circulatory switching laws. The method developed here is applicable to the observability analysis of normal switched linear systems.

Exact Controllability and Exact Observability of Descriptor Infinite Dimensional Systems

Necessary and sufficient conditions for the exact controllability and exact observability of a descriptor infinite dimensional system are obtained in the sense of distributional solution.These general results are used to examine the exact controllability and exact observability of the Dzektser equation in the theory of seepage and the exact controllability of wave equation.

Anticipating Degradation in State Estimation Accuracy via Online Nonlinear Observability Analysis

A methodology is proposed to enable real-time evaluation of the observability of local motions,and generate a local observability cost map to enable informed local motion planning in order to avoid potential degradation or degeneracy in state estimator performance.The proposed approach leverages efficient numerical techniques in nonlinear observability analysis and motion primitive-based planning technique to realize the local observability prediction with real-time performance.The degradation of the state estimation performance can be readily predicted with the local observability evaluation result.The proposed approach is specialized to a representative optimization-based monocular visual-inertial state estimation formulation and evaluated through simulation and experiments.The experimental results demonstrated the ability of the proposed methodology to correctly anticipate the potential state estimation degradation.

Optimal Observability Analysis of Gimbled Inertial Navigation System on the Moving Base

To investigate the observability of gimbled inertial navigation system when the base moves on the basis of piece-wise constant system's observability theory and singular value decomposition, the variation of the singular value in the observability matrix with time is discussed. The simulation results reveal that only if orientation angle is 60° and the flight route is S-figure in initial alignment, the optimal observability is obtained, thus a theoretical foundation for fast and accurate alignment of GINS is provided.

Three-Dimensional Discrete Observability Analysis for Air-to-Air Missile Target Tracking

The interception information of infrared（ IR）-guided air-to-air missiles（ AAM） is mainly estimated only using the basic bearing measurements. In order to intercept highly maneuverable targets,it is essential to study the system observability to improve the target tracking system performance.The uniqueness of this paper is that the observability analysis is derived based on a discrete three-dimensional （3D） system model. During the maneuvering scenario,the system is approximated by a segment-by-segment system. The relationship between missile-target motion and observability is given by direct and dual approaches. Meanwhile sufficient observability conditions are derived. Moreover,a numerical simulation is conducted and an alternate method is provided to reinforce the proposed observability analysis results.

Measuring observability by generalized information theoretic quantities

A normalized measure is established to provide the quantitative information about the degree of observability for the discrete-time, stochastically autonomous system. This measure is based on the generalized information theoretic quantities （generalized entropy, mutual information） of the system state and the observations, where the system state can be a discrete or a continuous random vector. Some important properties are presented. For the linear case, the explicit formula for the degree of observability is derived, and the equivalence between the proposed measure and the traditional rank condition is proved. The curves for the degree of observability are depicted in a simple example.