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IET International Conference on Radar Systems (Radar 2007)

作者： Anders Erik Nordsjo Saab Microwave Systems AB Jarfalla Sweden

The problem of deriving accurate algorithms for tracking of maneuvering targets is central in many applications, such as radar and sonar. Assuming that a certain model is indeed capable of describing the unknown system, it is still important to have a measure of the achievable accuracy. Clearly, the Cramer-Rao inequality has been applied to a large number of different parameterized models to obtain a lower bound of the variance of any unbiased estimate of the true system parameters. Also, in a tracking scenario it is of great interest to be able to quantify the best possible performance that can be achieved. For this purpose certain time-varying Cramer-Rao lower bounds, CRB's are derived in the following. These bounds are based on the assumption of a third-order model which incorporates both time-varying and time-invariant parameters. In addition, possible measurement nonlinearities are taken into account. The so obtained CRB's depend on not only the unknown filter parameters but also certain second-order statistics, namely the variance of the (presumedly random) target acceleration and the measurement noise. In general, it is of great importance to be able to quantify the impact of different values of these quantities, which typically are unknown in practice.

关键词： Target Tracking Cramer-Rao Bounds recursive prediction error method

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Sensitivity models for nonlinear filters with application to recursive parameter estimation for nonlinear state-space models

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IEE PROCEEDINGS-CONTROL THEORY AND APPLICATIONS 2001年第2期148卷 137-145页

作者： Bohn, C Unbehauen, H Continental AG Strateg Technol Dept D-30419 Hannover Germany Ruhr Univ Bochum Dept Elect Elect & Informat Sci Control Engn Lab D-44780 Bochum Germany

If a recursive prediction error method is applied for the parameter estimation of state-space models, a filter must be used as the predictor, resulting in an adaptive filtering problem. Whereas for linear systems the optimal linear filter, the Kalman filter, can be used, approximate nonlinear filters have to be employed for nonlinear systems. For the parameter estimation, the gradient of the prediction error, and maybe the gradient of its covariance matrix as well, are required. These can be obtained from a sensitivity model;however, the derivation of such a sensitivity model is tedious and has only been done for the extended Kalman filter. Sensitivity models for four common continuous-discrete nonlinear filters are derived: the extended Kalman filter, the first-order bias-corrected filter, the truncated second-order filter, and the modified Gaussian second-order filter. The derivation of these sensitivity models relies heavily on the use of matrix differential calculus, and utilises a reformulation of the approximate nonlinear filters derived earlier. Elementwise derivatives and bookkeeping over indices are thus entirely avoided. An adaptive filter is applied for real-time parameter identification and tracking for a laboratory three-tank process.

关键词： adaptive filtering problem first-order bias-corrected filter recursive estimation Simulation, modelling and identification truncated second-order filter recursive parameter estimation state-space methods continuous-discrete nonlinear filter nonlinear control systems Nonlinear control systems Kalman filters recursive prediction error method approximate nonlinear filters modified Gaussian second-order filter Other topics in statistics Control system analysis and synthesis methods flow control matrix differential calculus nonlinear filters laboratory three-tank process extended Kalman filter nonlinear state-space models Level, flow and volume control Signal processing theory sensitivity models

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Neural Networks for Optimal Control

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IFAC Proceedings Volumes 1995年第8期28卷 361-366页

作者： Ole Sørensen Aalborg University Inst. of Electronic Systems Dept. of Process Engineering Fredrik Bajers vej 7 DK-9220 Aalborg Ø Denmark phone +45 98 15 85 22 telefax +45 98 15 17 39

Two neural networks are trained to act as an observer and a controller, respectively, to control anon-linear, multi-variable process. The process model is the well-known Innovation State Space model. Firstly, the observer network is trained with a recursive prediction error method using a Gauss-Newton search direction to minimize the the prediction error. Next, the trained observer network is applied in a closed-loop simulation to train another neural network, the controller. During this training an optimal control cost function is minimized using a recursive, off-line, backward training method, similar to the Back Propagation Through Time (BPTT) method. Finally, a practical, non-linear, noisy and multi-variable example confirms, that the model and the training methods are a promising technique to control non-linear processes, which are difficult to model. 2 reseaux neuraux sont developpes pour agir respectivement comme un observateur et un controlleur, afin de controller un processus non lineaire et multi-variable. Le modele de ce processus est le bien connu modele des espaces d'etats (Innovation State Space Model). Premierement le reseau observateur est mis en place avec une methode recursive d'erreur de prediction (recursive prediction error method) utilisant une recherche de Gauss-Newton pour minimiser l'erreur de prediction. Ensuite ce reseau est applique dans une simulation a boucle fermee pour former un autre reseau neural, le controlleur. Pendant cette sequence de formation une fonction de cout de controle optimal est minimisee, utilisant une methode recursive, a priori, similaire a la propagation arriere a travers le temps (Back Propagation Through Time method). Finallement un exemple pratique, non lineaire, bruite, et multi-variable confirme que le modele et les methodes de mise en place de ce modele sont une technique promettante pour controler des processus non lineaires, qui sont difficiles a modeliser.

