Nonlinear regression models are more common as compared to linear ones for real life cases e. g. climatology, biology, earthquake engineering, economics etc. However, nonlinear regression models are much more complex ...
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Nonlinear regression models are more common as compared to linear ones for real life cases e. g. climatology, biology, earthquake engineering, economics etc. However, nonlinear regression models are much more complex to fit and to interpret. Classical parameter estimation methods such as least squares and maximum likelihood can also be adopted to fit the model in nonlinear regression as well, but explicit solutions can not be achieved unlike linear models. At this point, iterative algorithms are utilized to solve the problem numerically. Since there is no extensive study which compiles, classifies and compares the existing methods for nonlinear parameter estimation, the objective of this study is to fill this gap. In our study, we aim to compile the methods which are used for nonlinear parameter estimation purpose and compare them with respect to several criteria such as bias, execution time, number of iterations etc. The comparison will be conducted considering different scenarios which are small vs. large sample sizes, good vs. poor initial values, normal vs. non-normal error terms, simple vs complex models (with respect to number of parameters), and robustness. Both real and simulated data are used in the comparative study.
A fast iterative algorithm, with computation based on the fast Fourier transform (FFT), is presented. It can be used to control a sound field at several control points with a loudspeaker array from multiple reference ...
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A fast iterative algorithm, with computation based on the fast Fourier transform (FFT), is presented. It can be used to control a sound field at several control points with a loudspeaker array from multiple reference signals. It designs an equalizer able to invert long FIR filters and which achieves better performance than traditional FFT-based deconvolution methods with an equal number of coefficients in the inverse filters.
This paper addresses the problem of optical signal-to-noise ratio (OSNR) optimization problem in optical networks. Based on the extended OSNR Nash game formulation that includes power capacity constraints in [10], the...
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This paper addresses the problem of optical signal-to-noise ratio (OSNR) optimization problem in optical networks. Based on the extended OSNR Nash game formulation that includes power capacity constraints in [10], the Nash equilibrium (NE) solution is analytically intractable and highly nonlinear. We investigate the properties of the NE solution and based on these, we develop iterative algorithms to compute the NE solution: a parallel update algorithm (PUA) and a relaxed parallel update algorithm (r-PUA). We study their convergence with different conditions, both theoretically and numerically.
The iterative algorithm for minimum variance distortionless response filter based on auxiliary-vector (IMVDR-AV) is generalized in this paper from a different perspective. By extending the optimization criteria on fil...
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ISBN:
(纸本)0780376633
The iterative algorithm for minimum variance distortionless response filter based on auxiliary-vector (IMVDR-AV) is generalized in this paper from a different perspective. By extending the optimization criteria on filter design, it is generalized to an iterative algorithm of linear constrained minimum power filter (ILCMP-AV). Starting from this algorithm, we present an iterative algorithm of LCMP filter based on local optimization criterion (ILCMP-LOC) which converges rapidly by further generalizing the conditional optimization criterion on weighting coefficient computation. For any positive definite input autocorrelation matrix and any linear constraint, the ILCMP-AV algorithm recursively generates a sequence of auxiliary vectors by maximizing the magnitude cross correlation under some constraint conditions and its corresponding weighting coefficients by minimizing the filter output variance. Theoretical analysis illustrates that the combination of the updated filters and the weighted auxiliary vectors forms a sequence of filters that converges to the LCMP solution.
The use of the ordinary Poisson iterative reconstruction algorithm in PET requires the estimation of expected random coincidences. In a clinical environment, random coincidences are often acquired with a delayed coinc...
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The use of the ordinary Poisson iterative reconstruction algorithm in PET requires the estimation of expected random coincidences. In a clinical environment, random coincidences are often acquired with a delayed coincidence technique, and expected randoms are estimated through variance reduction (VR) of measured delayed coincidences. In this paper we present iterative VR algorithms for random compressed sinograms, when previously known methods are not applicable. iterative methods have the advantage of easy adaptation to any acquisition geometry and of allowing the estimation of singles rates at the crystal level when the number of crystals is relatively small. Two types of sinogram compression are considered: axial (span) rebinning and transaxial mashing. A monotonic sequential coordinate descent algorithm, which optimizes the Least Squares objective function, is investigated. A simultaneous update algorithm, which possesses the advantage of easy parallelization, is also derived for both cases of the Least Squares and Poisson Likelihood objective function. Measured data from a Siemens TruePoint clinical scanner are used to validate the algorithm performance.
We present a new approach to the problem of estimating multiple signal and parameter unknowns given noisy and incomplete data. Using cross-entropy, we fit a separable density to the given model density, then use this ...
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We present a new approach to the problem of estimating multiple signal and parameter unknowns given noisy and incomplete data. Using cross-entropy, we fit a separable density to the given model density, then use this separable density to estimate each unknown independently. Not only does this method include all the various MAP methods as degenerate cases, but it also directly leads to a simple iterative algorithm which can solve either the cross-entropy method or any of the MAP methods. This algorithm is particularly effective for exponential families of densities. Applications include estimation using grouped or quantized data, and a wide variety of reconstruction, smoothing, interpolation, extrapolation and modeling problems involving linear Gaussian systems.
The discrete-time envelope constrained (EC) filtering problem can be formulated as a quadratic programming (QP) problem with linear inequality constraints. In this paper, the QP problem is approximated by an unconstra...
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The discrete-time envelope constrained (EC) filtering problem can be formulated as a quadratic programming (QP) problem with linear inequality constraints. In this paper, the QP problem is approximated by an unconstrained minimization problem with two parameters. These parameters can be selected so that given an acceptable deviation from the norm of the optimal EC filter, the solution to the unconstrained problem satisfies both the deviation and envelope constraints. Newton's method with line search is applied to solve the unconstrained problem iteratively.
Two distinct iterative algorithms are proposed for obtaining locally optimal strategies for the dirty tape problem. Although the resulting strategies show only a slight performance improvement over the scalar Costa so...
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ISBN:
(纸本)142440505X
Two distinct iterative algorithms are proposed for obtaining locally optimal strategies for the dirty tape problem. Although the resulting strategies show only a slight performance improvement over the scalar Costa solutions, we have enough evidence to conjecture that these strategies are the optimal lattice strategies. Further, our techniques are applicable in a wider scenario, since these algorithms do not assume the additive noise to be Gaussian
Efficient iterative extended finite impulse response (EFIR) filtering algorithms are developed for nonlinear discrete-time state-space estimation. An advantage of the EFIR approach is that the noise statistics are not...
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ISBN:
(纸本)9781510823440
Efficient iterative extended finite impulse response (EFIR) filtering algorithms are developed for nonlinear discrete-time state-space estimation. An advantage of the EFIR approach is that the noise statistics are not required on a horizon of N opt points and zero mean noise is allowed to have any distribution and covariance. The EFIR algorithm is developed for nonlinear estimation over sensor networks that implies time-varying matrix structures. A modified EFIR algorithm employs the nonlinear-to-linear observation conversion. Applications are given to robot indoor self-localization over radio frequency identification tag grid excess channels.
To investigate the stabilization problem of the periodic linear systems,it is important to achieve the solution of the periodic Lyapunov matrix *** order to find the solution of the equation,novel iterative algorithms...
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To investigate the stabilization problem of the periodic linear systems,it is important to achieve the solution of the periodic Lyapunov matrix *** order to find the solution of the equation,novel iterative algorithms for discrete-time periodic Lyapunov equations are derived,respectively to the zero initial conditions and arbitrary initial ***’s more,the latest information estimation theory is utilized in the iterative *** validity of the algorithms are verified by numerical simulations.
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