The paper discusses two algorithms for solving the Zakai equation in the time-homogeneous diffusion filtering model with possible correlation between the state process and the observation noise. Both algorithms rely o...
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The paper discusses two algorithms for solving the Zakai equation in the time-homogeneous diffusion filtering model with possible correlation between the state process and the observation noise. Both algorithms rely on the Cameron-Martin version of the Wiener chaos expansion, so that the approximate filter is a finite linear combination of the chaos elements generated by the observation process. The coefficients in the expansion depend only on the deterministic dynamics of the state and observation processes. For real-time applications, computing the coefficients in advance improves the performance of the algorithms in comparison with most other existing methods of nonlinear filtering. The paper summarizes the main existing results about these Wiener chaos algorithms and resolves some open questions concerning the convergence of the algorithms in the noise-correlated setting. The presentation includes the necessary background on the Wiener chaos and optimal nonlinear filtering.
We present a novel method to online generation of time-optimal acceleration, velocity, and position trajectory values for servo-control systems using low-cost fixed-point processors with no on-chip multipliers. As in ...
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We present a novel method to online generation of time-optimal acceleration, velocity, and position trajectory values for servo-control systems using low-cost fixed-point processors with no on-chip multipliers. As in the case of many product designs, reducing system cost is a key constraint in our method. We address this constraint by optimizing required memory size, computational time, and introducing multiplication-free recursive algorithms most suitable for real-time implementation on low-cost microcontrollers. An efficient search algorithm is presented optimizing the trajectories with respect to total move time for any distance subject to physical constraints of the system. We also introduce a normalized set of first-order difference equations using only integer arithmetic and additions to compute the trajectory values. Complexity of the proposed method is compared with multiplication-based and lookup table methods using three popular microcontrollers with and without an on-chip hardware multiplier.
Tchebichef moment is a novel set of orthogonal moment applied in the fields of image analysis and pattern recognition. Less work has been made for the computation of Tchebichef moment and its inverse moment transform....
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Tchebichef moment is a novel set of orthogonal moment applied in the fields of image analysis and pattern recognition. Less work has been made for the computation of Tchebichef moment and its inverse moment transform. In this paper, both a direct recursive algorithm and a compact algorithm are developed for the computation of Tchebichef moment. The effective recursive algorithm for inverse Tchebichef moment transform is also presented. Clenshaw's recurrence formula was used in this paper to transform kernels of the forward and inverse Tchebichef moment transform. There is no need for the proposed algorithms to compute the Tchebichef polynomial values. The approaches presented are more efficient compared with the straightforward methods, and particularly suitable for parallel VLSI implementation due to their regular and simple filter structures. (c) 2005 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.
An efficient numerical procedure for computing the scattering coefficients of a radially stratified tilted cylinder is discussed. Compared with the previous algorithms, computations for scattering field in our code ar...
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An efficient numerical procedure for computing the scattering coefficients of a radially stratified tilted cylinder is discussed. Compared with the previous algorithms, computations for scattering field in our code are extended to fairly large parameters, up to more than 10,000 and a few millions in number of layers, and computational time is only a few seconds. The capabilities of our code depend also on the memory of computer. The algorithm can also be used for absorbing or nonabsorbing cylinders in different electromagnetic wave bands. Compared with the known results, the algorithm is validated. At last, the algorithm is used to simulate the intensity distributions of two-layered cylinders with large size parameter and of graded-index polymer optical fiber (GI-POF) at tilted incidence, which supplies information on non-intrusive measurement on-line of refractive index profile by light scattering. (c) 2006 Elsevier B.V. All rights reserved.
In this paper we consider stochastic recursive equations of sum type, X =(D) Sigma(K)(i-1) A(i)X(i) + b, and of max type, X =(D) max{A(i)X(i) + b(i) : l <= i <= k}, where A(i), b(i), and b are random, (X-i) are ...
