NDLI: An intrinsic Cramér-Rao bound on SO(3) for (dynamic) attitude filtering

Content Provider	IEEE Xplore Digital Library
Author	Bonnabel, Silvere Barrau, Axel
Copyright Year	2015
Description	Author affiliation: MINES ParisTech, PSL Research University, Centre for robotics, 60 Bd St Michel 75006 Paris, France (Bonnabel, Silvere; Barrau, Axel)
Abstract	In this note an intrinsic version of the Cramér-Rao bound on estimation accuracy is established on the Special Orthogonal group SO(3). It is intrinsic in the sense that it does not rely on a specific choice of coordinates on SO(3): the result is derived using rotation matrices, but remains valid when using other parameterizations, such as quaternions. For any estimator R̂ of R ∈ SO(3) we give indeed a lower bound on the covariance matrix of log((RR̂T), that is, the estimation error expressed in terms of group multiplication, whereas the usual estimation error (R̂-R) is meaningless on SO(3). The result is first applied to Whaba's problem. Then, we consider the problem of a continuous-time nonlinear deterministic system on SO(3) with discrete measurements subject to additive isotropic Gaussian noise, and we derive a lower bound to the estimation error covariance matrix. We prove the intrinsic Cramér-Rao bound coincides with the covariance matrix returned by the Invariant EKF, and thus can be computed online. This is in sharp contrast with the general case, where the bound can only be computed if the true trajectory of the system is known.
Starting Page	2158
Ending Page	2163
File Size	213340
Page Count	6
File Format	PDF
e-ISBN	9781479978861
DOI	10.1109/CDC.2015.7402526
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-12-15
Publisher Place	Japan
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Covariance matrices Estimation error Manifolds Trajectory Erbium Measurement uncertainty
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

A Cramér-Rao Bound for Multiple Target Tracking

On the Cramér-Rao bound for the constrained and unconstrained complex parameters

On Intrinsic Cramér-Rao Bounds for Riemannian Submanifolds and Quotient Manifolds

An intrinsic Cram\'er-Rao bound on SO(3) for (dynamic) attitude filtering

On the rate of error propagation in multihop range-based localization

Cyclic Bayesian Cramér-Rao bound for filtering in circular state space

Cramér-Rao Lower Bound for Point Based Image Registration With Heteroscedastic Error Model for Application in Single Molecule Microscopy

Least squares estimation and hybrid Cramér-Rao lower bound for absolute sensor registration

Cramér-Rao bound for channel estimation in amplify-and-forward relaying networks

An intrinsic Cramér-Rao bound on SO(3) for (dynamic) attitude filtering

Similar Documents

A Cramér-Rao Bound for Multiple Target Tracking

On the Cramér-Rao bound for the constrained and unconstrained complex parameters

On Intrinsic Cramér-Rao Bounds for Riemannian Submanifolds and Quotient Manifolds

An intrinsic Cram\'er-Rao bound on SO(3) for (dynamic) attitude filtering

On the rate of error propagation in multihop range-based localization

Cyclic Bayesian Cramér-Rao bound for filtering in circular state space

Cramér-Rao Lower Bound for Point Based Image Registration With Heteroscedastic Error Model for Application in Single Molecule Microscopy

Least squares estimation and hybrid Cramér-Rao lower bound for absolute sensor registration

Cramér-Rao bound for channel estimation in amplify-and-forward relaying networks

An intrinsic Cramér-Rao bound on SO(3) for (dynamic) attitude filtering