Tracking of ballistic target on re-entry using ensemble Kalman filter

Singh, Nitish Kumar; Bhaumik, Shovan; Bhattacharya, Sayantan

doi:10.1109/indcon.2012.6420671

Cited by 8 publications

(6 citation statements)

References 20 publications

(28 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…• Compute the posterior error covariance P P P a in ensemble space using (12) • Determine the Kalman gain K K K k , posterior ensemble mean xk|k , error covariance P P P k|k , ensemble perturbation X X X a , and inflated error covariance P P P Q k|k using ( 9)-( 11), ( 14), and (24), respectively • Determine the posterior ensemble {x i k|k } n i=1 by the ensemble sampling using (25) During the update (observation assimilation) phase, the posterior or updated position xk|k of the user, error covariances P P P k|k and P P P Q k|k , and ensemble perturbation X X X a are calculated by the predicted position xk|k−1 of the user, 2 × 2 identity matrix H k , positional observation z k estimated by the NBC-based fingerprinting scheme (refer to Section 4.2 in Sung et al [13]), and the posterior error covariance P P P a in ensemble space. The QETKF that uses the posterior ensemble {x i k|k } n i=1 obtained by Equation ( 25) can produce more inflated posterior ensemble spread than the ETKF; that is, it can avoid the systematic underestimation of the posterior error covariance appearing in the ETKF, thus providing better positioning results.…”

Section: Qetkf-based Localization Algorithmmentioning

confidence: 99%

“…To provide higher estimation accuracy in the positioning system, measurements from various sensors can be fused using Bayes filters, such as the particle filter (PF; Maohai et al [22]), Kalman filter (KF; Chen et al [23]), unscented Kalman filter (UKF; Zhan and Wan [24]), and ensemble-based Kalman filter (EBKF; Singh et al [25]). For example, many indoor positioning systems based on the PF, KF, and UKF have been proposed to achieve better localization results for the user by integrating noisy positional information obtained from the PDR and RSS fingerprinting using the smartphone [23].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Pedestrian Positioning Using an Enhanced Ensemble Transform Kalman Filter

Sung

2023

Sensors

View full text Add to dashboard Cite

Due to the unavailability of GPS indoors, various indoor pedestrian positioning approaches have been designed to estimate the position of the user leveraging sensory data measured from inertial measurement units (IMUs) and wireless signal receivers, such as pedestrian dead reckoning (PDR) and received signal strength (RSS) fingerprinting. This study is similar to the previous study in that it estimates the user position by fusing noisy positional information obtained from the PDR and RSS fingerprinting using the Bayes filter in the indoor pedestrian positioning system. However, this study differs from the previous study in that it uses an enhanced state estimation approach based on the ensemble transform Kalman filter (ETKF), called QETKF, as the Bayes filer for the indoor pedestrian positioning instead of the SKPF proposed in the previous study. The QETKF estimates the updated user position by fusing the predicted position by the PDR and the positional measurement estimated by the RSS fingerprinting scheme using the ensemble transformation, whereas the SKPF calculates the updated user position by fusing them using both the unscented transformation (UT) of UKF and the weighting method of PF. In the field of Earth science, the ETKF has been widely used to estimate the state of the atmospheric and ocean models. However, the ETKF algorithm does not consider the model error in the state prediction model; that is, it assumes a perfect model without any model errors. Hence, the error covariance estimated by the ETKF can be systematically underestimated, thereby yielding inaccurate state estimation results due to underweighted observations. The QETKF proposed in this paper is an efficient approach to implementing the ETKF applied to the indoor pedestrian localization system that should consider the model error. Unlike the ETKF, the QETKF can avoid the systematic underestimation of the error covariance by considering the model error in the state prediction model. The main goal of this study is to investigate the feasibility of the pedestrian position estimation for the QETKF in the indoor localization system that uses the PDR and RSS fingerprinting. Pedestrian positioning experiments performed using the indoor localization system implemented on the smartphone in a campus building show that the QETKF can offer more accurate positioning results than the ETKF and other ensemble-based Kalman filters (EBKFs). This indicates that the QETKF has great potential in performing better position estimation with more accurately estimated error covariances for the indoor pedestrian localization system.

show abstract

Section: Qetkf-based Localization Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Pedestrian Positioning Using an Enhanced Ensemble Transform Kalman Filter

Sung

2023

Sensors

View full text Add to dashboard Cite

show abstract

“…This indicates that the number of quadrature points rises exponentially with the order of system. A comprehensive description on GH quadrature rule along with necessary illustrations is provided in the in the master's thesis of Singh [18] and also in [19]. These references may be consulted for more details on GH quadrature rule.…”

Section: Algorithm For the Basic (Non-adaptive) Ghfmentioning

confidence: 99%

Adaptive Gauss–Hermite filter for non‐linear systems with unknown measurement noise covariance

Dey

Sadhu

Ghoshal

2015

IET Science, Measurement & Technology

View full text Add to dashboard Cite

“…Filtering methods based on the random sampling can also be applied in mobility tracking scenarios, such as the Ensemble Kalman filter (EnKF) and the Unscented Kalman filter (UKF). The EnKF performs a random sampling of the probability density function to represent the initial state estimate [14]. In contrast, the UKF relies on a deterministic choice of sampling points, called sigma points [15], [16].…”

Section: Introductionmentioning

confidence: 99%

Tracking With Sparse and Correlated Measurements via a Shrinkage-Based Particle Filter

et al. 2017

View full text Add to dashboard Cite

This paper presents a shrinkage-based particle filter method for tracking a mobile user in wireless networks. The proposed method estimates the shadowing noise covariance matrix using the shrinkage technique. The particle filter is designed with the estimated covariance matrix to improve the tracking performance. The shrinkage-based particle filter can be applied in a number of applications for navigation, tracking and localization when the available sensor measurements are correlated and sparse. The performance of the shrinkage-based particle filter is compared with the posterior Cramer-Rao lower bound, which is also derived in the paper. The advantages of the proposed shrinkage-based particle filter approach are demonstrated via simulation and experimental results.

show abstract

Tracking of ballistic target on re-entry using ensemble Kalman filter

Cited by 8 publications

References 20 publications

Pedestrian Positioning Using an Enhanced Ensemble Transform Kalman Filter

Pedestrian Positioning Using an Enhanced Ensemble Transform Kalman Filter

Adaptive Gauss–Hermite filter for non‐linear systems with unknown measurement noise covariance

Tracking With Sparse and Correlated Measurements via a Shrinkage-Based Particle Filter

Contact Info

Product

Resources

About