Low-complexity fractional phase estimation for totally blind channel estimation

To remove the scalar ambiguity in conventional blind channel estimation algorithms, totally blind channel estimation （TBCE） is proposed by using multiple constellations. To estimate the unknown scalar, its phase is decomposed into a fractional phase and an integer phase. However, the maximum-likelihood （ML） algorithm for the fractional phase does not have closed-form solutions and suffers from high computational complexity. By ex- ploring the structures of widely used constellations, this paper proposes a low-complexity fractional phase estimation algorithm which requires no exhaustive search. Analytical expressions of the asymptotic mean squared error （MSE） are also derived. The theo- retical analysis and simulation results indicate that the proposed fractional phase estimation algorithm exhibits almost the same performance as the ML algorithm but with significantly reduced computational burden.

Real-time total system error estimation: Modeling and application in required navigation performance

In required navigation performance（RNP）, total system error（TSE） is estimated to provide a timely warning in the presence of an excessive error. In this paper, by analyzing the underlying formation mechanism, the TSE estimation is modeled as the estimation fusion of a fixed bias and a Gaussian random variable. To address the challenge of high computational load induced by the accurate numerical method, two efficient methods are proposed for real-time application, which are called the circle tangent ellipse method（CTEM） and the line tangent ellipse method（LTEM）,respectively. Compared with the accurate numerical method and the traditional scalar quantity summation method（SQSM）, the computational load and accuracy of these four methods are extensively analyzed. The theoretical and experimental results both show that the computing time of the LTEM is approximately equal to that of the SQSM, while it is only about 1/30 and 1/6 of that of the numerical method and the CTEM. Moreover, the estimation result of the LTEM is parallel with that of the numerical method, but is more accurate than those of the SQSM and the CTEM. It is illustrated that the LTEM is quite appropriate for real-time TSE estimation in RNP application.

On the Navier-Stokes Equations for Exothermically Reacting Compressible Fluids

We analyze mathematical models governing planar flow of chemical reaction from unburnt gases to burnt gases in certain physical regimes in which diffusive effects such as viscosity and heat conduction are significant. These models can be then formulated as the Navier-Stokes equations for exothermically reacting compressible fluids. We first establish the existence and dynamic behavior, including stability, regularity, and large-time behavior, of global discontinuous solutions of large oscillation to the Navier-Stokes equations with constant adiabatic exponent γ and specific heat Cv. Our approach for the existence and regularity is to combine the difference approximation techniques with the energy methods, total variation estimates, and weak convergence arguments to deal with large jump discontinuities; and for large-time behavior is an a posteriori argument directly from the weak form of the equations. The approach and ideas we develop here can be applied to solving a more complicated model where γand cv vary as the phase changes; and we then describe this model in detail and contrast the results on the asymptotic behavior of the solutions of these two different models. We also discuss other physical models describing dynamic combustion.