Recursive filtering of multi-rate cyber-physical systems with unknown inputs under adaptive event-triggered mechanisms

Cyber-physical systems(CPSs)take on the characteristics of both multiple rates of information collection and processing and the dependency on information exchanges.The purpose of this paper is to develop a joint recursive filtering scheme that estimates both unknown inputs and system states for multi-rate CPSs with unknown inputs.In cyberspace,the information transmission between the local joint filter and the sensors is governed by an adaptive event-triggered strategy.Furthermore,the desired parameters of joint filters are determined by a set of algebraic matrix equations in a recursive way,and a sufficient condition verifying the boundedness of filtering error covariance is found by resorting to some algebraic operation.A state fusion estimation scheme that uses local state estimation is proposed based on the covariance intersection(CI)based fusion conception.Lastly,an illustrative example demonstrates the effectiveness of the proposed adaptive event-triggered recursive filtering algorithm.

A multi-scale second-order autoregressive recursive filter approach for the sea ice concentration analysis

To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.

A multi-scale high-order recursive filter approach for the sea ice concentration analysis

With the development and deployment of observation systems in the ocean,more precise passive and active microwave data are becoming available for the weather forecasting and the climate monitoring.Due to the complicated variability of the sea ice concentration(SIC)in the marginal ice zone and the scarcity of high-precision sea ice data,how to use less data to accurately reconstruct the sea ice field has become an urgent problem to be solved.A reconstruction method for gridding observations using the variational optimization technique,called the multi-scale high-order recursive filter(MHRF),which is a combination of Van Vliet fourth-order recursive filter and the three-dimensional variational(3D-VAR)analysis,has been designed in this study to reproduce the refined structure of sea ice field.Compared with the existing spatial multi-scale first-order recursive filter(SMRF)in which left and right filter iterative processes are executed many times,the MHRF scheme only executes the same filter process once to reduce the analysis errors caused by multiple filters and improve the filter precision.Furthermore,the series connected transfer function in the high-order recursive filter is equivalently replaced by the paralleled one,which can carry out the independent filter process in every direction in order to improve the filter efficiency.Experimental results demonstrate that this method possesses a good potential in extracting the observation information to successfully reconstruct the SIC field in computational efficiency.

Application of a Recursive Filter to a Three-Dimensional Variational Ocean Data Assimilation System

In order to improve the efficiency of the Ocean Variational Assimilation System （OVALS）, which has been widely used in various applications, an improved OVALS （OVALS2） is developed based on the recursive filter （RF） algorithm. The first advantage of OVALS2 is that memory storage can be substantially reduced in practice because it implicitly computes the background error covariance matrix; the second advantage is that there is no inversion of the background error covariance by preconditioning the control variable. For comparing the effectiveness between OVALS2 and OVALS, a set of experiments was implemented by assimilating expendable bathythermograph （XBT） and ARGO data into the Tropical Pacific circulation model. The results show that the efficiency of OVALS2 is much higher than that of OVALS. The computational time and the computer storage in the assimilation process were reduced by 83% and 77%, respectively. Additionally, the corresponding results produced by the RF are almost as good as those obtained by OVALS. These results prove that OVALS2 is suitable for operational numerical oceanic forecasting.

Assimilation of temperature and salinity using isotropic and anisotropic recursive filters in Tropic Pacific

A data assimilation scheme used in the updated Ocean three-dimensional Variational Assimila- tion System （OVALS）, OVALS2, is described. Based on a recursive filter （RF） to estimate the background error covariance （BEC） over a predetermined scale, this new analysis system can be implemented with anisotropic and isotropic BECs. Similarities and differences of these two BEC schemes are briefly discussed and their impacts on the model simulation are also investigated. An idealized experiment demonstrates the ability of the updated analysis system to construct different BECs. Furthermore, a set of three years experiments is implemented by assimilating expendable bathythermograph （XBT） and ARGO data into a Tropical Pacific circulation model. The TAO and WOA01 data are used to validate the assimilation results. The results show that the model simu- lations are substantially improved by OVALS2. The inter-comparison of isotropic and anisotropic BEC shows that the corresponding temperature and salinity produced by the anisotropic BEC are almost as good as those obtained by the isotropic one. Moreover, the result of anisotropic RF is slightly closer to WOA01 and TAO than that of isotropic RF in some special area （e.g. the cold tongue area in the Tropic Pacific）.

A variational successive corrections approach for the sea ice concentration analysis

The sea ice concentration observation from satellite remote sensing includes the spatial multi-scale information.However,traditional data assimilation methods cannot better extract the valuable information due to the complicated variability of the sea ice concentration in the marginal ice zone.A successive corrections analysis using variational optimization method,called spatial multi-scale recursive filter(SMRF),has been designed in this paper to extract multi-scale information resolved by sea ice observations.It is a combination of successive correction methods(SCM)and minimization algorithms,in which various observational scales,from longer to shorter wavelengths,can be extracted successively.As a variational objective analysis scheme,it gains the advantage over the conventional approaches that analyze all scales resolved by observations at one time,and also,the specification of parameters is more convenient.Results of single-observation experiment demonstrate that the SMRF scheme possesses a good ability in propagating observational signals.Further,it shows a superior performance in extracting multi-scale information in a two-dimensional sea ice concentration(SIC)experiment with the real observations from Special Sensor Microwave/Imager SIC(SSMI).

