9 results on '"SAMPLING errors"'
Search Results
2. Near Minimax Line Spectral Estimation.
- Author
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Tang, Gongguo, Bhaskar, Badri Narayan, and Recht, Benjamin
- Subjects
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SIGNAL processing , *SPECTRAL lines , *NOISE measurement , *SIGNAL frequency estimation , *SAMPLING errors - Abstract
This paper establishes a nearly optimal algorithm for denoising a mixture of sinusoids from noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a sparse recovery problem with a continuous, infinite dictionary. We show how to compute the estimator via semidefinite programming and provide guarantees on its mean-squared error rate. We derive a complementary minimax lower bound on this estimation rate, demonstrating that our approach nearly achieves the best possible estimation error. Furthermore, we establish bounds on how well our estimator localizes the frequencies in the signal, showing that the localization error tends to zero as the number of samples grows. We verify our theoretical results in an array of numerical experiments, demonstrating that the semidefinite programming approach outperforms three classical spectral estimation techniques. [ABSTRACT FROM PUBLISHER]
- Published
- 2015
- Full Text
- View/download PDF
3. Fractional Order Differentiation by Integration and Error Analysis in Noisy Environment.
- Author
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Liu, Da-Yan, Gibaru, Olivier, Perruquetti, Wilfrid, and Laleg-Kirati, Taous-Meriem
- Subjects
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JACOBIAN matrices , *NOISE measurement , *ERROR analysis in mathematics , *SAMPLING errors , *ROBUST control , *TIME delay systems - Abstract
The integer order differentiation by integration method based on the Jacobi orthogonal polynomials for noisy signals was originally introduced by Mboup, Join and Fliess. We propose to extend this method from the integer order to the fractional order to estimate the fractional order derivatives of noisy signals. Firstly, two fractional order differentiators are deduced from the Jacobi orthogonal polynomial filter, using the Riemann–Liouville and the Caputo fractional order derivative definitions respectively. Exact and simple formulae for these differentiators are given by integral expressions. Hence, they can be used for both continuous-time and discrete-time models in on-line or off-line applications. Secondly, some error bounds are provided for the corresponding estimation errors. These bounds allow to study the design parameters' influence. The noise error contribution due to a large class of stochastic processes is studied in discrete case. The latter shows that the differentiator based on the Caputo fractional order derivative can cope with a class of noises, whose mean value and variance functions are polynomial time-varying. Thanks to the design parameters analysis, the proposed fractional order differentiators are significantly improved by admitting a time-delay. Thirdly, in order to reduce the calculation time for on-line applications, a recursive algorithm is proposed. Finally, the proposed differentiator based on the Riemann–Liouville fractional order derivative is used to estimate the state of a fractional order system and numerical simulations illustrate the accuracy and the robustness with respect to corrupting noises. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
4. Optimal Memory for Discrete-Time FIR Filters in State-Space.
- Author
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Ramirez-Echeverria, Felipe, Sarr, Amadou, and Shmaliy, Yuriy S.
- Subjects
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POLYNOMIALS , *KALMAN filtering , *ORTHOGONAL decompositions , *SAMPLING errors , *STATE-space methods - Abstract
In this correspondence, we propose an efficient estimator of optimal memory (averaging interval) for discrete-time finite impulse response (FIR) filters in state-space. Its crucial property is that only real measurements and the filter output are involved with no reference and noise statistics. Testing by the two-state polynomial model has shown a very good correspondence with predicted values. Even in the worst case of the harmonic model, the estimator demonstrates practical applicability. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
5. Model-Based Subspace Projection Beamforming for Deep Interference Nulling.
- Author
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Landon, Jonathan, Jeffs, Brian D., and Warnick, Karl F.
- Subjects
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BEAMFORMING , *ARRAY processors , *SIGNAL processing , *SAMPLING errors , *NOISE measurement , *POLYNOMIALS - Abstract
This paper considers the problem of adaptive array processing for interference canceling to drive very deep nulls in difficult signal environments. In many practical scenarios, the achievable null depth is limited by covariance matrix estimation error leading to poor identification of the interference subspace. We address the particularly troublesome cases of low interference-to-noise ratio (INR), relatively rapid interference motion, and correlated noise across the receiving array. A polynomial-based model is incorporated in the proposed algorithm to track changes in the array covariance matrix over time, mitigate interference subspace estimation errors, and improve canceler performance. The application of phased array feeds for radio astronomical telescopes is used to illustrate the problem and proposed solution. Here even weak residual interference after cancelation may obscure a signal of interest, so very deep beampattern nulls are required. Performance for conventional subspace projection (SP) is compared with polynomial-augmented SP using simulated and real experimental data, showing null-depth improvement of 6 to 30 dB. [ABSTRACT FROM PUBLISHER]
