The Experts below are selected from a list of 56472 Experts worldwide ranked by ideXlab platform
Eric Simon - One of the best experts on this subject based on the ideXlab platform.
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Simplified Random-Walk-Model-Based Kalman Filter for Slow to Moderate Fading Channel Estimation in OFDM Systems
IEEE Transactions on Signal Processing, 2014Co-Authors: Huaqiang Shu, Laurent Ros, Eric SimonAbstract:This study deals with multi-path channel estimation for orthogonal frequency division multiplexing systems under slow to moderate fading conditions. Advanced algorithms exploit the channel time-domain correlation by using Kalman Filters (KFs) Based on an approximation of the time-varying channel. Recently, it was shown that under slow to moderate fading, near optimal channel multi-path complex amplitude estimation can be obtained by using the integrated Random Walk (RW) model as the channel approximation. To reduce the complexity of the high-dimensional RW-KF for joint estimation of the multi-path complex amplitudes, we propose using a lower dimensional RW-KF that estimates the complex amplitude of each path separately. We demonstrate that this amounts to a simplification of the joint multi-path Kalman gain formulation through the Woodbury's identities. Hence, this new algorithm consists of a superposition of independent single-path single-carrier KFs, which were optimized in our previous studies. This observation allows us to adapt the optimization to the actual multi-path multi-carrier scenario, to provide analytic formulae for the mean-square error performance and the optimal tuning of the proposed estimator directly as a function of the physical parameters of the channel (Doppler frequency, Signal-to-Noise-Ratio, Power Delay Profile). These analytic formulae are given for the first-, second-, and third-order RW models used in the KF. The proposed per-path KF is shown to be as efficient as the exact KF (i.e., the joint multipath KF), and outperforms the autoregressive-model-Based KFs proposed in the literature.
Eric Pierre Simon - One of the best experts on this subject based on the ideXlab platform.
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simplified random walk model Based Kalman Filter for slow to moderate fading channel estimation in ofdm systems
IEEE Transactions on Signal Processing, 2014Co-Authors: Eric Pierre SimonAbstract:This study deals with multi-path channel estimation for orthogonal frequency division multiplexing systems under slow to moderate fading conditions. Advanced algorithms exploit the channel time-domain correlation by using Kalman Filters (KFs) Based on an approximation of the time-varying channel. Recently, it was shown that under slow to moderate fading, near-optimal channel multi-path complex amplitude estimation can be obtained by using the integrated random walk (RW) model as the channel approximation. To reduce the complexity of the high-dimensional RW-KF for joint estimation of the multi-path complex amplitudes, we propose using a lower dimensional RW-KF that estimates the complex amplitude of each path separately. We demonstrate that this amounts to a simplification of the joint multi-path Kalman gain formulation through the Woodbury's identities. Hence, this new algorithm consists of a superposition of independent single-path single-carrier KFs, which were optimized in our previous studies. This observation allows us to adapt the optimization to the actual multi-path multi-carrier scenario, to provide analytic formulas for the mean-square error performance and the optimal tuning of the proposed estimator directly as a function of the physical parameters of the channel (Doppler frequency, signal-to-noise-ratio, power delay profile). These analytic formulae are given for the first-, second-, and third-order RW models used in the KF. The proposed per-path KF is shown to be as efficient as the exact KF (i.e., the joint multi-path KF), and outperforms the autoregressive-model-Based KFs proposed in the literature.
Maria V. Kulikova - One of the best experts on this subject based on the ideXlab platform.
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ECC - Some New Array Information Formulations of the UD-Based Kalman Filter
2019 18th European Control Conference (ECC), 2019Co-Authors: Julia V. Tsyganova, Maria V. Kulikova, A.v. TsyganovAbstract:The paper addresses the UD factorization Based Kalman Filtering (KF) implementation methods. We propose two new numerically favored and convenient array information formulations of the UD-Based KF: the UD-Based array Information Filter (algorithm UD-IF) and the extended UD-Based array Information Filter (algorithm eUD-IF). To confirm the correctness of our results, we have proved that the newly constructed UD Based array computational schemes are algebraically equivalent to the “straight” (conventional) information Filter. Although all these information-type algorithms are theoretically equivalent, their computational properties are different. The newly proposed algorithms are numerically robust to machine round-off errors due to the numerically stable orthogonal transformations applied on each iteration. Additionally, algorithm eUD-IF has the extended array form, i. e., it allows updating absolutely all required Filter quantities with the use of the numerically stable modified weighted Gram-Schmidt orthogonalization procedure. So, our results extend the existing class of numerically efficient KF implementation methods and can be used in practical applications.
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Numerically Robust SVD-Based Kalman Filter Implementations
2018 22nd International Conference on System Theory Control and Computing (ICSTCC), 2018Co-Authors: Maria V. KulikovaAbstract:The so-called factored-form Kalman Filter (KF) implementations are designed to deal with the problem of numerical instability of the conventional KF. They include Cholesky factorization-Based, UD-Based and singular value decomposition (SVD) algorithms. The SVD-Based estimators are the most recent developments in this realm. They were shown to be more robust with respect to roundoff than the classical KF implementation and the previously derived factored-form methods. This paper discusses further improvements in estimation accuracy and numerical robustness of the recently proposed SVD-Based estimators.
