Oblique Projection

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Herbert Werner - One of the best experts on this subject based on the ideXlab platform.

  • lpv model order reduction by parameter varying Oblique Projection
    IEEE Transactions on Control Systems and Technology, 2018
    Co-Authors: Julian Theis, Peter Seiler, Herbert Werner
    Abstract:

    A method to reduce the dynamic order of linear parameter-varying (LPV) systems in grid representation is developed in this paper. It consists of an Oblique Projection and is novel in its use of a parameter-varying nullspace to define the direction of this Projection. Parameter-varying state transformations in general lead to parameter rate dependence in the model. The proposed Projection avoids this dependence and maintains a consistent state space basis for the reduced-order system. This extension of the Projection framework lends itself very naturally to balanced truncation and related approaches that employ Gramian-based information to quantify the importance of subspaces. The proposed method is first compared to LPV balancing and truncation on a numerical example and then used to approximate two LPV systems: the longitudinal dynamics model of an aeroservoelastic unmanned aerial vehicle and the far wake model of a wind turbine.

  • Model order reduction by parameter-varying Oblique Projection
    Proceedings of the American Control Conference, 2016
    Co-Authors: Julian Theis, Peter Seiler, Herbert Werner
    Abstract:

    A method to reduce the dynamic order of linear parameter-varying (LPV) systems in grid representation is developed in this paper. It approximates balancing and truncation by an Oblique Projection onto a dominant subspace. The approach is novel in its use of a parameter-varying kernel to define the direction of this Projection. Parameter-varying state transformations in general lead to parameter rate dependence in the model. The proposed Projection avoids this dependence and maintains a consistent state space basis for the reduced-order system. The method is compared with LPV balancing and truncation for a nonlinear mass-spring-damper system. It is shown to yield similar accuracy, while the required computation time is reduced by a factor of almost 100,000.

Xingpeng Mao - One of the best experts on this subject based on the ideXlab platform.

  • localization and identification of unknown target signal using Oblique Projection
    Eurasip Journal on Wireless Communications and Networking, 2018
    Co-Authors: Liping Huo, Huijun Hou, Xingpeng Mao
    Abstract:

    The problem of source localization and waveform identification is the key of array signal processing. In this paper, an Oblique Projection-based localization and identification (OPLI) algorithm is proposed without known prior DOA or waveform information of the sources. The proposed OPLI is implemented iteratively. In each iteration, Oblique Projection is employed to separate the multiple incident signals into a series of single signal groups. After that, the procedure of waveform and DOA estimation for each single signal is implemented. Theoretical analysis and simulation result verify the performance and effectiveness of the proposed OPLI.

  • Oblique Projection for direction of arrival estimation of hybrid completely polarised and partially polarised signals with arbitrary polarimetric array configuration
    Iet Signal Processing, 2017
    Co-Authors: Huijun Hou, Xingpeng Mao, Yongtan Liu
    Abstract:

    This study deals with the direction-of-arrival (DOA) estimation problem for hybrid completely polarised (CP) and partially polarised (PP) source signals using arbitrary polarimetric antenna arrays. An Oblique Projection-based polarisation insensitive direction estimation (OPPIDE) algorithm is proposed by exploiting the spatial-sparsity property of the sources. The OP technique is utilised to provide spatial filters, which are insensitive to the state of polarisation of signals, so that the potential source signals in the spatial domain can be separated later. The DOA estimation is finally implemented by identifying the sources’ spatially sparse structure with the separated signals. Theoretical analysis indicates that the OPPIDE is applicable to any hybrid CP and PP signals, and is independent of special polarimetric array configurations. The effectiveness and superiority of the proposed OPPIDE are substantiated through making performance comparison with the present counterpart algorithms.

