Posterior Cramer-Rao lower bounds for multitarget bearings-only tracking

Usually, only the Cramer-Rao lower bound （CRLB） of single target is taken into consideration in the state estimate of passive tracking systems. As for the case of multitarget, there are few works done due to its complexity. The recursion formula of the posterior Cramer-Rao lower bound （PCRLB） in multitarget bearings-only tracking with the three kinds of data association is presented. Meanwhile, computer simulation is carried out for data association. The final result shows that the accuracy probability of data association has an important impact on the PCRLB.

Optimization of Generator Based on Gaussian Process Regression Model with Conditional Likelihood Lower Bound Search

The noise that comes from finite element simulation often causes the model to fall into the local optimal solution and over fitting during optimization of generator.Thus,this paper proposes a Gaussian Process Regression(GPR)model based on Conditional Likelihood Lower Bound Search(CLLBS)to optimize the design of the generator,which can filter the noise in the data and search for global optimization by combining the Conditional Likelihood Lower Bound Search method.Taking the efficiency optimization of 15 kW Permanent Magnet Synchronous Motor as an example.Firstly,this method uses the elementary effect analysis to choose the sensitive variables,combining the evolutionary algorithm to design the super Latin cube sampling plan;Then the generator-converter system is simulated by establishing a co-simulation platform to obtain data.A Gaussian process regression model combing the method of the conditional likelihood lower bound search is established,which combined the chi-square test to optimize the accuracy of the model globally.Secondly,after the model reaches the accuracy,the Pareto frontier is obtained through the NSGA-II algorithm by considering the maximum output torque as a constraint.Last,the constrained optimization is transformed into an unconstrained optimizing problem by introducing maximum constrained improvement expectation(CEI)optimization method based on the re-interpolation model,which cross-validated the optimization results of the Gaussian process regression model.The above method increase the efficiency of generator by 0.76%and 0.5%respectively;And this method can be used for rapid modeling and multi-objective optimization of generator systems.

Combined load bearing capacity of rigid piles embedded in a crossanisotropic clay deposit using 3D finite element lower bound

In this study,an iterative-based three-dimensional finite element lower bound in association with the second-order cone programming method is adopted to evaluate the limit load of a single pile embedded in cross-anisotropic soils under general loading condition.The lower bound solutions of the pile embedded in an anisotropic soil deposit can be found by formulating the element equilibrium,equilibrium of shear and normal stresses along discontinuities,boundary conditions,yield function,and optimizing the objective function through the second-order cone programming method in conjunction with an iterative-based update procedure.A general loading condition is considered to profile the expansion of the safe load in the vertical-horizontal-moment(V-H-M)space.The results of this study are compared and validated against three different cases including an isotropic lateral loading,anisotropic end bearing capacity,and a pile embedded in an isotropic soil deposit under general loading condition.A parametric study is conducted to evaluate the impact of different influencing factors.It was found that the effect of anisotropy on the variation of lateral limit load of a single pile is more pronounced than the corresponding vertical and bending moment limit loads,whereas the interface properties have more significant effects on the vertical and bending moment limit loads in comparison to the lateral limit load.

Lower Bounds of Decay Rates for Solution to the Single-Layer Quasi-Geostrophic Model

In this paper, we study the long-time behavior of solutions of the single-layer quasi-geostrophic model arising from geophysical fluid dynamics. We obtain the lower bound of the decay estimate of the solution. Utilizing the Fourier splitting method, under suitable assumptions on the initial data, for any multi-index α, we show that the solution Ψ satisfies .

Lower bound on BER performance for maximal ratio combining with weighting errors

The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower bounds for different channel Doppler spectra are derived. Based on the obtained lower bounds on mean squared channel estimation errors, the limits on bit error rate （BER） for maximal ratio combining （MRC） with Gaussian distributed weighting errors on independent and identically distributed （i. i. d） fading channels are presented. Numerical results show that the BER performances of ideal MRC are the lower bounds on the BER performances of non-ideal MRC and deteriorate as the maximum Doppler frequency increases or the SNR of channel estimate decreases.

CRAMER-RAO BOUNDS OF THE FREQUENCY ESTIMATION IN THE TIME SELECTIVE RADIO CHANNELS WITH DOPPLER SPREAD

The mobile channel is slow fading and time selective, thus the multiplicative and additive noise of the channel will smear the spectral line, or arouse Doppler spread. This spread will make the parameters estimation accuracy degrade. The goal of this paper is to analytically assess this degradation when Carrier Frequency Offset (CFO) and Doppler shift exist jointly. Then the finite-sample Cramer-Rao Lower Bound (CRLB) is derived and close-form asymptotical expression is given for large-sample CRLB. These expressions give insights into the performance room for frequency estimation. Also the variance of Doppler shift estimator is simulated to illustrate the theoretical results.

The Estimation for Lower Bounds of the Solutions of Fermat's Equation

Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|xyz, x<y<z, then y>p^(6p-2)/2.

LOWER BOUNDS ESTIMATE FOR THE BLOW-UP TIME OF A NONLINEAR NONLOCAL POROUS MEDIUM EQUATION

The lower bounds for the blow-up time of blow-up solutions to the nonlinear nolocal porous equation ut=△u^m＋u^p∫Ωu^qdxwith either null Dirichlet boundary condition or homogeneous Neumann boundary condi- tion is given in this article by using a differential inequality technique.

ON THE LOWER BOUND FOR A CLASS OF HARMONIC FUNCTIONS IN THE HALF SPACE

The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n 〉 2. To this end, we first generalize the Carleman＇s formula for harmonic functions in the half plane to higher dimensional half space, and then establish a Nevanlinna＇s representation for harmonic functions in the half sphere by using HSrmander＇s theorem.