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In this paper we consider stochastic recursive equations of sum type, X =(D) Sigma(K)(i-1) A(i)X(i) + b, and of max type, X =(D) max{A(i)X(i) + b(i) : l <= i <= k}, where A(i), b(i), and b are random, (X-i) are independent, identically distributed copies of X, and '=(D)' denotes equality in distribution. Equations of these types typically characterize limits in the probabilistic analysis of algorithms, in combinatorial optimization problems, and in many other problems having a recursive structure. We develop some new contraction properties of minimal L-s-metrics which allow us to establish general existence and uniqueness results for solutions without imposing any moment conditions. As an application we obtain a one-to-one relationship between the set of solutions to the homogeneous equation and the set of solutions to the inhomogeneous equation, for sum- and max-type equations. We also give a stochastic interpretation of a recent transfer principle of Rosler from nonnegative solutions of sum type to those of max type, by means of random scaled Weibull distributions.
Exponential tail bounds are derived for solutions of max-recursive equations and for max-recursive random sequences, which typically arise as functionals of recursive structures, of random trees or in recursive algori...
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Exponential tail bounds are derived for solutions of max-recursive equations and for max-recursive random sequences, which typically arise as functionals of recursive structures, of random trees or in recursive algorithms. In particular they arise in the worst case analysis of divide and conquer algorithms, in parallel search algorithms or in the height of random tree models. For the proof we determine asymptotic bounds for the moments or for the Laplace transforms and apply a characterization of exponential tail bounds due to Kasahara (1978).
In this paper we study a queueing system with state-dependent services and state-dependent vacations, or simply G/M（n）/1/K. Since the service rate is state-dependent, this system includes G/M/c and G/M/c/K queues wi...
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In this paper we study a queueing system with state-dependent services and state-dependent vacations, or simply G/M（n）/1/K. Since the service rate is state-dependent, this system includes G/M/c and G/M/c/K queues with various types of station vacations as special cases. We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. The only input requirement is the Laplace-Stieltjes transform of the interarrival distribution as well as the state-dependent service rate and state-dependent vacation rate. In a subsequent companion paper, we study its dual system M（n）/G/1/K queue with statedependent vacations.
In this article we examine the possibility of improving the recursive algorithm for computation of box-dimension of complex sets. The known method of box-counting is simplified down to the simple sign counting operati...
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ISBN:
(纸本)9537138054
In this article we examine the possibility of improving the recursive algorithm for computation of box-dimension of complex sets. The known method of box-counting is simplified down to the simple sign counting operation. Our target set is a "cloud" of amorphous points since many fractal sets are given in this form. The key of the algorithm are affine transformations from the world coordinate system to the parametric one and renormalization using as elementary operations as binary dilatation and unit shift transformations. The verification of the quality of results of the generated algorithm is established in the testing phase of the algorithm.
A new efficient algorithm for generating polarity matrix elements of ternary fixed polarity arithmetic transform is presented. The algorithm directly operates on the truth vector of a ternary function and it calculate...
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ISBN:
(纸本)9781424403868
A new efficient algorithm for generating polarity matrix elements of ternary fixed polarity arithmetic transform is presented. The algorithm directly operates on the truth vector of a ternary function and it calculates the spectral coefficients of all or selected fixed polarity arithmetic expansions for the function. It is simple and works in a recursive manner. Computational cost for the new algorithm has been derived and it is shown that the new algorithm has low computational costs.
A new method for establishing the equations of motion of multibody mechanisms based on canonical momenta is introduced in this paper. In absence of constraints, the proposed forward dynamics formulation results in a H...
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A new method for establishing the equations of motion of multibody mechanisms based on canonical momenta is introduced in this paper. In absence of constraints, the proposed forward dynamics formulation results in a Hamiltonian set of 2n first order ODEs in the generalized coordinates q and the canonical momenta p. These Hamiltonian equations are derived from a recursive Newton Euler formulation. As an example, it is shown how, in the case of a serial structure with rotational joints, an O(n) formulation is obtained. The amount of arithmetical operations is considerably less than acceleration based O(n) formulations.
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