  • a generalized Oblique Projection filter with flexible parameter for interference suppression
    International Journal of Antennas and Propagation, 2015
    Co-Authors: Yiming Wang, Xingpeng Mao, Hong Hong, Jie Zhang, Yumei Cui
    Abstract:

    A generalized Oblique Projection (GOP) with an adjustable parameter defined as interference suppression cost (ISC) is proposed. Therefore, an optional optimized signal to interference-plus-noise ratio (SINR) and user controlled actions on the interference filtering are presented in this GOP framework. Theoretical analysis and numerical simulation demonstrate that when the ISC is derived from minimum variance distortionless response (MVDR) algorithm, the SINR performance of GOP filter is better than both MVDR and Oblique Projection (OP) filters. Further, an application of GOP filter in ionospheric clutter cancellation in a high frequency surface wave radar (HFSWR) system is given. The ISC is designed specifically to introduce an extra coherent loss to the clutters and a satisfying clutter suppression result is achieved. Besides the examples given, more designs of GOP filter can be inspired by the flexibility of ISC. As a generalized form of OP filter, GOP filter expands the connotation of Oblique Projection based technique and could be used in spatial filtering, polarization filtering, and other array signal processing applications.

  • an Oblique Projection filtering based doa estimation algorithm without a priori knowledge
    IEEE Radar Conference, 2014
    Co-Authors: Huijun Hou, Hong Hong, Xingpeng Mao, Aijun Liu
    Abstract:

    The high resolution multiple signal classification (MUSIC) algorithm provides an efficient way to estimate direction- of-arrival (DOA). However, it performs poorly when weak signals are accompanied with strong ones. To solve this problem, an Oblique Projection filtering based DOA estimation algorithm is proposed without using a priori knowledge of the sources, such as directions, strength, modulation modes, etc. Numerical results verify the effectiveness of the proposed algorithm. It is shown that a high resolution DOA estimation of the incident sources can be achieved. The detection performances for weak signals are more stable and superior than that of the MUSIC algorithm.

  • narrow band null phase shift spatial filter based on Oblique Projection
    IEEE Radar Conference, 2013
    Co-Authors: Hong Hong, Xingpeng Mao, Weibo Deng, Ran Guo, Peng Jiang
    Abstract:

    Normal methods of spatial filtering methods may change the coherent characteristic of the target, which reduces the effect of accumulation in coherent systems despite the improvement of signal-to-interference and noise ratio (SINR). To avoid the amplitude and phase distortion introduced by the filters, null phase-shift spatial filter (NPSF) is proposed in this paper. NPSF can suppress the interference while keeping the original information of the target signal. However, the performance of NPSF will be influenced by the estimation error of the target's spatial parameter. To solve this problem, an improved NPSF, narrow-band null phase-shift spatial filter (NNPSF), is proposed. The method to construct the weight vector of NNPSF is introduced. Theoretical analysis and simulation results demonstrate that the NNPSF is a valid spatial filtering technology. With reducing the accuracy of estimation, NNPSF is more suitable and robust in practical systems.

Julian Theis - One of the best experts on this subject based on the ideXlab platform.

  • lpv model order reduction by parameter varying Oblique Projection
    IEEE Transactions on Control Systems and Technology, 2018
    Co-Authors: Julian Theis, Peter Seiler, Herbert Werner
    Abstract:

    A method to reduce the dynamic order of linear parameter-varying (LPV) systems in grid representation is developed in this paper. It consists of an Oblique Projection and is novel in its use of a parameter-varying nullspace to define the direction of this Projection. Parameter-varying state transformations in general lead to parameter rate dependence in the model. The proposed Projection avoids this dependence and maintains a consistent state space basis for the reduced-order system. This extension of the Projection framework lends itself very naturally to balanced truncation and related approaches that employ Gramian-based information to quantify the importance of subspaces. The proposed method is first compared to LPV balancing and truncation on a numerical example and then used to approximate two LPV systems: the longitudinal dynamics model of an aeroservoelastic unmanned aerial vehicle and the far wake model of a wind turbine.

