Minimax Estimation Problem for Periodically Correlated Stochastic Processes

The problem of optimal linear estimation of the functional Aξ =10^∞a（t）ζ（（t）dt depending on the unknown values of periodically correlated stochastic process ζ（t） from observations of this process for t 〈 0 is considered. Formulas that determine the greatest value of mean square error and the minimax estimation for the functional are proposed for the given class of admissible processes. It is shown that one-sided moving average stationary sequence gives the greatest value of the mean square error.

STOCHASTIC MODEL OF PERIODIC OPERATION PERFORMANCE FOR THE CONTINUOUS COUNTER－CURRENT ADSORPTION PROCESS

A stochastic model is developed to predict the peniodic operation performance ofthe continuous counter-current adsorption process. The model takes into account theeffects of random backmixing of particles, axial dispersion of liquid phase, liquid- film mass transfer, intraparticle diffusion and panticle shape, and can revealclearly the behavior of solid and liquid phase in adsorption process. The simulation results agree with the experimental data rather well.

SEVERAL PROBLEMS IN DESIGNING DBS SYSTEMS FOR AIRBORNE PULSE DOPPLER RADAR

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Estimation of extreme wind speed in SCS and NWP by a non-stationary model

In offshore engineering design, it is considerably significant to have an adequately accurate estimation of marine environmental parameters, in particular, the extreme wind speed of tropical cyclone （TC） with different return periods to guarantee the safety in projected operating life period. Based on the 71-year （1945-2015） TC data in the Northwest Pacific （NWP） by the Joint Typhoon Warning Center （JTWC） of US, a notable growth of the TC intensity is observed in the context of climate change. The fact implies that the traditional stationary model might be incapable of predicting parameters in the extreme events. Therefore, a non-stationary model is proposed in this study to estimate extreme wind speed in the South China Sea （SCS） and NWP. We find that the extreme wind speeds of different return periods exhibit an evident enhancement trend, for instance, the extreme wind speeds with different return periods by non- stationary model are 4.1%-4.4% higher than stationary ones in SCS. Also, the spatial distribution of extreme wind speed in NWP has been examined with the same methodology by dividing the west sea areas of the NWP 0°-45°N, 105°E-130°E into 45 subareas of 5° × 5°, where oil and gas resources are abundant. Similarly, remarkable spacial in-homogeneity in the extreme wind speed is seen in this area： the extreme wind speed with 50-year return period in the subarea （15°N-20°N, 115°E-120°E） of Zhongsha and Dongsha Islands is 73.8 m/s, while that in the subarea of Yellow Sea （30°N-35°N, 120°E-125°E） is only 47.1 m/s. As a result, the present study demonstrates that non-stationary and in-homogeneous effects should be taken into consideration in the estimation of extreme wind speed.

Fast approximate maximum likelihood period estimation from incomplete timing data

To estimate the period of a periodic point process from noisy and incomplete observations, the classical periodogram algorithm is modified. The original periodogram algorithm yields an estimate by performing grid search of the peak of a spectrum, which is equivalent to the periodogram of the periodic point process, thus its performance is found to be sensitive to the chosen grid spacing. This paper derives a novel grid spacing formula, after finding a lower bound of the width of the spectral mainlobe. By employing this formula, the proposed new estimator can determine an appropriate grid spacing adaptively, and is able to yield approximate maximum likelihood estimate （MLE） with a computational complexity of O（n2）. Experimental results prove that the proposed estimator can achieve better trade-off between statistical accuracy and complexity, as compared to existing methods. Simulations also show that the derived grid spacing formula is also applicable to other estimators that operate similarly by grid search.

Phase group synchronization between any signals and its physical characteristics

The phase group synchronization between any signals is further revealed,which is based on proposing the new concepts of the greatest common factor frequency,the least common multiple period,quantized phase shift resolution,equivalent phase comparison frequency and so on.Then the problem of phase comparison and processing between different frequency signals is solved and shown in detail.Using the basic principle and the variation law of group phase difference,the frequency stability better than 10-14/s can be easily obtained in the time&frequency measurement and control domain,and experimental results also show the phase relations between atomic energy level transition signal and the locked crystal oscillator signal in an active hydrogen atomic clock are strict phase group synchronization,and locked precision with 10-13/s can be reached based on phase group synchronization.The phase group synchronization can provide technical support to frequency linking among radio frequency,microwave and light frequency.

Composite quantile regression estimation for P-GARCH processes

We consider the periodic generalized autoregressive conditional heteroskedasticity(P-GARCH) process and propose a robust estimator by composite quantile regression. We study some useful properties about the P-GARCH model. Under some mild conditions, we establish the asymptotic results of proposed estimator.The Monte Carlo simulation is presented to assess the performance of proposed estimator. Numerical study results show that our proposed estimation outperforms other existing methods for heavy tailed distributions.The proposed methodology is also illustrated by Va R on stock price data.