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SVD-Based Kalman Filter Derivative Computation
IEEE Transactions on Automatic Control, 2017Co-Authors: Julia V. Tsyganova, Maria V. KulikovaAbstract:Recursive adaptive Filtering methods are often used for solving the problem of simultaneous state and parameters estimation arising in many areas of research. The gradient-Based schemes for adaptive Kalman Filtering (KF) require the corresponding Filter sensitivity computations. The standard approach is Based on the direct differentiation of the KF equations. The shortcoming of this strategy is a numerical instability of the conventional KF (and its derivatives) with respect to roundoff errors. For decades, special attention has been paid in the KF community for designing efficient Filter implementations that improve robustness of the estimator against roundoff. The most popular and beneficial techniques are found in the class of square-root (SR) or UD factorization-Based methods. They imply the Cholesky decomposition of the corresponding error covariance matrix. Another important matrix factorization method is the singular value decomposition (SVD) and, hence, further encouraging KF algorithms might be found under this approach. Meanwhile, the Filter sensitivity computation heavily relies on the use of matrix differential calculus. Previous works on the robust KF derivative computation have produced the SR- and UD-Based methodologies. Alternatively, in this paper we design the SVD-Based approach. The solution is expressed in terms of the SVD-Based KF covariance quantities and their derivatives (with respect to unknown system parameters). The results of numerical experiments illustrate that although the newly-developed SDV-Based method is algebraically equivalent to the conventional approach and the previously derived SR- and UD-Based strategies, it outperforms the mentioned techniques for estimation accuracy in ill-conditioned situations.
H Kaufman - One of the best experts on this subject based on the ideXlab platform.
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boundary value selection problem for image restoration using the reduced order model Based Kalman Filter
International Conference on Acoustics Speech and Signal Processing, 1991Co-Authors: S Koch, H KaufmanAbstract:The reduced order-model Kalman Filter (ROMKF) is a low order state-space model Based Kalman Filter. The motivation for introducing the ROM was the reduction in the amount of computation involved in a 2-D Kalman Filter with full state-space model representation. Because of the way in which the state vector and the covariance are defined in the ROM, it is necessary to give careful consideration to the selection of the 2-D boundary conditions. A discussion is presented of such considerations, and it is shown, using both error indices and visual results, that proper boundary selection will significantly improve image restoration. >
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ICASSP - Boundary value selection problem for image restoration using the reduced order model Based Kalman Filter
[Proceedings] ICASSP 91: 1991 International Conference on Acoustics Speech and Signal Processing, 1991Co-Authors: S Koch, H KaufmanAbstract:The reduced order-model Kalman Filter (ROMKF) is a low order state-space model Based Kalman Filter. The motivation for introducing the ROM was the reduction in the amount of computation involved in a 2-D Kalman Filter with full state-space model representation. Because of the way in which the state vector and the covariance are defined in the ROM, it is necessary to give careful consideration to the selection of the 2-D boundary conditions. A discussion is presented of such considerations, and it is shown, using both error indices and visual results, that proper boundary selection will significantly improve image restoration. >
Michael Barlage - One of the best experts on this subject based on the ideXlab platform.
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Revising the Ensemble-Based Kalman Filter Covariance for the Retrieval of Deep-Layer Soil Moisture
Journal of Hydrometeorology, 2010Co-Authors: Shu Wen Zhang, Xubin Zeng, Weidong Zhang, Michael BarlageAbstract:Abstract Previous studies have demonstrated that soil moisture in the top layers (e.g., within the top 1-m depth) can be retrieved by assimilating near-surface soil moisture observations into a land surface model using ensemble-Based data assimilation algorithms. However, it remains a challenging issue to provide good estimates of soil moisture in the deep layers, because the error correlation between the surface and deep layers is low and hence is easily influenced by the physically limited range of soil moisture, probably resulting in a large noise-to-signal ratio. Furthermore, the temporally correlated errors between the surface and deep layers and the nonlinearity of the system make the retrieval even more difficult. To tackle these problems, a revised ensemble-Based Kalman Filter covariance method is proposed by constraining error covariance estimates in deep layers in two ways: 1) explicitly using the error covariance at the previous time step and 2) limiting the increase of the soil moisture error ...
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NOTES AND CORRESPONDENCE Revising the Ensemble-Based Kalman Filter Covariance for the Retrieval of Deep-Layer Soil Moisture
2010Co-Authors: Shu Wen Zhang, Xubin Zeng, Weidong Zhang, Michael BarlageAbstract:Previous studies have demonstrated that soil moisture in the top layers (e.g., within the top 1-m depth) can be retrieved by assimilating near-surface soil moisture observations into a land surface model using ensembleBased data assimilation algorithms. However, it remains a challenging issue to provide good estimates of soil moisture in the deep layers, because the error correlation between the surface and deep layers is low and hence is easily influenced by the physically limited range of soil moisture, probably resulting in a large noiseto-signal ratio. Furthermore, the temporally correlated errors between the surface and deep layers and the nonlinearity of the system make the retrieval even more difficult. To tackle these problems, a revised ensemble-Based Kalman Filter covariance method is proposed by constraining error covariance estimates in deep layers in two ways: 1) explicitly using the error covariance at the previous time step and 2) limiting the increase of the soil moisture error correlation with the increase of the vertical distance between the two layers. This method is then tested at three separate point locations representing different precipitation regimes. It is found that the proposed method can effectively control the abrupt changes of error covariance estimates between the surface layer and two deep layers. It significantly improves the estimates of soil moisture in the two deep layers with daily updating. For example, relative to the initial background error, after 150 daily updates, the error in the deepest layer reduces to 11.4%, 32.3%, and 27.1% at the wet, dry, and medium wetness locations, only reducing to 62.3%, 80.8%, and 47.5% with the original method, respectively. However, the improvement of deep-layer soil moisture retrieval is very slight when the updating frequency is reduced to once every three days.