  • Model order reduction by parameter-varying Oblique Projection
    Proceedings of the American Control Conference, 2016
    Co-Authors: Julian Theis, Peter Seiler, Herbert Werner
    Abstract:

    A method to reduce the dynamic order of linear parameter-varying (LPV) systems in grid representation is developed in this paper. It approximates balancing and truncation by an Oblique Projection onto a dominant subspace. The approach is novel in its use of a parameter-varying kernel to define the direction of this Projection. Parameter-varying state transformations in general lead to parameter rate dependence in the model. The proposed Projection avoids this dependence and maintains a consistent state space basis for the reduced-order system. The method is compared with LPV balancing and truncation for a nonlinear mass-spring-damper system. It is shown to yield similar accuracy, while the required computation time is reduced by a factor of almost 100,000.

Weibo Deng - One of the best experts on this subject based on the ideXlab platform.

  • blind signal recovery using generalized Oblique Projection under unknown and spatially nonstationary noise
    International Conference on Control Engineering and Communication Technology, 2013
    Co-Authors: Weibo Deng
    Abstract:

    A novel approach of blind signal recovery based on generalized Oblique Projection (OP) is proposed. The background noise is assumed to be unknown and spatially nonstationary. Firstly, both the correlation and the eigenvalue decomposition arithmetic are used to estimate the array manifold. Then, a minimized interference constrained generalized Oblique Projection (MIGOP) operator is utilized to cancel unwanted signals and keep the signal of interest unchanged. Finally, the desired signal is restored without introducing amplitude or phase distortion and the nonstationary array noise turns to white after the least square transformation. Through theoretical analyses and numerical simulations, the proposed algorithm not only shows a better performance than the conventional OP filter, but also has a similar performance to the theoretical MIGOP filter. Moreover, the proposed approach is more practical and more effective in contrast with the existing OP filters since it is not depend on the prior knowledge of the steering vectors or the background noise covariance matrix.

  • narrow band null phase shift spatial filter based on Oblique Projection
    IEEE Radar Conference, 2013
    Co-Authors: Hong Hong, Xingpeng Mao, Weibo Deng, Ran Guo, Peng Jiang
    Abstract:

    Normal methods of spatial filtering methods may change the coherent characteristic of the target, which reduces the effect of accumulation in coherent systems despite the improvement of signal-to-interference and noise ratio (SINR). To avoid the amplitude and phase distortion introduced by the filters, null phase-shift spatial filter (NPSF) is proposed in this paper. NPSF can suppress the interference while keeping the original information of the target signal. However, the performance of NPSF will be influenced by the estimation error of the target's spatial parameter. To solve this problem, an improved NPSF, narrow-band null phase-shift spatial filter (NNPSF), is proposed. The method to construct the weight vector of NNPSF is introduced. Theoretical analysis and simulation results demonstrate that the NNPSF is a valid spatial filtering technology. With reducing the accuracy of estimation, NNPSF is more suitable and robust in practical systems.

  • Oblique Projection polarisation filtering for interference suppression in high frequency surface wave radar
    Iet Radar Sonar and Navigation, 2012
    Co-Authors: Xingpeng Mao, Hong Hong, Huijun Hou, A J Liu, R Guo, Weibo Deng
    Abstract:

    Polarisation filtering is a valid approach for interference suppression in high-frequency surface wave radar (HFSWR) and other systems. Based on the fundamental principle of the Oblique Projection and polarised filtering, an Oblique Projection polarisation filter (OPPF), which can be constructed from the polarisation subspaces of the target signal and those of the interference or directly from experimental data, is proposed in this study. Generalised methods for constructing the OPPF operators (theoretical OPPF and improved OPPF) are provided and the impact on the performance caused by the estimation errors is also discussed. Numerical results from simulation and experimental data demonstrate that the proposed filter is an effective means of interference cancellation. It is proved that OPPF is an extension of the conventional polarised filter, whereas the improved OPPF is more suitable for the situation where the interference is unknown.

