Localization of mobile transmitters by means of linear state estimation using RSS measurements

This paper investigates the problem of estimating the location and velocity of a mobile agent using the received signal strength (RSS) measurements. Typical power measurements are inherently nonlinear and in this approach we derive a linear measurement scheme using an analytical measurement conversion technique which can readily be used with RSS measuring sensors. Power measurements are hence used in our robust version of a linear Kalman filter to estimate the dynamic parameters of the moving transmitter.

Vision-based target tracking and surveillance with robust set-valued state estimation

Tracking a target from a video stream (or a sequence of image frames) involves nonlinear measurements in Cartesian coordinates. However, the target dynamics, modeled in Cartesian coordinates, result in a linear system. We present a robust linear filter based on an analytical nonlinear to linear measurement conversion algorithm. Using ideas from robust control theory, a rigorous theoretical analysis is given which guarantees that the state estimation error for the filter is bounded, i.e., a measure against filter divergence is obtained. In fact, an ellipsoidal set-valued estimate is obtained which is guaranteed to contain the true target location with an arbitrarily high probability. The algorithm is particularly suited to visual surveillance and tracking applications involving targets moving on a plane.

A robust set-valued state estimation approach to the problem of vision based SLAM for mobile robots

The problem of visual simultaneous localization and mapping (SLAM) is examined in this paper using ideas and algorithms from robust control and estimation theory. Using a stereo-vision based sensor, a nonlinear measurement model is derived which leads to nonlinear measurements of the landmark coordinates along with optical flow based measurements of the relative robot-landmark velocity. Using a novel analytical measurement transformation, the nonlinear SLAM problem is converted into the linear filter is guaranteed stable and the ALAM state estimation error is bounded within an ellipsoidal set. No similar results are available for the commonly employed extended Kalman filter which is known to exhibit divergent and inconsistency characteristics in practice.

Fusion based 3D tracking of mobile transmitters via robust set-valued state estimation with RSS measurements

This paper investigates the problem of location and velocity detection of a mobile agent using Received Signal Strength (RSS) measurements captured by geographically distributed seed nodes. With inherently nonlinear power measurements, we derive a powerful linear measurement scheme using an analytical measurement conversion technique which can readily be used with RSS measuring sensors. We also employ the concept of sensor fusion in conjunction for the case of redundant measurements to further enhance the estimation accuracy.

New results in robust functional state estimation using two sliding mode observers in cascade

 This paper presents a functional observer scheme using two sliding mode observers in cascade. A coordinate transformation is performed on the system such that existing sliding mode observer theory can be directly applied to achieve functional state estimation. The necessary and sufficient existence conditions for the scheme (in terms of the original system matrices) are also investigated, and they are found to be less stringent than earlier work on functional state estimation using one sliding mode observer; this could have benefits in terms of cost and simplicity. A numerical example verifies the effectiveness of the scheme.

ε-bounded state estimation for time-delay systems with bounded disturbances

A new problem on ε-bounded functional state estimation for time-delay systems with unknown bounded disturbances is studied in this paper. In the presence of unknown bounded disturbances, the common assumption regarding the observers matching condition is no longer required. In this regard, instead of achieving asymptotic convergence for the observer error, the error is now required to converge exponentially within a ball with a small radius ε > 0. This means that the estimate converges exponentially within an ε-bound of the true value. A general observer that utilises multiple-delayed output and input information is proposed. Sufficient conditions for the existence of the proposed observer are first given. We then employ an extended Lyapunov-Krasovskii functional which combines the delay-decomposition technique with a triple-integral term to study the ε-convergence problem of the observer error system. Moreover, the obtained results are shown to be more effective than the existing results for the cases with no disturbances and/or no time delay. Three numerical examples are given to illustrate the obtained results.

Partial state estimation for linear systems with output and input time delays.

This paper deals with the problem of partial state observer design for linear systems that are subject to time delays in the measured output as well as the control input. By choosing a set of appropriate augmented Lyapunov-Krasovskii functionals with a triple-integral term and using the information of both the delayed output and input, a novel approach to design a minimal-order observer is proposed to guarantee that the observer error is ε-convergent with an exponential rate. Existence conditions of such an observer are derived in terms of matrix inequalities for the cases with time delays in both the output and input and with output delay only. Constructive design algorithms are introduced. Numerical examples are provided to illustrate the design procedure, practicality and effectiveness of the proposed observer.

