Spectral Estimation of Periodically Moving Part Modulation Based on AIDME Algorithm

The Periodicallg Moving Part Modulation (PMPM) for the moving parts in targetprovides important signatures for target recognition. However, most radars operate inmultiple-target mode and can only get discontinuous clusters of the returned pulses, which makes itextremely difficult to extract PMPM signature from the echoes. This paper puts forward theAlternative Iteration Deconvolution based on Minimum Entropy criteria (AIDME) for spectralestimation of extended target's echoes, utilizing the special feature that the PMPM spectra usuallyhave simple structures. Experimental results show that this method can effectively eliminate thesevere influence caused hy the convolution kernel and gain a satisfactory spectral estimation thatapproaches to the true spectrum.

Robust Spectral Estimation of Track Irregularity

Because the existing spectral estimation methods for railway track irregularity analysis are very sensitive to outliers, a robust spectral estimation method is presented to process track irregularity signals. The proposed robust method is verified using 100 groups of clean/contaminated data reflecting he vertical profile irregularity taken from Bejing-Guangzhou railway with a sampling frequency of 33 data every ~10 m, and compared with the Auto Regressive (AR) model. The experimental results show that the proposed robust estimation is resistible to noise and insensitive to outliers, and is superior to the AR model in terms of efficiency, stability and reliability.

Low-rank spectral estimation algorithm of learning Markov model

This paper proposes a low-rank spectral estimation algorithm of learning Markov model.First,an approximate projection algorithm for the rank-constrained frequency matrix set is proposed,and thereafter its local Lipschitzian error bound established.Then,we propose a low-rank spectral estimation algorithm for estimating the state transition frequency matrix and the probability matrix of Markov model by applying the approximate projection algorithm to correct the maximum likelihood estimation of the frequency matrix,and prove that there is only a multiplying constant difference in estimation errors between the low-rank spectral estimation and the maximum likelihood estimation under appropriate conditions.Finally,numerical comparisons with the prevailing maximum likelihood estimation,spectral estimation,and rank-constrained maxi-mum likelihood estimation show that the low-rank spectral estimation algorithm is effective.

Multivariate spectral estimation based on THREE

Power spectrum estimation is to use the limited length of data to estimate the power spectrum of the signal. In this paper, we study the recently proposed tunable high-resolution estimator（THREE）, which is based on the best approximation to a given spectrum, with respect to different notions of distance between power spectral densities. We propose and demonstrate a different distance for the optimization part to estimate the multivariate spectrum. Its effectiveness is tested through Matlab simulation. Simulation shows that our approach constitutes a valid estimation procedure. And we also demonstrate the superiority of the method, which is more reliable and effective compared with the standard multivariate identification techniques.

THE SPECTRAL ESTIMATION OF SODAR SIGNAL

In this paper, the autoregressive (AR) and FFT methods are used to estimate the power spectra of deterministic narrow-band signal with theoretic autocorrelation functions and signal samples, stochastic narrow-band signal with samples, and sodar signal. Some satisfying results are obtained. That is in the case of sodar signal, for two closer spectral peaks, the resolution of the AR method is lower than the FFT's; for two spectral peaks which are a little far apart from each other and single spectral peak, the precision of the AR method is better than the FFT's. The power spectrum curves of the AR method are smooth and low sidelobes at any case. We consider that a good spectral estimation method for sodar signal is the combination of the AR and the FFT methods.

Parameter Estimation of Time-Varying ARMA Model

The auto-regressive moving-average (ARMA) model with time-varying parameters is analyzed. The time-varying parameters are assumed to be a linear combination of a set of basis time-varying functions, and the feedback linear estimation algorithm is used to estimate the time-varying parameters of the ARMA model. This algorithm includes 2 linear least squares estimations and a linear filter. The influence of the order of basis time-(varying) functions on parameters estimation is analyzed. The method has the advantage of simple, saving computation time and storage space. Theoretical analysis and experimental results show the validity of this method.

