Abstract
In this work, we study the inconsistency problem of extended Kalman filter (EKF)-based simultaneous localization and mapping (SLAM) from the perspective of observability. We analytically prove that when the Jacobians of the process and measurement models are evaluated at the latest state estimates during every time step, the linearized error-state system employed in the EKF has an observable subspace of dimension higher than that of the actual, non-linear, SLAM system. As a result, the covariance estimates of the EKF undergo reduction in directions of the state space where no information is available, which is a primary cause of the inconsistency. Based on these theoretical results, we propose a general framework for improving the consistency of EKF-based SLAM. In this framework, the EKF linearization points are selected in a way that ensures that the resulting linearized system model has an observable subspace of appropriate dimension. We describe two algorithms that are instances of this paradigm. In the first, termed observability constrained (OC)-EKF, the linearization points are selected so as to minimize their expected errors (i.e. the difference between the linearization point and the true state) under the observability constraints. In the second, the filter Jacobians are calculated using the first-ever available estimates for all state variables. This latter approach is termed first-estimates Jacobian (FEJ)-EKF. The proposed algorithms have been tested both in simulation and experimentally, and are shown to significantly outperform the standard EKF both in terms of accuracy and consistency.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 502-528 |
| Number of pages | 27 |
| Journal | International Journal of Robotics Research |
| Volume | 29 |
| Issue number | 5 |
| DOIs | |
| State | Published - Apr 1 2010 |
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Keywords
- Estimator inconsistency
- Extended Kalman filter
- Linearization errors
- Nonlinear estimation
- Observability
- Simultaneous localization and mapping
Cite this
Observability-based rules for designing consistent EKF SLAM estimators. / Huang, Guoquan P.; Mourikis, Anastasios I.; Roumeliotis, Stergios.
In: International Journal of Robotics Research, Vol. 29, No. 5, 01.04.2010, p. 502-528.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Observability-based rules for designing consistent EKF SLAM estimators
AU - Huang, Guoquan P.
AU - Mourikis, Anastasios I.
AU - Roumeliotis, Stergios
PY - 2010/4/1
Y1 - 2010/4/1
N2 - In this work, we study the inconsistency problem of extended Kalman filter (EKF)-based simultaneous localization and mapping (SLAM) from the perspective of observability. We analytically prove that when the Jacobians of the process and measurement models are evaluated at the latest state estimates during every time step, the linearized error-state system employed in the EKF has an observable subspace of dimension higher than that of the actual, non-linear, SLAM system. As a result, the covariance estimates of the EKF undergo reduction in directions of the state space where no information is available, which is a primary cause of the inconsistency. Based on these theoretical results, we propose a general framework for improving the consistency of EKF-based SLAM. In this framework, the EKF linearization points are selected in a way that ensures that the resulting linearized system model has an observable subspace of appropriate dimension. We describe two algorithms that are instances of this paradigm. In the first, termed observability constrained (OC)-EKF, the linearization points are selected so as to minimize their expected errors (i.e. the difference between the linearization point and the true state) under the observability constraints. In the second, the filter Jacobians are calculated using the first-ever available estimates for all state variables. This latter approach is termed first-estimates Jacobian (FEJ)-EKF. The proposed algorithms have been tested both in simulation and experimentally, and are shown to significantly outperform the standard EKF both in terms of accuracy and consistency.
AB - In this work, we study the inconsistency problem of extended Kalman filter (EKF)-based simultaneous localization and mapping (SLAM) from the perspective of observability. We analytically prove that when the Jacobians of the process and measurement models are evaluated at the latest state estimates during every time step, the linearized error-state system employed in the EKF has an observable subspace of dimension higher than that of the actual, non-linear, SLAM system. As a result, the covariance estimates of the EKF undergo reduction in directions of the state space where no information is available, which is a primary cause of the inconsistency. Based on these theoretical results, we propose a general framework for improving the consistency of EKF-based SLAM. In this framework, the EKF linearization points are selected in a way that ensures that the resulting linearized system model has an observable subspace of appropriate dimension. We describe two algorithms that are instances of this paradigm. In the first, termed observability constrained (OC)-EKF, the linearization points are selected so as to minimize their expected errors (i.e. the difference between the linearization point and the true state) under the observability constraints. In the second, the filter Jacobians are calculated using the first-ever available estimates for all state variables. This latter approach is termed first-estimates Jacobian (FEJ)-EKF. The proposed algorithms have been tested both in simulation and experimentally, and are shown to significantly outperform the standard EKF both in terms of accuracy and consistency.
KW - Estimator inconsistency
KW - Extended Kalman filter
KW - Linearization errors
KW - Nonlinear estimation
KW - Observability
KW - Simultaneous localization and mapping
UR - http://www.scopus.com/inward/record.url?scp=77951109530&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77951109530&partnerID=8YFLogxK
U2 - 10.1177/0278364909353640
DO - 10.1177/0278364909353640
M3 - Article
VL - 29
SP - 502
EP - 528
JO - International Journal of Robotics Research
JF - International Journal of Robotics Research
SN - 0278-3649
IS - 5
ER -