Reduced order functional observers with application to partial state estimation of linear systems with input delay

Reduced order multi-functional observer design for multi-input multi-utput (MIMO) linear time-invariant (LTI) systems with constant delayed inputs is studied. This research is useful in the input estimation of LTI systems with actuator delay, as well as system monitoring and fault detection of these systems. Two approaches for designing an asymptotically stable functional observer for the system are proposed: delay-dependent and delay-free. The delay-dependent observer is infinite-dimensional, while the delay-free structure is finite-dimensional. Moreover, since the delay-free observer does not require any information on the time delay, it is more practical in real applications. However, the delay-dependent observer contains less restrictive assumptions and covers more variety of systems. The proposed observer design schemes are novel, simple to implement, and have improved numerical features compared to some of the other available approaches to design (unknown-input) functional observers. In addition, the proposed observers usually possess lower order than ordinary Luenberger observers, and the design schemes do not need the observability or detectability requirements of the system. The necessary and sufficient conditions of the existence of an asymptoticobserver in each scenario are explored. The extensions of the proposed observers to systems with multiple delayed-inputs are also discussed. Several numerical examples and simulation results are employed to support our theories.

New results in common functional state estimation for two linear systems with unknown inputs

This paper presents new developments in common functional observers for two systems. We improve an existing common functional observer scheme by reducing its order, and then investigate its existence conditions in terms of the original system matrices. These conditions have never been explored and they enable the users to know at the outset the class of systems for which the scheme is applicable. They also show that both observers can be designed independently of each other which significantly simplifies the design process. A numerical simulation verifies the findings.

Partial state estimation: a new design approach

© 2014 IEEE. There are three different approaches for functional observer design for Linear Time-Invariant (LTI) systems within the literature. One of the most common methods has been proposed by Aldeen [1] and further developed by others. We found several examples in which the necessary and sufficient conditions for the existence of a functional observer are actually not sufficient for this methodology. This finding motivated us to develop a new methodology for designing functional observers. Our new method provides enough degrees of freedom for the observer design parameter and it improves the weakness within the Aldeen's method in solving the observer coupled matrix equations. In this paper, we present the reason and an example to show the insufficiency of the former method. Furthermore, we present our new developed methodology. An illustrative algorithm also describes the design procedure step by step. A numerical example and simulation results support our findings and performance of the proposed method.

Partial state estimation of LTI systems with multiple constant time-delays

Functional observer design for Multi-Input Multi-Output (MIMO) Linear Time-Invariant (LTI) systems with multiple mixed time delays in the states of the system is addressed. Two structures for the design of a minimum-order observer are considered: 1 - delay-dependent, and 2 - internal-delay independent. The parameters of the delay-dependent observer are designed using the Lyapunov Krasovskii approach. The delay-dependent exponential stability of the observer for a specified convergence rate and delay values is guaranteed upon the feasibility of a set of Linear Matrix Inequalities (LMIs) together with a rank condition. Using the descriptor transformation, a modified Jensen's inequality, and improved Park's inequality, the results can be less conservative than the available functional observer design methods that address LTI systems with single state delay. Furthermore, the necessary and sufficient conditions of the asymptotic stability of the internal-delay independent observer are obtained, which are shown to be independent of delay. Two illustrative numerical examples and simulation studies confirm the validity and highlight the performance of the proposed theoretical achievements.

Minimum-order filter design for partial state estimation of linear systems with multiple time-varying state delays and unknown input delays

Designing delay-dependent functional observers for LTI systems with multiple known time-varying state delays and unknown time-varying input delays is studied. The input delays are arbitrary, but the state delays should be upper-bounded. In addition, two scenarios of slow-varying and fast-varying state delays are investigated. The results of the paper can also be considered as one of the first contributions considering unknown-input functional observer design for linear systems with multiple time-varying state delays. Based on the Lyapunov Krasovskii approach, delay-dependent sufficient conditions of the exponential stability of the observer in each scenario are established in terms of linear matrix inequalities. Because of using effective techniques, such as the descriptor transformation and an advanced weighted integral inequality, the proposed stability criteria can result in larger stability regions compared with the other papers that study functional observers for time-varying delay systems. Furthermore, to help with the design procedure, a genetic algorithm-based scheme is proposed to adjust a weighting matrix in the established linear matrix inequalities. Two numerical examples illustrate the design procedure and demonstrate the efficacy of the proposed observer in each scenario.

Partial state estimation of time-delay systems.

This thesis broadly studies three crucial and rigorous inter-related control theoretical subjects: (i) Partial state estimation of linear systems; (ii) Stability analysis of time-delay systems with interval time-varying delays; and (iii) Functional observer design for time-delay systems.

Simultaneous estimation of optical flow and object state: A modified approach to optical flow calculation

Differential optical flow methods are widely used within the computer vision community. They are classified as being either local, as in the Lucas-Kanade method, or global, as in the Horn-Schunck technique. As the physical dynamics of an object is inherently coupled into the behavior of its image in the video stream, in this paper, we use such dynamic parameter information in calculating optical flow when tracking a moving object using a video stream. Indeed, we use a modified error function in the minimization that contains physical parameter information. Further, the refined estimates of optical flow is used for better estimation of the physical parameters of the object in the simultaneous estimation of optical flow and object state(SEOS).