Gridless Variational Bayesian Inference of Line Spectral from Quantized Samples

Efficient estimation of line spectral from quantized samples is of significant importance in information theory and signal processing,e.g.,channel estimation in energy efficient massive MIMO systems and direction of arrival estimation.The goal of this paper is to recover the line spectral as well as its corresponding parameters including the model order,frequencies and amplitudes from heavily quantized samples.To this end,we propose an efficient gridless Bayesian algorithm named VALSE-EP,which is a combination of the high resolution and low complexity gridless variational line spectral estimation(VALSE)and expectation propagation(EP).The basic idea of VALSE-EP is to iteratively approximate the challenging quantized model of line spectral estimation as a sequence of simple pseudo unquantized models,where VALSE is applied.Moreover,to obtain a benchmark of the performance of the proposed algorithm,the Cram′er Rao bound(CRB)is derived.Finally,numerical experiments on both synthetic and real data are performed,demonstrating the near CRB performance of the proposed VALSE-EP for line spectral estimation from quantized samples.

New low-rank optimization model and algorithms for spectral compressed sensing

In this paper, we investigate the recovery of an undamped spectrally sparse signal and its spectral components from a set of regularly spaced samples within the framework of spectral compressed sensing and super-resolution. We show that the existing Hankel-based optimization methods suffer from the fundamental limitation that the prior knowledge of undampedness cannot be exploited. We propose a new low-rank optimization model partially inspired by forward-backward processing for line spectral estimation and show its capability to restrict the spectral poles to the unit circle. We present convex relaxation approaches with the model and show their provable accuracy and robustness to bounded and sparse noise. All our results are generalized from one-dimensional to arbitrary-dimensional spectral compressed sensing. Numerical simulations are provided to corroborate our analysis and show the efficiency of our model and the advantageous performance of our approach in terms of accuracy and resolution compared with the state-of-the-art Hankel and atomic norm methods.

EXTRAPOLATION OF RF ECHO DATA BASED ON AR MODELING

Autoregressive (AR) modeling is applied to data extrapolation of radio frequency (RF) echo signals, and Burg algorithm, which can be computed in small amount and lead to a stable prediction filter, is used to estimate the prediction parameters of AR modeling. The complex data samples are directly extrapolated to obtain the extrapolated echo data in the frequency domain. The small rotating angle data extrapolation and the large rotating angular data extrapolation are considered separately in azimuth domain. The method of data extrapolation for the small rotating angle is the same as that in frequency domain, while the amplitude samples of large rotating angle echo data are extrapolated to obtain extrapolated echo amplitude, and the complex data of large rotating angle echo samples are extrapolated to get the extrapolated echo phase respectively. The calculation results show that the extrapolated echo data obtained by the above mentioned methods are accurate.

Analysis of the dynamic characteristics and stochastic simulation on variations of beach volumes

This paper analyzes the dynamic characteristics of the variations of the beach volumes for three level zonesof the Yanjing Beach in the Shuidong Bay of the western Guangdong Province by using the methods of dynamic systemanalysis and the multi-dimensional spectral estimation. The results show that the variations of the beach volume arecharaCterized by the multiband oscillations with a dominant semimonth period. Upwards the low tide level, the beachtends to be stable. The estimates of the partial coherences and the partial phases indicate that the variations of thebeach volumes are mainly the results of the direct actions of the waves which are influenced by the tidal level changesand driven by the wind stress. The simulation results of the beach volume series for different beach heart zones bythreshold mixed regressive models indicate that the influence of the tide on the variations of the beach volumes is weakened and the direct actions of the wave energy and the wind stress are apparently enhanced with the increase of thebeach height.(This project was supported by the National Natural Science Foundation of China.)

