Kalman Filtering with Uncertain Noise Covariances

In this paper the robustness of Kalman filtering against uncertainties in process and measurement noise covariances is discussed. It is shown that a standard Kalman filter may not be robust enough if the process and measurement noise covariances are changed. A new filter is proposed which addresses the uncertainties in process and measurement noise covariances and gives better results than the standard Kalman filter. This new filter is used in simulation to estimate the health parameters of an aircraft gas turbine engine

Unified Forms for Kalman and Finite Impulse Response Filtering and Smoothing

The Kalman filter and smoother are optimal state estimators under certain conditions. The Kalman filter is typically presented in a predictor/corrector format, but the Kalman smoother has never been derived in that format. We derive the Kalman smoother in a predictor/corrector format, thus providing a unified form for the Kalman filter and smoother. We also discuss unbiased finite impulse response (UFIR) filters and smoothers, which can provide a suboptimal but robust alternative to Kalman estimators. We derive two unified forms for UFIR filters and smoothers, and we derive lower and upper bounds for their estimation error covariances

Unified Forms for Kalman and Finite Impulse Response Filtering and Smoothing

The Kalman filter and smoother are optimal state estimators under certain conditions. The Kalman filter is typically presented in a predictor/corrector format, but the Kalman smoother has never been derived in that format. We derive the Kalman smoother in a predictor/corrector format, thus providing a unified form for the Kalman filter and smoother. We also discuss unbiased finite impulse response (UFIR) filters and smoothers, which can provide a suboptimal but robust alternative to Kalman estimators. We derive two unified forms for UFIR filters and smoothers, and we derive lower and upper bounds for their estimation error covariances

Centralized Fusion of Unscented Kalman Filter Based on Huber Robust Method for Nonlinear Moving Target Tracking

We propose a robust method for tracking nonlinear target with the fusion unscented Kalman filter (FUKF). We noticed that when some outliers exist in the measurements of the sensors, they cannot track the target accurately by using the standard Kalman filters. The robust statistics theory is used in this paper to solve this problem. The measurement noise variance which is at the time of the outlier is restructured through minimizing the designed cost function. Then, the standard fusion unscented Kalman filter is used to track the target in order to avoid the bias brought by the linear approximation. Compared to the traditional tracking method and Huber robust method (HFUKF), this method has a more accurate performance and can track the target efficiently while the outliers exist. Last, simulation examples in three different conditions are given and the simulation results show the advantages of the proposed method over the fusion unscented Kalman filter (FUKF) and the Huber robust method (HFUKF)

Commande à haute performance et sans capteur mécanique du moteur synchrone à aimants permanents

Les moteurs synchrones à aimants permanents sont de plus en plus utilisés dans les servo-méchanisme grâce à leurs performances supérieures aux autres moteurs à courants alternatifs. Cette thèse porte sur la commande à hautes performances du moteur synchrone à aimants permanents. La première partie traite de la commande avec capteur mécanique en cherchant des performances dynamiques élevées. La deuxième partie s'intéresse à la commande sans capteur mécanique. A partir de l'analyse comportementale des observateurs de couple de type Luenberger d’ordre complet et d'ordre réduit, un observateur basé sur le filtre de Kalman est mise à jour. La vitesse, la position et le couple de charge sont observés à partir de la mesure de la position par le capteur avec résolution limitée. Ensuite, le couple observé est utilisé pour une compensation directe dans le but de minimiser des ondulations de la vitesse pendant l'impact de la charge. Une loi de commande par retour d'état associé à un filtre de Kalman est présentée où les régulateurs traditionnels de la vitesse et la position sont combinés et unifiés. Cette loi de commande peut s'appliquer aux moteurs à pôles saillants et aux moteurs à pôles lisses. Une méthode pour estimer la position et la vitesse du rotor, basée sur le filtre de Kalman étendu est présentée. Les équations dans le repère tournant sont utilisées, donc l’observateur peut s'appliquer au moteur avec pièces polaires. Par extension, le couple de charge est observé par le filtre de Kalman étendu et est utilisé pour la compensation sur le couple par modification de la grandeur de commande. Les courants filtrés par le filtre de Kalman sont également utilisés à la place des courants mesurés pour éliminer les effets du bruit. Une méthode de démarrage du moteur synchrone à aimants permanents est proposée pour presque toutes les méthodes d’estimation de la position du rotor basées sur les équations de tension dans le repère tournant au synchronisme. A partir de l’analyse des équilibres du système, une compensation sur l’axe quadrature (axe q) est adoptée pour briser les équilibres non souhaités et faire converger l'observateur vers un équilibre souhaité. Donc le moteur peut démarrer à partir des toutes les positions initiales inconnues. Pour estimer la position et la vitesse en basse vitesse, une méthode d’injection d’un signal haute fréquence associée avec le filtre de Kalman est proposée. Le filtre de Kalman traite les signaux haute fréquence par les courants mesurés et remplace ainsi tous les filtres traditionnels (passe haut, passe bas, passe bande). Cette méthode est simple et efficace et améliore les résultats traditionnels. De nombreuses expérimentations sur le moteur à aimants collés en surface sont conduites afin de valider les performances obtenues en simulation. ABSTRACT : The permanent magnet synchronous motors (PMSM) are more and more used because of their high performance compared with other AC motors. This thesis is about the high performance control of permanent magnet synchronous motors. The first part is about the control system with mechanical sensor to improve control performance. The second part is about the mechanical sensorless control system. After the analyses of the full-order and reduced-order Luenberger observer, a load torque observer based on Kalman filter is proposed. The precise rotor position, speed and load torque are observed using the rotor position given by a mechanical sensor with only limited resolution. Feed-forward compensation by observed load torque is used to improve the control performance during load torque’s changes. A novel position controller based on state feedback is proposed associated with a Kalman filter. The traditional position and speed controllers are replaced by a single controller which outputs the reference electromagnet torque directly. The feed-forward compensations made by position reference can reduce the overshoot in position control. The parameters of the controller can be easily obtained by the selection of poles and the analyses of the transfer function.  The control algorithm can be applied on both salient and non-salient motors. An observer based on extended Kalman filter (EKF) is built up to observe rotor position and speed precisely. The equations in rotor flux oriented synchronous coordinates are adopted, so the observer can be easily applied on both salient and non-salient motors. By extension, the load torque can also be observed by the extended Kalman filter and be used as feed-forward compensation on reference torque. Furthermore, the observed stator currents are used as feedback for the current controllers instead of direct measured ones to reduce the effects of disturbances and noises. A novel start up method of PMSM is proposed and can be used on almost all the rotor position estimation methods based on dq-axes voltages equations. Based on the analyses of the equilibrium points, by adding some compensation in q-axe equation to break the balance of unexpected equilibrium points, the observer can converge to the expected equilibrium point globally. So the motor can start up successfully from any unknown initial positions. To estimate the rotor position and speed in low speed region, a high frequency signal injection method with Kalman filter is proposed. Only two Kalman filters dealing with all the signal processing are used instead of all the traditional low-pass, high-pass and band-pass filters. This method is simple and can improve the performance of the high frequency method. Experiments on surface mounted motors are carried out to verify the performance obtained in simulatio