NEW LOWER BOUNDS FOR LEE DISCREPANCY ON TWO AND THREE MIXED LEVELS FACTORIALS

The objective of this paper is to study the issue of uniformity on asymmetrical designs with two and three mixed levels in terms of Lee discrepancy. Based on the known formulation, we present a new lower bound of Lee discrepancy of fractional factorial designs with two and three mixed levels. Our new lower bound is sharper and more valid than other existing lower bounds in literature, which is a useful complement to the lower bound theory of discrepancies.

LOWER BOUNDS OF BLOW UP TIME FOR A SYSTEM OF SEMI-LINEAR HYPERBOLIC PETROVSKY EQUATIONS

Li et al. in [3] obtained blow-up results for a system of Petrovskey equations in some different cases. In this article we obtain lower bounds for the blow up time under some considerations on initial data.

A LOWER BOUND APPROACH TO THE YIELD LOCI OF POROUS MATERIALS

A lower bound approach is proposed for the first time to solve the macroscopic yield loci of porous materials.The results are then compared with Gurson's upper bound yield loci and those of the experiments.It is shown that the present analysis is much more in accordance with the experimen- tal results than the Gurson's.

Cramer-Rao bound and signal-to-noise ratio gain in distributed coherent aperture radar

This paper studies the estimation performance of the coherent processing parameter （CPP）, including time delay differences and phase synchronization errors among different apertures of the distributed coherent aperture radar （DCAR）. Firstly, three architectures of signal processing in the DCAR are introduced. Secondly, the closed-form Cramer-Rao bound （CRB） of the CPP estimation is derived and compared. Then, the closed-form CRB is verified by numerical simulations. Finally, when the next generation radar works in a fully coherent mode, the closed-form signal-to-noise ratio （SNR） gain of the three architectures is presented.

Cramer-Rao bound of joint estimation of target location and velocity for coherent MIMO radar

The optimal estimation performance of target parameters is studied. First, the general form of Cramer-Rao bound （CRB） for joint estimation of target location and velocity is derived for coherent multiple input multiple output （MIMO） radars. To gain some insight into the behavior of the CRB, the CRB with a set of given orthogonal waveforms is studied as a specific case. Second, a maximum likelihood （ML） estimation algorithm is proposed. The mean square error （MSE） of the ML estimation of target location and velocity is obtained by Monte Carlo simulation and it approaches CRB in the high signal-to-noise ratio （SNR） region.

LOWER BOUND LIMIT ANALYSIS OF THREE-DIMENSIONAL ELASTOPLASTIC STRUCTURES BY BOUNDARY ELEMENT METHOD

Based on the lower bound theorem of limit analysis, a solution procedure for limit analysis of three_dimensional elastoplastic structures was established using conventional boundary element method (BEM). The elastic stress field for lower bound limit analysis was computed directly by three_dimensional boundary element method (3_D BEM). The self_equilibrium stress field was constructed by the linear combination of several self_equilibrium “basis vectors” which can be computed by elastic_plastic incremental iteration of 3_D BEM analysis. The lower bound limit analysis problem was finally reduced to a series of nonlinear programming sub_problems with relatively few optimal variables. The complex method was used to solve the nonlinear programming sub_problems. The numerical results show that the present solution procedure has good accuracy and high efficiency.

Lower bounds and modified LPT algorithm for k-partitioning problems with partition matroid constraint

In this paper, the k-partitioning problem with partition matroid constraint is considered. LPT algorithm is modified to fit the problem and its worst-ease performance is analyzed. The lower bounds of optimal solution for the min-max problem are given.

THE ENERGY CONSERVATIONS AND LOWER BOUNDS FOR POSSIBLE SINGULAR SOLUTIONS TO THE 3D INCOMPRESSIBLE MHD EQUATIONS

In this note,we give a new proof to the energy conservation for the weak solutions of the incompressible 3D MHD equations.Moreover,we give the lower bounds for possible singular solutions to the incompressible 3D MHD equations.

A Lower and Upper Bound Method for Complex System Reliability Evaluation

It is hard for the existing methods to obtain the expression of the system reliability for most of the practical complex systems with a large number of components and possible stales. A new regression algorithm based on the lower and upper bounds is presented in this paper, which can obtain the system reliability analytically without concerning the structure of the complex system. The method has been applied to a real system and the reliability results are compared with those acquired by the classical method and the parametric method. The effectiveness and accuracy of the proposed method have been testified.

AN ASYMPTOTIC-NUMERICAL ANALYSIS FOR THE LOWER BOUND DYNAMIC BUCKLING ESTIMATES

A finite element asymptotic analysis for determining the lower bound dynamic buckling estimates of imperfection-sensitive structures under step load of infinite duration is presented. The lower bound dynamic buckling loads and the corresponding displacements are sought in the form of asymptotic expansions based on the static stability criterion and they can be determined by solving numerically (FEM) several linear problems with a single nonsingular sub-stiffness matrix.

Lower bound for the security of differential phase shift quantum key distribution against a one-pulse-attack

Quantum key distribution is the art of sharing secret keys between two distant parties, and has attracted a lot of attention due to its unconditional security. Compared with other quantum key distribution protocols, the differential phase shift quantum key distribution protocol has higher efficiency and simpler apparatus. Unfortunately, the uncondi- tional security of differential phase shift quantum key distribution has not been proved. Utilizing the sharp continuity of the von Neuman entropy and some basic inequalities, we estimate the upper bound for the eavesdropper Eve＇s infor- mation. We then prove the lower bound for the security of the differential phase shift quantum key distribution protocol against a one-pulse attack with Devatak-Winter＇s secret key rate formula.