  • Oblique Projection polarization filtering and its performance in high frequency surface wave radar
    International Conference on Microwave and Millimeter Wave Technology, 2010
    Co-Authors: Aijun Liu, Xingpeng Mao, Weibo Deng
    Abstract:

    A novel polarization filtering method based on the Oblique Projection operator is proposed to improve the target detection performance for High Frequency Surface Wave Radar (HFSWR) system in this paper. The performance of the proposed Oblique Projection polarization filter (OPPF) is detailedly analyzed in presence of additive Gaussian white noise and the desired signal's Mean Square Error (MSE) with the estimation error of the interference polarization parameter is discussed in detail. Numerical simulation results show that the proposed OPPF can enhance the target while mitigate the interference perfectly.

Johan Ak Suykens - One of the best experts on this subject based on the ideXlab platform.

  • functional form estimation using Oblique Projection matrices for ls svm regression models
    PLOS ONE, 2019
    Co-Authors: Alexander Caicedo, Carolina Varon, Sabine Van Huffel, Johan Ak Suykens
    Abstract:

    Kernel regression models have been used as non-parametric methods for fitting experimental data. However, due to their non-parametric nature, they belong to the so-called "black box" models, indicating that the relation between the input variables and the output, depending on the kernel selection, is unknown. In this paper we propose a new methodology to retrieve the relation between each input regressor variable and the output in a least squares support vector machine (LS-SVM) regression model. The method is based on Oblique subspace projectors (ObSP), which allows to decouple the influence of input regressors on the output by including the undesired variables in the null space of the Projection matrix. Such functional relations are represented by the nonlinear transformation of the input regressors, and their subspaces are estimated using appropriate kernel evaluations. We exploit the properties of ObSP in order to decompose the output of the obtained regression model as a sum of the partial nonlinear contributions and interaction effects of the input variables, we called this methodology Nonlinear ObSP (NObSP). We compare the performance of the proposed algorithm with the component selection and smooth operator (COSSO) for smoothing spline ANOVA models. We use as benchmark 2 toy examples and a real life regression model using the concrete strength dataset from the UCI machine learning repository. We showed that NObSP is able to outperform COSSO, producing stable estimations of the functional relations between the input regressors and the output, without the use of prior-knowledge. This methodology can be used in order to understand the functional relations between the inputs and the output in a regression model, retrieving the physical interpretation of the regression models.

  • Functional form estimation using Oblique Projection matrices for LS-SVM regression models
    'Public Library of Science (PLoS)', 2019
    Co-Authors: Caicedo Alexander, Varon Carolina, Van Huffel Sabine, Johan Ak Suykens
    Abstract:

    Kernel regression models have been used as non-parametric methods for fitting experimental data. However, due to their non-parametric nature, they belong to the so-called "black box" models, indicating that the relation between the input variables and the output, depending on the kernel selection, is unknown. In this paper we propose a new methodology to retrieve the relation between each input regressor variable and the output in a least squares support vector machine (LS-SVM) regression model. The method is based on Oblique subspace projectors (ObSP), which allows to decouple the influence of input regressors on the output by including the undesired variables in the null space of the Projection matrix. Such functional relations are represented by the nonlinear transformation of the input regressors, and their subspaces are estimated using appropriate kernel evaluations. We exploit the properties of ObSP in order to decompose the output of the obtained regression model as a sum of the partial nonlinear contributions and interaction effects of the input variables, we called this methodology Nonlinear ObSP (NObSP). We compare the performance of the proposed algorithm with the component selection and smooth operator (COSSO) for smoothing spline ANOVA models. We use as benchmark 2 toy examples and a real life regression model using the concrete strength dataset from the UCI machine learning repository. We showed that NObSP is able to outperform COSSO, producing stable estimations of the functional relations between the input regressors and the output, without the use of prior-knowledge. This methodology can be used in order to understand the functional relations between the inputs and the output in a regression model, retrieving the physical interpretation of the regression models.status: publishe