Extended Kalman Filter (EKF) and K-means clustering approach for state space decomposition of autonomous mobile robots

2012 ◽  
Author(s):  
Md. Nasir Uddin Laskar ◽  
Md. Nurul Ahad Tawhid ◽  
TaeChoong Chung
Keyword(s):  
Kalman Filter ◽  
Mobile Robots ◽  
State Space ◽  
Extended Kalman Filter ◽  
Autonomous Mobile Robots ◽  
Space Decomposition ◽  
Clustering Approach

A Localization Algorithm for Autonomous Mobile Robots via a Fuzzy Tuned Extended Kalman Filter

2010 ◽  
Vol 24 (1-2) ◽  
pp. 179-206 ◽  
Author(s):  
Y. L. Ip ◽  
A. B. Rad ◽  
Y. K. Wong ◽  
Y. Liu ◽  
X. M. Ren
Keyword(s):  
Kalman Filter ◽  
Mobile Robots ◽  
Extended Kalman Filter ◽  
Autonomous Mobile Robots ◽  
Localization Algorithm

A Floating-point Extended Kalman Filter Implementation for Autonomous Mobile Robots

2008 ◽  
Vol 56 (1) ◽  
pp. 41-50 ◽  
Author(s):  
Vanderlei Bonato ◽  
Eduardo Marques ◽  
George A. Constantinides
Keyword(s):  
Kalman Filter ◽  
Mobile Robots ◽  
Extended Kalman Filter ◽  
Autonomous Mobile Robots ◽  
Floating Point

scholarly journals A comparison of assimilation results from the ensemble Kalman Filter and a reduced-rank extended Kalman Filter

2003 ◽  
Vol 10 (6) ◽  
pp. 477-491 ◽  
Author(s):  
X. Zang ◽  
P. Malanotte-Rizzoli
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Extended Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Forecast Error ◽  
High Viscosity ◽  
Empirical Orthogonal Functions ◽  
Reduced Rank ◽  
Low Viscosity ◽  
Reduced State

Abstract. The goal of this study is to compare the performances of the ensemble Kalman filter and a reduced-rank extended Kalman filter when applied to different dynamic regimes. Data assimilation experiments are performed using an eddy-resolving quasi-geostrophic model of the wind-driven ocean circulation. By changing eddy viscosity, this model exhibits two qualitatively distinct behaviors: strongly chaotic for the low viscosity case and quasi-periodic for the high viscosity case. In the reduced-rank extended Kalman filter algorithm, the model is linearized with respect to the time-mean from a long model run without assimilation, a reduced state space is obtained from a small number (100 for the low viscosity case and 20 for the high viscosity case) of leading empirical orthogonal functions (EOFs) derived from the long model run without assimilation. Corrections to the forecasts are only made in the reduced state space at the analysis time, and it is assumed that a steady state filter exists so that a faster filter algorithm is obtained. The ensemble Kalman filter is based on estimating the state-dependent forecast error statistics using Monte Carlo methods. The ensemble Kalman filter is computationally more expensive than the reduced-rank extended Kalman filter.The results show that for strongly nonlinear case, chaotic regime, about 32 ensemble members are sufficient to accurately describe the non-stationary, inhomogeneous, and anisotropic structure of the forecast error covariance and the performance of the reduced-rank extended Kalman filter is very similar to simple optimal interpolation and the ensemble Kalman filter greatly outperforms the reduced-rank extended Kalman filter. For the high viscosity case, both the reduced-rank extended Kalman filter and the ensemble Kalman filter are able to significantly reduce the analysis error and their performances are similar. For the high viscosity case, the model has three preferred regimes, each with distinct energy levels. Therefore, the probability density of the system has a multi-modal distribution and the error of the ensemble mean for the ensemble Kalman filter using larger ensembles can be larger than with smaller ensembles.

Generalized Polynomial Chaos-Based Extended Kalman Filter: Improvement and Expansion

2013 ◽  
Author(s):  
Jeremy Kolansky ◽  
Corina Sandu
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Extended Kalman Filter ◽  
Polynomial Chaos ◽  
Computationally Efficient ◽  
Generalized Polynomial Chaos ◽  
Parameter Estimations ◽  
Generalized Polynomial ◽  
State Estimations ◽  
Polynomial Chaos Expansions

The generalized polynomial chaos (gPC) method for propagating uncertain parameters through dynamical systems (previously developed at Virginia Tech) has been shown to be very computationally efficient. This method seems also to be ideal for real-time parameter estimation when merged with the Extended Kalman Filter (EKF). The resulting technique is shown in the present paper for systems in state-space representations, and then expanded to systems in regressions formulations. Due to the way the filter interacts with the polynomial chaos expansions, the covariance matrix is forced to zero in finite time. This problem shows itself as an inability to perform state estimations and causes the parameters to converge to incorrect values for state space systems. In order to address this issue, improvements to the method are implemented and the updated method is applied to both state space and regression systems. The resultant technique shows high accuracy of both state and parameter estimations.

Odometry in Cooperative Multi-Mobile Robots

1999 ◽  
Vol 11 (5) ◽  
pp. 411-416
Author(s):  
Masafumi Hashimoto ◽  
◽  
Takanori Kurazumi ◽  
Fuminori Oba ◽  
Keyword(s):  
Kalman Filter ◽  
Mobile Robots ◽  
Extended Kalman Filter ◽  
Position Sensor ◽  
Location Errors ◽  
Exchange Information ◽  
Sensor Information

We propose odometry in cooperative multi-mobile robots by integrating conventional odometry and interrobot position sensor information. In our odometry, each robot is considered a moving landmark with imprecise location. Robots in the group locally estimate their own absolute positions based on conventional odometry and find the relative positions of each other using interrobot position sensors. They communicate and exchange information on local estimates and relative positions. The information is integrated decentralized based on the extended Kalman filter and robots improve their absolute positions. Simulation and experiments show that our odometry eliminates large robot location errors found in conventional odometry.

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