Considering the advantage of Empirical Mode Decomposition (EMD) for extracting the geophysical signals and filtering out the noise, this paper will first apply the EMD approach to post-process the Gravity Recovery and Climate Experiment (GRACE) monthly gravity field models. A 14-year time-series of Release 06 (RL06) monthly gravity field models from the Center for Space Research (CSR) truncated to degree and order 60 from the period April 2002 to August 2016 are analyzed using the EMD approach compared with traditional Gaussian smoothing filtering. Almost all fitting errors of GRACE spherical harmonic coefficients by the EMD approach are smaller than those by Gaussian smoothing, indicating that EMD can retain more information of the original spherical harmonic coefficients. The ratios of latitude-weighted RMS over the land and ocean signals are adopted to evaluate the efficiency of eliminating noise. The results show that almost all ratios of RMS for the EMD approach are higher than those of Gaussian smoothing, with the mean ratio of RMS of 3.61 for EMD and 3.41 for Gaussian smoothing, respectively. Therefore, we can conclude that the EMD method can filter noise more effectively than Gaussian smoothing, especially for the high-degree coefficients, and retain more geophysical signals with less leakage effects.
Doubly stochastic point processes driven by non-Gaussian Ornstein-Uhlenbeck type processes are studied. The problem of nonlinear filtering is investigated. For temporal point processes the characteristic form for the differential generator of the driving process is used to obtain a stochastic differential equation for the conditional distribution. The main result in the spatio-temporal case leads to the filtering equation for the conditional mean.
This paper discusses a novel approach to tuning 2DOF PID controllers for a positional control system, with a special focus on filters. It is based on the multiple real dominant pole method, applicable to both standard and series PID control. In the latter case it may be generalized by using binomial nth order filters. These offer filtering properties scalable in a much broader range than those allowed by a standard controller. It is shown that in terms of a modified total variance, controllers with higher order binomial filters allow a significant reduction of excessive control effort due to the measurement noise. When not limited by the sampling period choice, a significant performance increase may be achieved by using third order filters, which can be further boosted using higher order filters. Furthermore, all of the derived tuning procedures keep the controller design sufficiently simple so as to be attractive for industrial applications. The proposed approach is applied to the position control of electrical drives, where quantization noise can occur as a result of angular velocity reconstruction using the differentiated outputs of incremental position sensors.
The paper deals with Cox point processes in time and space with Lévy based driving intensity. Using the generating functional, formulas for theoretical characteristics are available. Because of potential applications in biology a Cox process sampled by a curve is discussed in detail. The filtering of the driving intensity based on observed point process events is developed in space and time for a parametric model with a background driving compound Poisson field delimited by special test sets. A hierarchical Bayesian model with point process densities yields the posterior. Markov chain Monte Carlo "Metropolis within Gibbs" algorithm enables simultaneous filtering and parameter estimation. Posterior predictive distributions are used for model selection and a numerical example is presented. The new approach to filtering is related to the residual analysis of spatio-temporal point processes.