关键词： Neural network innovation model extended Kalmann filter recursive prediction error method non-linear control optimal control

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IDENTIFICATION OF RUDDER YAW AND RUDDER ROLL STEERING MODELS BY USING recursive prediction error TECHNIQUES

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OPTIMAL CONTROL APPLICATIONS & methodS 1994年第2期15卷 101-114页

作者： ZHOU, WW CHERCHAS, DB CALISAL, S UNIV BRITISH COLUMBIA DEPT MECH ENGNVANCOUVER V6T 1W5BCCANADA

Linear and non-linear recursive prediction error (RPE) methods have been employed for the purpose of identification of the dynamics of ship rudder-yaw and -roll motions. The evaluations of the goodness of model structures have been carried out by comparing simulated outputs from the identified model with real measurements. In the linear case Nomoto's first-order model has been initially considered for the transfer functions between rudder-yaw and -sway, with a second-order model for rudder-roll with coupling effects considered only between sway-yaw and -roll. Identification results have shown that such a model is not appropriate. Changing the model to second-order between rudder-sway and -yaw and further considering the coupling effects between roll angle-sway and -yaw shows that a significant improvement is achieved, while the coupling effect between yaw and roll appears negligible. In the non-linear case effects due to various non-linear terms have been studied with the non-linear RPE algorithm.

关键词： IDENTIFICATION recursive prediction error method SHIP STEERING DYNAMICS RUDDER ROLL DYNAMICS

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Estimation of the State and Parameters of a Bioprocess Using the recursive prediction error method

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IFAC Proceedings Volumes 1989年第6期22卷 507-512页

作者： J.M. Flaus A. Chéruy Labomtoire d'Automatique de Grenoble INPG. Grenoble France

This paper presents an alternative to the Extended Kalman filter for the estimation of the state and parameters of a bioprocess. This method called recursive prediction error method has been developped by Ljung [83]and can be applied on a model of any degree of complexity as EKF, but stability and convergences properties can be analyzed more easily. From a practical point of view, another advantage is that the tuning parameters of the algorithm have a simpler meaning, and then made the algorithm easier to use.

关键词： recursive Estimation Biotechnology recursive prediction error method Kalman filters

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ADAPTIVE STATE TRACKING

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IEE PROCEEDINGS-D CONTROL THEORY AND APPLICATIONS 1988年第6期135卷 429-435页

作者： LIU, L SINHA, NK Department of Electrical & Computer Engineering McMaster University Hamilton Canada

The problem of adaptive state tracking is considered, where a specified state is required to follow the reference input signal. It is assumed that the system is completely controllable and observable, but the particular state is not directly available for measurement and the measurements are contaminated with stochastic noise. It is also assumed that there is little prior knowledge of the reference input, and its parameters have to be detected by the control system. The recursive prediction error (RPE) method is used for joint estimation of the parameters and states of the process to be controlled. The controller design is based on the placement of the poles and zeros of the state tracking error transfer function. As a result, adaptive state tracking is obtained for arbitrary external reference signals.

关键词： Self-adjusting control systems poles and zeros poles controllability adaptive state tracking transfer functions Simulation, modelling and identification adaptive systems state estimation adaptive systems, controllability state tracking error transfer function zeros recursive prediction error method observability parameter estimation Control system analysis and synthesis methods adaptive control

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Identification methods for Nonlinear MISO Systems

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IFAC Proceedings Volumes 1987年第5期20卷 233-238页

作者： M. Kortmann H. Unbehauen Department of Electrical Engineering Ruhr-University Bochum Automatic Control Laboratory D-4630 Bochum 1 FRG

Two new on-line identification algorithms for the recursive estimation of the parameters of a multi-input single-output nonlinear process which can be described by a multi-input single-output Hammerstein model are proposed. The first method is an extension of the recursive least squares identification scheme for linear MISO systems while the other method is derived from a recursive prediction error algorithm. It is shown that the second method has the important property for on-line identification that no redundancy in the parameters to be estimated results as in the first algorithm. In contrast to the first method the second algorithm has the advantage that no extended dynamic parts of the Hammerstein submodels are obtained by application of the estimation procedure. The results of a simulation study are included to illustrate the efficiency of the derived methods.

关键词： Identification nonlinear systems parameter estimation difference equations recursive least-squares method recursive prediction error method

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MODIFIED APPROACH TO STATE-SPACE SELF-TUNING CONTROL WITH POLE ASSIGNMENT

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IEE PROCEEDINGS-D CONTROL THEORY AND APPLICATIONS 1985年第6期132卷 257-262页

作者： OMANI, FK SINHA, NK Department of Electrical & Computer Engineering McMaster University Hamilton Canada

The paper presents a modified approach to state-space self-tuning pole-assignment control. The recursive prediction error method is used for joint state and parameter estimation in the controllable canonical form. This simplifies the state feedback law by eliminating the online computation of transformation matrices. The resulting algorithm is thus a feasible solution to the adaptive control of nonminimum-phase systems.

关键词： Self-adjusting control systems poles and zeros state feedback law Simulation, modelling and identification state-space methods state-space self-tuning pole-assignment control state estimation nonminimum-phase systems self-adjusting systems recursive prediction error method parameter estimation Control system analysis and synthesis methods adaptive control

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Adaptive Control in Practice: Possibilities and Constraints

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IFAC Proceedings Volumes 1985年第15期18卷 133-137页

作者： M.W. Tijsseling H.J. de Groot Dow Chemical Company Terneuzen The Netherlands Gist Brocades Company Delft The Netherlands

Feedback is the most frequently used method for controlling a process variable. It does not require precise tuning, but it may turn out slow for fast upsets. Feedforward is able to handle these disturbances if it is tuned taylormade to the process dynamics. Non linear systems may need adaptive feedforward. This paper describes a cooler with non linear dynamics where adaptive control can not be used. However, the identification algorithm gives enough information to tune the feedforward properly.

关键词： Discrete time systems adaptive control feedforward control direct digital control identification recursive prediction error method

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