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591	Beiträge zur expliziten Fehlerabschätzung im zentralen Grenzwertsatz Paditz, Ludwig 27 April 1989 (has links) In der Arbeit wird das asymptotische Verhalten von geeignet normierten und zentrierten Summen von Zufallsgrößen untersucht, die entweder unabhängig sind oder im Falle der Abhängigkeit als Martingaldifferenzfolge oder stark multiplikatives System auftreten. Neben der klassischen Summationstheorie werden die Limitierungsverfahren mit einer unendlichen Summationsmatrix oder einer angepaßten Folge von Gewichtsfunktionen betrachtet. Es werden die Methode der charakteristischen Funktionen und besonders die direkte Methode der konjugierten Verteilungsfunktionen weiterentwickelt, um quantitative Aussagen über gleichmäßige und ungleichmäßige Restgliedabschätzungen in zentralen Grenzwertsatz zu beweisen. Die Untersuchungen werden dabei in der Lp-Metrik, 1<p<oo oder p=1 bzw. p=oo, durchgeführt, wobei der Fall p=oo der üblichen sup-Norm entspricht. Darüber hinaus wird im Fall unabhängiger Zufallsgrößen der lokale Grenzwertsatz für Dichten betrachtet. Mittels der elektronischen Datenverarbeitung neue numerische Resultate zu erhalten. Die Arbeit wird abgerundet durch verschiedene Hinweise auf praktische Anwendungen. / In the work the asymptotic behavior of suitably centered and normalized sums of random variables is investigated, which are either independent or occur in the case of dependence as a sequence of martingale differences or a strongly multiplicative system. In addition to the classical theory of summation limiting processes are considered with an infinite summation matrix or an adapted sequence of weighting functions. It will be further developed the method of characteristic functions, and especially the direct method of the conjugate distribution functions to prove quantitative statements about uniform and non-uniform error estimates of the remainder term in central limit theorem. The investigations are realized in the Lp metric, 1 <p <oo or p = 1 or p = oo, where in the case p = oo it is the usual sup-norm. In addition, in the case of independent random variables the local limit theorem for densities is considered. By means of electronic data processing new numerical results are obtained. The work is finished by various references to practical applications. info:eu-repo/classification/ddc/510 ddc:510
592	Evaluation of Target Tracking Using Multiple Sensors and Non-Causal Algorithms Vestin, Albin, Strandberg, Gustav January 2019 (has links) Today, the main research field for the automotive industry is to find solutions for active safety. In order to perceive the surrounding environment, tracking nearby traffic objects plays an important role. Validation of the tracking performance is often done in staged traffic scenarios, where additional sensors, mounted on the vehicles, are used to obtain their true positions and velocities. The difficulty of evaluating the tracking performance complicates its development. An alternative approach studied in this thesis, is to record sequences and use non-causal algorithms, such as smoothing, instead of filtering to estimate the true target states. With this method, validation data for online, causal, target tracking algorithms can be obtained for all traffic scenarios without the need of extra sensors. We investigate how non-causal algorithms affects the target tracking performance using multiple sensors and dynamic models of different complexity. This is done to evaluate real-time methods against estimates obtained from non-causal filtering. Two different measurement units, a monocular camera and a LIDAR sensor, and two dynamic models are evaluated and compared using both causal and non-causal methods. The system is tested in two single object scenarios where ground truth is available and in three multi object scenarios without ground truth. Results from the two single object scenarios shows that tracking using only a monocular camera performs poorly since it is unable to measure the distance to objects. Here, a complementary LIDAR sensor improves the tracking performance significantly. The dynamic models are shown to have a small impact on the tracking performance, while the non-causal application gives a distinct improvement when tracking objects at large distances. Since the sequence can be reversed, the non-causal estimates are propagated from more certain states when the target is closer to the ego vehicle. For multiple object tracking, we find that correct associations between measurements and tracks are crucial for improving the tracking performance with non-causal algorithms. evaluation target tracking multiple sensors non-causal smoother smoothing tracking vehicle tracking camera lidar estimate estimation prediction vehicle dynamics sensor fusion real-time tracking extended kalman filter filter validation validation position estimation velocity estimation dynamic model model complexity multi object tracking multiple object tracking single object tracking data association tracking fundamentals iterated kalman filter track management gnn global nearest neighbour mahalanobis mahalanobis distance performance evaluation differential gps dgps roi ego several sensors sensors rmse root mean square error invertible motion anti-causal motion anti-causal tracking constant velocity gnn imu tfs two filter smoother ekf rts radar inertial measurement unit nonlinear nonlinear systems mono camera monocular camera noise model tracking performance fixed interval smoothing m/n logic centralized fusion non-causal object tracker car tracking car dynamics automotive active safety object tracking automotive industry thesis master reverse dynamics reverse tracking reverse sequence sequence tracking data propagation ground truth estimating ground truth additional sensors mounted sensors true estimates environment comparison algorithm independent targets overlapping measurements occluded track switch improve lower uncertainty more certain state process noise covariance sampling image sprt adas cnn cv pdf track target ego tracker tentative track observatiom online tracking offline tracking online offline recorded sequences robust self driving self-driving car traffic trajectory true state scenario scenarios future accurate output advanced driver assistance systems non-linear complex noise pedestrian truck bus maneuvering vehicles processed measurement frame state correction probability density function tuning likelihood transition measurement motion model recursion gaussian approximation distribution linear jacobian multiplicative noise ratio ad hoc ad hoc state space approach backward auction euclidean distance statistical threshold gating association margin normalize covariance matrix fusion confirmed rejected tentative history absolute error modular ego motion parameters variables logg hardware specification fused causal factorization independent uncorrelated transform moving rotation translation oncoming overtaking Control Engineering Reglerteknik

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Beiträge zur expliziten Fehlerabschätzung im zentralen Grenzwertsatz

Evaluation of Target Tracking Using Multiple Sensors and Non-Causal Algorithms