Stochastic Cloning Unscented Kalman filtering for pedestrian localization applications

Amirhosseini, Sara Fazel; Romanovas, Michailas; Schwarze, Tobias; Schwaab, Manuel; Traechtler, Martin; Manoli, Yiannos

doi:10.1109/ipin.2013.6817893

Cited by 2 publications

(13 citation statements)

References 19 publications

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“…(as in other works) or by

{\overset{P}{true}}_{x x}^{v, k false| k - 1} = true \sum_{i = 1}^{N} w_{i}^{c} ((), {\overset{χ}{true}}_{i}^{v, k false| k - 1} - {\overset{x}{true}}_{k false| k - 1}^{v}) {false(⋄ false)}^{T}

…”

Section: Unscented Kalman Filters For Quaternionic Systemsmentioning

confidence: 88%

“…Within the literature, more than one solution has been given to the problem of creating UFs for quaternionic systems (see, eg, other works). Some works use the same algorithms of the UKFs for Euclidean systems to estimate the state of quaternionic systems (these works are not studied in this work), that is, they do not take unit quaternions norm constraint into account (see, eg, the works of Enayati et al and Vaccarella et al); others do take this constraint into account and can be divided into three groups: a first treats unit quaternion norms but does not preserve them in any problematic item (first row of Table ); a second preserves unit quaternion norms only in some (but not all) problematic items (second row of Table ); and a third preserves unit quaternion norms in all problematic items (third row of Table ). …”

Section: Unscented Kalman Filters For Quaternionic Systemsmentioning

confidence: 99%

“…Consider system , and suppose that at time step k ,

{\overset{x}{true}}_{k - 1 false| k - 1}

(the previous state estimate) and

{\overset{P}{true}}_{x x}^{v, k false| k - 1}

(the covariance of a vector parameterization of the previous state) are given. Then, the previous deviation vector σ R is obtained by

{\overset{χ}{true}}^{v, k - 1 false| k - 1} : = {({}, {\overset{χ}{true}}_{i}^{v, k - 1 false| k - 1}, w_{i}^{m}, w_{i}^{c}, w_{i}^{c c})}_{i = 1}^{N} = σ normalR ((), {false[0 false]}_{1 \times n_{x}}, {\overset{P}{true}}_{x x}^{v, k - 1 false| k - 1})

(as in other works) or by

{\overset{χ}{true}}^{v, k - 1 false| k - 1} : = {({}, {\overset{χ}{true}}_{i}^{v, k - 1 false| k - 1}, w_{i}^{m}, w_{i}^{c}, w_{i}^{c c})}_{i = 1}^{N} = σ normalR ((), {false[0 false]}_{1 \times n_{x}}, {\overset{P}{true}}_{x x}^{v, k - 1 false| k - 1} + Q_{k}^{v})

(as in other works), where

Q_{k}^{v} \in

…”

Section: Unscented Kalman Filters For Quaternionic Systemsmentioning

confidence: 99%

“…In this work, we analyze all diverse additive unscented filters (UFs; meaning UKFs and SRUKFs) for quaternionic systems proposed in the literature; considering essentially distinct algorithms, we can enumerate the following works …”

Section: Introductionmentioning

confidence: 99%

“…We restrict ourselves to additive UKFs because the majority of the UKFs for rotating systems based on unit quaternions are additive filters (cf) and because augmented UKFs can be obtained by simple manipulations of the additive UKFs (cf the works of Julier and Uhlmann, and Menegaz).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Unscented and square‐root unscented Kalman filters for quaternionic systems

Menegaz

Ishihara

2018

Intl J Robust & Nonlinear

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Proper construction of an unscented Kalman filter (UKF) for unit quaternionic systems is not straightforward due to the incompatibility between the algebraic properties of the unit quaternions and the common real vector space operations (additions and scalar multiplications) needed in the steps of a filter algorithm. This work studies, in detail, all UKFs and square-root UKFs for quaternionic systems proposed in the literature. First, we classify the algorithms according to the preservation of the unity norm of the quaternion variables. Second, we propose two new algorithms: the quaternionic additive unscented Kalman filter (QuAdUKF) and a square-root variant of it. The QuAdUKF encompasses all known UKFs for quaternionic systems of the literature preserving, in all steps, the norm of the unit quaternion variables. Besides, it can also yield new UKFs with this norm preservation property. The QuAdUKF's square-root variant has better properties in comparison with all the square-root UKFs for quaternionic systems of the literature. Numerical experiments for a spacecraft attitude estimation problem illustrate the theoretical results. KEYWORDS attitude estimation, square-root unscented Kalman filter (SRUKF), unit quaternion, unscented Kalman filter (UKF)In the control literature, the most common state space models are those where the underlying state, input, and output variables are real vectors, that is, elements that lie in a Euclidean vector space ℝ n . For bodies under two-dimensional or three-dimensional (3D) motions, these Euclidean models fit for dimensionless material points, that is, linear displacements and velocities. However, for large rigid bodies, besides these linear displacement characteristics, the body pointing direction and angular (rotational) movements become important. [1][2][3] It is well known that rotations of rigid bodies in a 3D space are mathematically represented by state trajectories, restricted to a compact manifold called the special orthogonal group, SO(3). The high nonlinearity of this manifold, due to the restriction of variables in specific regions, leads to difficulties in dealing with these variables. In estimation algorithms, performing calculations with variables in SO(3) is often computationally expensive, and more computationally-efficient rotation parameterizations were proposed in the literature. Among the alternative rotation parameterizations, such as Euler angles, rotation vectors (RoVs), and unit quaternions, the unit quaternions are often chosen because, unlike other 4500

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“…(as in other works) or by