Citation Context

...mate shows that dependencies are local, an effect that is exploited by some algorithms that build local maps. in Equation (7) can be calculated conveniently using the standard Kalman filter equations =-=[49, 64, 103]: µ ′ t−1 = µt−1 + But Σ ′ t−1 = Σt��-=-�1 + Σcontrol Kt = Σ ′ t−1C T (CΣ ′ t−1C T + Σmeasure) −1 µt = µ ′ t−1 + Kt(o − Cµ ′ t−1) Σt = (I − KtC)Σ ′ t−1 (12) As the reader may verify, these equations are eq...

Citation Context

...ation σ + for positive labeled samples and P (−1|fj(x)) by N (µ − , σ − ) for negative labeled samples. For this purpose we incrementally estimate the mean and variance by a Kalman filtering approach =-=[32]-=-. We build a simple state space model for estimation the (constant) mean and achieve µt = µt−1 + vt and σ2 t = σ2 t−1 + vt for the variance. vt ∼ N (0, R) is a random noise processes with variance R. ...

Citation Context

...vision and pattern recognition, image processing, connectionist systems, etc. Most of the problems have been addressed based on statistical modeling, such as PCA, HMMs [3], [7], [8], Kalman filtering =-=[9]-=-, more advanced particle filtering [10], [11] and condensation algorithms [12]–[14]. FSM has been effectively employed in modeling human gestures [15]–[18]. Computer vision and pattern recognition tec...

Citation Context

...be found in Chapter 1 of [31], while a more complete introductory discussion can be found in [40], which also contains some interesting historical narrative. More extensive references can be found in =-=[7,18,24,28,31,46]-=-. The Kalman filter has been employed previously for virtual environment tracking estimation and prediction. For example see [2,5,12,14,42], and most recently [32]. In each of these cases however the ...

Citation Context

...s filters. their properties in the context of mobile robot localization. An overview of the different algorithms is given in Figure 1. Kalman filters are the most widely used variant of Bayes filters =-=[47, 32, 72, 80]-=-. They approximate beliefs by their first and second moments, i.e. mean and covariance. Kalman filters are optimal under the assumptions that the initial state uncertainty is unimodal Gaussian and tha...

Citation Context

...n often applied to 3D tracking. In fact, most of the algorithms described in the next sections can be used in conjunction with a Kalman filter. There are many extensive references to Kalman filtering =-=[18, 140]-=-, and we only introduce it here in its most basic form. [45] is also a good reference dedicated to 3D tracking. Linear Case The successive states st ∈ Rn of a discrete-time controlled process are assu...

Citation Context

...orithm with precandidates, and, at a higher level, making useful inferences about pedestrian behavior (e.g., walking direction). 2.5.1 Review Franke et al. propose the use of two Kalman filters [54], =-=[115]-=-, one controlling lateral motion (yaw rate of the own vehicle is used) and the other controlling longitudinal motion, to determine the speed and acceleration of detected objects. Later, in [55], [70],...

Citation Context

...be found in Chapter 1 of [17], while a more complete introductory discussion can be found in [20], which also contains some interesting historical narrative. More extensive references can be found in =-=[7, 12, 14, 16, 17, 30]-=-. The Kalman filter has been used previously to address similar or related problems. See for example [2, 3, 9, 10, 18, 23], and most recently [11]. The SCAAT approach in particular is described in gre...