Tides and short-term variabilities in the Kuroshio west of Yonakuni-jima

Direct current measurements at the mooring station M southwest of Yonakuni-jima are carried out from May 18 to June 1, 1996. The Observed Kuroshio Current at 290 and 594 m depths of the mooring station M is quite steady ddring the pened of Observation. The rotary spectral estimates of the current data by the maximum entropy method show that there are prominent diurnal and semidiurnal spectral peaks. The semidiurnal tide is predominant at 290 m depth while there is the current fluctuation with the inertial period except for the tidal oscillation at 594 m depth. There are also peaks at the pened of 4-7 d. There is a significant coherence between two time series of currents at 290 and 594 m depths in the pened range of 3 - 5 d. The Japan Meteorological Agency (JMA) wind data during the same period as the oceanic measurement are used in comparison with the current meter data. Rotary spectral estimates for the wind data show significant peaks at the period of 3 - 5 d. It is concluded from the cross spectra between the wind and the current that the current fluctuation of 3 - 5 d period at 290 m depth response to the wind fluctuation of the same periods with time lags smaller than 1 d.

A Maximum-Entropy Method for Estimating the Spectrum

Based on the maximunl-entropy （ME） principle, a new power spectral estimator for random waves is derived in the form of S（ω）=a/8H^2^-（2π）^（d＋2）exp[-b（2π/ω）^n],1）y solving a variational problem subject to some quite general constraints. This robust method is comprehensive enough to describe the wave spectra even in extreme wave conditions and is superior to periodogranl method that is not suit＇able to process comparatively short or intensively unsteady signals for its tremendous boundary effect and some inherent defects of FKF. Fortunately, the newly derived method for spectral estimation works fairly well, even though the sample data sets are very short and unsteady, and the reliability and efficiency of this spectral estimator have been preliminarily proved.

BANDWIDTH SELECTION IN NONPARAMETRIC SPECTRAL DENSITY ESTIMATION OF THE STATIONARY GAUSSIAN PROCESS

We propose a method for estimating mean squared error and bandwidth in the windowedspectral density estimation of a stationary Gaussian process, and also provide a method forestimating the second order derivative of the spectral density function. The asymptotic propertiesand the convergence rates of the estimators are given.

Remarks on Sharp Interface Limit for an Incompressible Navier-Stokes and Allen-Cahn Coupled System

The authors are concerned with the sharp interface limit for an incompressible Navier-Stokes and Allen-Cahn coupled system in this paper.When the thickness of the diffuse interfacial zone,which is parameterized by ε,goes to zero,they prove that a solution of the incompressible Navier-Stokes and Allen-Cahn coupled system converges to a solution of a sharp interface model in the L^(∞)(L^(2))∩L^(2)(H^(1))sense on a uniform time interval independent of the small parameterε.The proof consists of two parts:One is the construction of a suitable approximate solution and another is the estimate of the error functions in Sobolev spaces.Besides the careful energy estimates,a spectral estimate of the linearized operator for the incompressible Navier-Stokes and Allen-Cahn coupled system around the approximate solution is essentially used to derive the uniform estimates of the error functions.The convergence of the velocity is well expected due to the fact that the layer of the velocity across the diffuse interfacial zone is relatively weak.

Vision algorithms for fixed-wing unmanned aerial vehicle landing system

Autonomous landing has become a core technology of unmanned aerial vehicle（UAV）guidance,navigation and control system

Estimates on the amplitude of the first Dirichlet eigenvector in discrete frameworks

Consider a finite absorbing Markov generator, irreducible on the non-absorbing states. PerronFrobenius theory ensures the existence of a corresponding positive eigenvector ψ. The goal of the paper is to give bounds on the amplitude max ψ/ min ψ. Two approaches are proposed: One using a path method and the other one, restricted to the reversible situation, based on spectral estimates. The latter approach is extended to denumerable birth and death processes absorbing at 0 for which infinity is an entrance boundary. The interest of estimating the ratio is the reduction of the quantitative study of convergence to quasi-stationarity to the convergence to equilibrium of related ergodic processes, as seen by Diaconis and Miclo(2014).

Notes on the Norm Estimates for the Sum of Two Matrices

This is a lecture note of my joint work with Chi-Kwong Li concerning various results on the norm structure of n 2 n matrices (as Hilbert-space operators). The main result says that the triangle inequality serves as the ultimate norm estimate for the upper bounds of summation of two matrices. In the case of summation of two normal matrices, the result turns out to be a norm estimate in terms of the spectral variation for normal matrices.