Abstract: Bayesian approach can be used for parameter identification and extraction in state space models and its ability for analyzing sequence of data in dynamical system is proved in different literatures. In this paper, adaptive Kalman filter with Bayesian approach for identification of variances in measurement parameter noise is developed. Next, it is applied for estimation of the dynamical state and measurement data in discrete linear dynamical system. This algorithm at each step time estimates noise variance in measurement noise and state of system with Kalman filter. Next, approximation is designed at each step separately and consequently sufficient statistics of the state and noise variances are computed with a fixed-point iteration of an adaptive Kalman filter. Different simulations are applied for showing the influence of noise variance in measurement data on algorithm. Firstly, the effect of noise variance and its distribution on detection and identification performance is simulated in Kalman filter without Bayesian formulation. Then, simulation is applied to adaptive Kalman filter with the ability of noise variance tracking in measurement data. In these simulations, the influence of noise distribution of measurement data in each step is estimated, and true variance of data is obtained by algorithm and is compared in different scenarios. Afterwards, one typical modeling of nonlinear state space model with inducing noise measurement is simulated by this approach. Finally, the performance and the important limitations of this algorithm in these simulations are explained.
Abstract: In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δi are discussed. An algorithm that avoids matrix inversion with the case -1
Abstract: In this paper, the exponential stability of periodic solutions in inertial neural networks with unbounded delay are investigated. First, using variable substitution the system is transformed to first order differential equation. Second, by the fixed-point theorem and constructing suitable Lyapunov function, some sufficient conditions guaranteeing the existence and exponential stability of periodic solutions of the system are obtained. Finally, two examples are given to illustrate the effectiveness of the results.
Abstract: Harmonic pollution and low power factor in power
systems caused by power converters have been of great concern. To
overcome these problems several converter topologies using
advanced semiconductor devices and control schemes have been
proposed. This investigation is to identify a low cost, small size,
efficient and reliable ac to dc converter to meet the input performance
index of UPS. The performance of single phase and three phase ac to
dc converter along with various control techniques are studied and
compared. The half bridge converter topology with linear current
control is identified as most suitable. It is simple, energy efficient
because of single switch power loss and transformer-less operation of
UPS. The results are validated practically using a prototype built
using IGBT and analog controller. The performance for both single
and three-phase system is verified. Digital implementation of closed
loop control achieves higher reliability. Its cost largely depends on
chosen bit precision. The minimal bit precision for optimum
converter performance is identified as 16-bit with fixed-point
operation. From the investigation and practical implementation it is
concluded that half bridge ac – dc converter along with digital linear
controller meets the performance index of UPS for single and three
phase systems.
Abstract: The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based" algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition.
Abstract: This paper describes Independent Component Analysis (ICA) based fixed-point algorithm for the blind separation of the convolutive mixture of speech, picked-up by a linear microphone array. The proposed algorithm extracts independent sources by non- Gaussianizing the Time-Frequency Series of Speech (TFSS) in a deflationary way. The degree of non-Gaussianization is measured by negentropy. The relative performances of algorithm under random initialization and Null beamformer (NBF) based initialization are studied. It has been found that an NBF based initial value gives speedy convergence as well as better separation performance
Abstract: Fixed-point simulation results are used for the performance measure of inverting matrices using a reconfigurable processing element. Matrices are inverted using the Cholesky decomposition algorithm. The reconfigurable processing element is capable of all required mathematical operations. The fixed-point word length analysis is based on simulations of different condition numbers and different matrix sizes.
Abstract: Using the concept of measure of noncompactness, we present some results concerning the existence, uniform local attractivity and global attractivity of solutions for a functional integral equation. Our results improve and extend some previous known results and based on weaker conditions. Some examples which show that our results are applicable when the previous results are inapplicable are also included.
Abstract: Fixed-point simulation results are used for the
performance measure of inverting matrices by Cholesky
decomposition. The fixed-point Cholesky decomposition algorithm
is implemented using a fixed-point reconfigurable processing
element. The reconfigurable processing element provides all
mathematical operations required by Cholesky decomposition. The
fixed-point word length analysis is based on simulations using
different condition numbers and different matrix sizes. Simulation
results show that 16 bits word length gives sufficient performance
for small matrices with low condition number. Larger matrices and
higher condition numbers require more dynamic range for a fixedpoint
implementation.
Abstract: In this paper, we present two new one-step iterative
methods based on Thiele-s continued fraction for solving nonlinear
equations. By applying the truncated Thiele-s continued fraction
twice, the iterative methods are obtained respectively. Analysis of
convergence shows that the new methods are fourth-order convergent.
Numerical tests verifying the theory are given and based on the
methods, two new one-step iterations are developed.
Abstract: In this study, the existence and uniqueness of the solution of a nonlinear singular integral equation that is defined on a region in the complex plane is proven and a method is given for finding the solution.