S. Julier, J. Uhlman and H. Durrant-Whyte, A New Method for the Transformation of Means and Covariances in Filters and Estimators, IEEE Trans. on Automatic Control, Vol. 45, No. 3, pp. 477-482, 2000.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....are possible, such as entropy [23] or a weighted trace of the covariance matrix, respectively the Fisher information matrix at the final configuration estimate. The covariance matrix results from a stochastic estimator: standard linear Kalman filter (KF) 11] extended KF [1] unscented KF [10], or other Kalman filtering technique. One feature of our approach is that the optimal trajectory is generated as a linear combination of sine functions. This parameterization is appealing because: 1) the complete path can be characterized by a limited number of parameters; 2) all primitives ....

....can be solved in a similar way to the case with a reference trajectory. 4 Simulation Studies This Section presents simulation results showing the performance of the multisine approach. The state estimation used throughout the present paper is based on the Unscented Kalman Filter (UKF) [10], 26] The unscented transformation approximates a probability distribution based on a small number of deterministically chosen test points, referred to as sigma points which have the same first, second and possibly higher moments, as the estimate. The UKF is implemented here in its form with an ....

S. Julier, J. Uhlman, and H. Durrant-Whyte, A new method for the transformation of means and covariances in filters and estimators, IEEE Trans. on AC 45 (2000), no. 3, 477--482.

....constraints (for the robot velocity, steering and orientation angles) # 1 and # 2 are dimensionless positive weighting coe#cients. Here is in the form = tr(WP ) 7) where P is the covariance matrix of the estimated states (at the goal configuration) computed by an Unscented Kalman filter [16] and W is a weighting matrix) The cost term is assumed to be the relative time = t total t r,total , where t total is the total time for reaching the goal configuration on the modified trajectory, t r,total the respective time over the reference trajectory. The weighting matrix W ....

S. Julier, J. Uhlman, and H. Durrant-Whyte, "A new method for the transformation of means and covariances in filters and estimators," IEEE Trans. on AC, vol. 45, no. 3, pp. 477--482, 2000.

....sensing is considered as a global optimization problem with constraints. Several optimization criteria are possible, such as a weighted trace of the covariance matrix of the final configuration estimate. The covariance matrix results from a stochastic estimator, as the Unscented Kalman filter [3]. A feature of our approach is that the optimal trajectory is generated as a linear combination of sine functions. This parameterization is appealing because: 1) the complete path can be characterized by a limited number of parameters; 2) all primitives satisfy, at least partially, the boundary ....

....a similar way, e.g. about the rate of change of v k , the rate of change of # k . 4 Simulation Studies This Section presents simulation results showing the performance of the multisine approach. The state estimation used throughout the present paper is based on the Unscented Kalman Filter (UKF) [3, 13]. The sigma points and their weights are calculated using the scaled Unscented Transform [14, 13] It does not require linearization, nor explicit calculation of Jacobians and Hessians and it is numerically stable due to its factorization based form. Example 1. The WMR is moving in the presence ....

S. Julier, J. Uhlman, and H. Durrant-Whyte, "A new method for the transformation of means and covariances in filters and estimators," IEEE Trans. on AC, vol. 45, no. 3, pp. 477--482, 2000.

.... . The criterion introduced in this way is a dimensionless scalar. As good are considered trajectories which at the goal configuration have the first term within the range D I . The state estimation in the present paper is carried out based on the Unscented Kalman Filter (UKF) [10], 11] for state vector estimation. The UKF is implemented in its form with an augmented state vector (a concatenation of the states and the noises) 11] The sigma points and their weights are calculated using the scaled Unscented Transform [11] The WMR and beacon models, 1) and (2) are highly ....

....C q p ii . The beacon is located in a point with coordinates , It is assumed that FEHG p: ii 1 3F2 EHG 1 and C . The UKF is implemented with the following parameters, recommendable for systems with Gaussian noises and of order (so that ) [10], 11] The initial state estimate vector and covariance matrix are: z y ; C q q q C C ; Q . The noise covariance matrices are: l z # y ; o C c C c C c ; Q , m # y ; C q C CFC Q CFC ; is the distance from the ....

S. Julier, J. Uhlman, and H. Durrant-Whyte, "A new method for the transformation of means and covariances in filters and estimators," IEEE Trans. on AC, vol. 45, pp. 477--482, 2000.

....the models for each CF and its EKFs, an IMM estimator is implemented. So, the CFs can be monitored on line, using the information provided by the IMM mode probabilities. The nonlinear character of the measurement equations requires the use of EKFs or other nonlinear filtering techniques, such as [6] which needs no computation of derivatives. The present work estimates the state vectors through EKFs. Each EKF is of the form i,kq 1 kq 1 : i,kq 1 k q Ki,kq lYi,kq 1, 6) i,kq 1 k : i,k k, 7) Pi,k l k Pi,k k q Qi,k, 8) Ki,k l Pi,k l kyTi,k lSi l, 9) Pi,k l,k l ....

S. Julier, J. Uhhnan and H. Durrant-Whyte, A New Method for the Transformation of Means and Covariances in Filters and Estimators, IEEE Trans. on Automatic Control, Vol. 45, No. 3, pp. 477-482, 2000.

....the models for each CF and its EKFs, an IMM estimator is implemented. So, the CFs can be monitored on line, using the information provided by the IMM mode probabilities. The nonlinear character of the measurement equations requires the use of EKFs or other nonlinear filtering techniques, such as [6] which needs no computation of derivatives. The present work estimates the state vectors through EKFs. Each EKF is of the form G G : G : 1 (6) G G : 7) H G : H G : 6 G : 8) G : ....

S. Julier, J. Uhlman and H. Durrant-Whyte, A New Method for the Transformation of Means and Covariances in Filters and Estimators, IEEE Trans. on Automatic Control, Vol. 45, No. 3, pp. 477-482, 2000.

....the models for each CF and its EKFs, an IMM estimator is implemented. So, the CFs can be monitored on line, using the information provided by the IMM mode probabilities. The nonlinear character of the measurement equations requires the use of EKFs or other nonlinear filtering techniques, such as [6] which needs no computation of derivatives. The present work estimates the state vectors through EKFs. Each EKF is of the form H H 9 9 H 9 1 (6) H H 9 (7) I H 9 I H 9 5 H 9 (8) H 9 ....

S. Julier, J. Uhlman and H. Durrant-Whyte, A New Method for the Transformation of Means and Covariances in Filters and Estimators, IEEE Trans. on Automatic Control, Vol. 45, No. 3, pp. 477-482, 2000.

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S. Julier, J. Uhlman and H. Durrant-Whyte, A New Method for the Transformation of Means and Covariances in Filters and Estimators, IEEE Trans. on Automatic Control, Vol. 45, No. 3, pp. 477-482, 2000.

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S. Julier, J. Uhlman, H. Durrant-Whyte, A new method for the transformation of means and covariances in filters and estimators, IEEE Transactions on Automatic Control 45 (3) (2000) 477--482.

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