Robust fixed-lag smoother for linear systems including outliers in the system and observation noises

Tanaka, M.; Katayama, Tohru

doi:10.1080/00207728808964116

Cited by 9 publications

(12 citation statements)

References 6 publications

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“…For the KF corrector update, consider the LS formulation of the KF; see e.g., [27]. The corrector update can be derived as a regularized LS criterion, which will also be useful to account for the sparsity attribute.…”

Section: Kf For Tracking Tssgmentioning

confidence: 99%

Tracking Target Signal Strengths on a Grid using Sparsity

Farahmand,

Giannakis,

Leus

et al. 2011

Preprint

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Multi-target tracking is mainly challenged by the nonlinearity present in the measurement equation, and the difficulty in fast and accurate data association. To overcome these challenges, the present paper introduces a grid-based model in which the state captures target signal strengths on a known spatial grid (TSSG). This model leads to linear state and measurement equations, which bypass data association and can afford state estimation via sparsity-aware Kalman filtering (KF). Leveraging the grid-induced sparsity of the novel model, two types of sparsity-cognizant TSSG-KF trackers are developed: one effects sparsity through ℓ 1 -norm regularization, and the other invokes sparsity as an extra measurement.Iterative extended KF and Gauss-Newton algorithms are developed for reduced-complexity tracking, along with accurate error covariance updates for assessing performance of the resultant sparsity-aware state estimators. Based on TSSG state estimates, more informative target position and track estimates can be obtained in a follow-up step, ensuring that track association and position estimation errors do not propagate back into TSSG state estimates. The novel TSSG trackers do not require knowing the number of targets or their signal strengths, and exhibit considerably lower complexity than the benchmark hidden Markov model filter, especially for a large number of targets. Numerical simulations demonstrate that sparsity-cognizant trackers enjoy improved root mean-square error performance at reduced complexity when compared to their sparsity-agnostic counterparts.

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Section: Kf For Tracking Tssgmentioning

confidence: 99%

Tracking Target Signal Strengths on a Grid using Sparsity

Farahmand,

Giannakis,

Leus

et al. 2011

Preprint

View full text Add to dashboard Cite

show abstract

“…The optimal HMM filter exhibits the best performance but requires accurate knowledge of the target signal strength. Figure 4 depicts the RMSE of the sparsity-aware TSSG-IEKF tracker of (18), with μ k = 1 and for different values of σ k . This tracker incorporates sparsity as an extra measurement and selects the sparsity model ρ(x k ) as the 1 -norm function.…”

Section: Single-target Casementioning

confidence: 99%

“…For the KF corrector update, consider the LS formulation of the KF; see, e.g., [18]. The corrector update can be derived as a regularized LS criterion, which will also be useful to account for the sparsity attribute.…”

Section: Kf For Tracking Tssgmentioning

confidence: 99%

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Tracking target signal strengths on a grid using sparsity

Farahmand

Giannakis

Leus

et al. 2014

EURASIP J. Adv. Signal Process.

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Multi-target tracking is mainly challenged by the nonlinearity present in the measurement equation and the difficulty in fast and accurate data association. To overcome these challenges, the present paper introduces a grid-based model in which the state captures target signal strengths on a known spatial grid (TSSG). This model leads to linear state and measurement equations, which bypass data association and can afford state estimation via sparsity-aware Kalman filtering (KF). Leveraging the grid-induced sparsity of the novel model, two types of sparsity-cognizant TSSG-KF trackers are developed: one effects sparsity through 1 -norm regularization, and the other invokes sparsity as an extra measurement. Iterative extended KF and Gauss-Newton algorithms are developed for reduced-complexity tracking, along with accurate error covariance updates for assessing performance of the resultant sparsity-aware state estimators. Based on TSSG state estimates, more informative target position and track estimates can be obtained in a follow-up step, ensuring that track association and position estimation errors do not propagate back into TSSG state estimates. The novel TSSG trackers do not require knowing the number of targets or their signal strengths and exhibit considerably lower complexity than the benchmark hidden Markov model filter, especially for a large number of targets. Numerical simulations demonstrate that sparsity-cognizant trackers enjoy improved root-mean-square error performance at reduced complexity when compared to their sparsity-agnostic counterparts. Comparison with the recently developed additive likelihood moment filter reveals the better performance of the proposed TSSG tracker.

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“…A simple Kalman estimation step without the sparsity and the non-negativity constraint can be formulated as the following weighted least squares optimization problem [34]:…”

Section: Estimation Of U Tmentioning

confidence: 99%

Dynamic rainfall monitoring using microwave links

Roy

Gishkori

Leus

2016

EURASIP J. Adv. Signal Process.

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In this work, we propose a sparsity-exploiting dynamic rainfall monitoring methodology using rain-induced attenuation measurements from microwave links. To estimate rainfall field intensity dynamically from a limited number of non-linear measurements, we exploit physical properties of the rainfall such as spatial sparsity and non-negativity along with the dynamics of rainfall intensity. We develop a dynamic state estimation algorithm, where the aforementioned spatial properties are utilized as prior information. To exploit spatial sparsity, we use a basis function to tailor the sparse representation of the rainfall intensity. The basis is selected based on some criteria for sparse reconstruction such as orthonormality and mutual coherence. The tuning parameter that controls the sparsity in the spatial rainfall distribution is dynamically updated at every correction step. The developed methodology is applied to dynamically monitor the rainfall field intensity in an area with a specified spatial resolution using less number of simulated non-linear measurements than pixels. The proposed methodology can be generalized for any dynamic field reconstruction, where the limited number of non-linear measurements are field intensities integrated over a linear path.

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Robust fixed-lag smoother for linear systems including outliers in the system and observation noises

Cited by 9 publications

References 6 publications

Tracking Target Signal Strengths on a Grid using Sparsity

Tracking Target Signal Strengths on a Grid using Sparsity

Tracking target signal strengths on a grid using sparsity

Dynamic rainfall monitoring using microwave links

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