- Published
- 2012
- Full Text
- View/download PDF
6. Optimal Distributed Kalman Filtering Fusion With Singular Covariances of Filtering Errors and Measurement Noises.
- Author
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Song, Enbin, Xu, Jie, and Zhu, Yunmin
- Subjects
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NOISE measurement , *KALMAN filtering , *SAMPLING errors , *COVARIANCE matrices , *PROBLEM solving , *ALGORITHMS - Abstract
In this paper, we present the globally optimal distributed Kalman filtering fusion with singular covariances of filtering errors and measurement noises. The following facts motivate us to consider the problem. First, the invertibility of estimation error covariance matrices is a necessary condition for most of the existing distributed fusion algorithms. However, it can not be guaranteed to exist in practice. For example, when state estimation for a given dynamic system is subject to state equality constraints, the estimation error covariance matrices must be singular. Second, the proposed fused state estimate is still exactly the same as the centralized Kalman filtering using all sensor raw measurements. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
7. Moving Horizon Estimation for Networked Systems With Quantized Measurements and Packet Dropouts.
- Author
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Liu, Andong, Yu, Li, Zhang, Wen-An, and Chen, Michael Z. Q.
- Subjects
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DISCRETE time filters , *ESTIMATION theory , *SWITCHING circuits , *COST functions , *PROBABILITY theory , *STOCHASTIC convergence , *SAMPLING errors - Abstract
This paper is concerned with the moving horizon estimation (MHE) problem for linear discrete-time systems with limited communication, including quantized measurements and packet dropouts. The measured output is quantized by a logarithmic quantizer and the packet dropout phenomena is modeled by a binary switching random sequence. The main purpose of this paper is to design an estimator such that, for all possible quantized errors and packet dropouts, the state estimation error sequence is convergent. By choosing a stochastic cost function, the optimal estimator is obtained by solving a regularized least-squares problem with uncertain parameters. The proposed method can be used to deal with the estimation and prediction problems for systems with quantized errors and packet dropouts in a unified framework. The stability properties of the optimal estimator are also studied. The obtained stability condition implicitly establishes a relation between the upper bound of the estimation error and two parameters, namely, the quantization density and the packet dropout probability. Moreover, the maximum quantization density and the maximum packet dropout probability are given to ensure the convergence of the upper bound of the estimation error sequence. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]
- Published
- 2013
- Full Text
- View/download PDF
8. A Nonlinear High-Gain Observer for Systems With Measurement Noise in a Feedback Control Framework.
- Author
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Prasov, Alexis A. and Khalil, Hassan K.
- Subjects
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OBSERVABILITY (Control theory) , *FEEDBACK control systems , *NOISE measurement , *NONLINEAR control theory , *NONLINEAR systems , *TRANSIENTS (Dynamics) , *SAMPLING errors - Abstract
We address the problem of state estimation for a class of nonlinear systems with measurement noise in the context of feedback control. It is well-known that high-gain observers are robust against model uncertainty and disturbances, but sensitive to measurement noise when implemented in a feedback loop. This work presents the benefits of a nonlinear-gain structure in the innovation process of the high-gain observer, in order to overcome the tradeoff between fast state reconstruction and measurement noise attenuation. The goal is to generate a larger observer gain during the transient response than in the steady-state response. Thus, by reducing the observer gain after achieving satisfactory state estimates, the effect of noise on the steady-state performance is reduced. Moreover, the nonlinear-gain observer presented in this paper is shown to surpass the system performance achieved when using comparable linear-gain observers. The proof argues boundedness and ultimate boundedness of the closed-loop system under the proposed output feedback. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
9. Non Adaptive Second-Order Generalized Integrator for Identification of a Biased Sinusoidal Signal.
- Author
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Fedele, Giuseppe and Ferrise, Andrea
- Subjects
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ADAPTIVE control systems , *SIGNAL frequency estimation , *SOUND measurement , *SAMPLING errors , *PARAMETER estimation , *LEAST squares , *COMPUTER algorithms - Abstract
This note presents a new algorithm that is designed to identify the frequency, magnitude, phase and offset of a biased sinusoidal signal. The structure of the algorithm includes an orthogonal system generator based on a second-order generalized integrator. The proposed strategy has the advantages of a fast and accurate signal reconstruction capability and a good rejection to noise. [ABSTRACT FROM PUBLISHER]
- Published
- 2012
- Full Text
- View/download PDF
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