The Variability of the Snow and Ice Melt in Alpine Rivers in Northwestern China

The study of snow and ice melt （SIM） is important in water-scarce arid regions for the assessment of water supply and quality. These studies involve unique difficulties, especially in the calibration of hydro-models because there is no direct way to continuously measure the SIM at hydrostations. The recursive digital filter （RDF） and the isotopic hydro-geochemical method （IHM） were coupled to separate the SIM from eight observed series of alpine streamflows in northwestern China. Validation of the calibrated methods suggested a good capture of the SIM characteristics with fair accuracy in both space and time. Applications of the coupled methods in the upper reaches of the Hei River Basin （HRB） suggested a double peak curve of the SIM fraction to streamflow for the multi-component recharged （MCR） rivers, while a single peak curve was suggested for the rainfall-dominant recharged （RDR） rivers. Given inter-annual statistics of the separation, both types of the alpine rivers have experienced an obvious decrease of SIM since 196os. In the past 10 years, the SIM in the two types of rivers has risen to the levels of the 1970s, but has remained lower than the level of the 1960s. The study provided a considerable evidence to quantify the alpine SIMbased on the separation of observed data series at gauge stations. Application of the coupled method could be helpful in the calibration and validation of SIM-related hydro-models in alpine regions.

Anisotropic Total Variation Regularization Based NAS-RIF Blind Restoration Method for OCT Image

Based on anisotropic total variation regularization(ATVR), a nonnegativity and support constraints recursive inverse filtering(NAS-RIF) blind restoration method is proposed to enhance the quality of optical coherence tomography(OCT) image. First, ATVR is introduced into the cost function of NAS-RIF to improve the noise robustness and retain the details in the image.Since the split Bregman iterative is used to optimize the ATVR based cost function, the ATVR based NAS-RIF blind restoration method is then constructed. Furthermore, combined with the geometric nonlinear diffusion filter and the Poisson-distribution-based minimum error thresholding, the ATVR based NAS-RIF blind restoration method is used to realize the blind OCT image restoration. The experimental results demonstrate that the ATVR based NAS-RIF blind restoration method can successfully retain the details in the OCT images. In addition, the signal-to-noise ratio of the blind restored OCT images can be improved, along with the noise robustness.

New Method for 2D Image Edge-detection in Layer-layer 3D Testing System

A new method based on the material removal and cross-section optical scanning is investigated.The advantage of this method is that the internal and external information of the specimen can be obtained at same precision. In order to eliminate the pulse and Gaussian noise, the multi-scale dyadic wavelet methods are presented and discussed. The experimental results show that the multi-scale dyadic wavelet methods can successfully extract the features from noise image.The accuracy of 2D edge detection is 5.4 μm with the resolution of 2.7 μm.

Recursive Projected Filter Algorithm with Binary-Valued Observations

This paper focuses on the state estimate for a class of systems with both process noise and measurement noise under binary-valued observations,in which the Gaussian assumption on the predicted density of the state is not required.A recursive projected filter algorithm with time-varying thresholds is constructed to estimate the state under binary-valued observations.The time-varying thresholds are designed as the prediction value of the measurement,which can provide more information about the system state.The convergence property is established with some suitable stability,boundedness and observability conditions.In particular,the estimation error between state and estimate is proved to be asymptotically bounded in the mean-square sense,whose upper bound is related to the variance of process noise.Finally,the theoretical results are demonstrated via numerical examples of first-order and high-order systems.

Optimal filtering for uncertain systems with stochastic nonlinearities, correlated noises and missing measurements

The globally optimal recursive filtering problem is studied for a class of systems with random parameter matrices,stochastic nonlinearities, correlated noises and missing measurements. The stochastic nonlinearities are presented in the system model to reflect multiplicative random disturbances, and the additive noises, process noise and measurement noise, are assumed to be one-step autocorrelated as well as two-step cross-correlated.A series of random variables is introduced as the missing rates governing the intermittent measurement losses caused by unfavorable network conditions. The aim of the addressed filtering problem is to design an optimal recursive filter for the uncertain systems based on an innovation approach such that the filtering error is globally minimized at each sampling time. A numerical simulation example is provided to illustrate the effectiveness and applicability of the proposed algorithm.

A Very Efficient Approach for the Synthesis of 2-D Recursive Fan Filters

In this paper, we present a very efficient approath for the synthesis of twodimensional (2-D) re-cursive fan filters based on 1-D filter design. The investigation of the elliptical approximation theory mekesit possible to decompose a 1-D analogue filter into a series-parallel combination of all-pass sections. The 1-Ddigital filter obtained from this decomposition, while used as the prototype for 2-D filter synthesis, results ina grearly simplified realization architecture for fan filters. The final transfer function of the fan filter,which is reduced lo a combination of several lower-order all-pass sections, not only has fewer coefficients butalso enjoys optimal magnitude response. Some illustrative examples are given in this paper to show the effec-tiveness and simplicity of the proposed method.

An optimized baseflow separation method for assessment of seasonal and spatial variability of baseflow and the driving factors

Baseflow is an important component of river or streamflow.It plays a vital role in water utilization and management.An improved Eckhardt recursive digital filter(IERDF)is proposed in this study.The key filter parameter and maximum baseflow index(BFImax)were estimated using the minimum smoothing method to improve baseflow estimation accuracy.The generally considered BFImax of 0.80,0.50 and 0.25 according to the drainage basin’s predominant geological characteristics often leads to significant errors in the regions that have complex subsurface and hydrologic conditions.The IERDF improved baseflow estimation accuracy by avoiding arbitrary parameter values.The proposed method was applied for baseflow separation in the upstream of Yitong River,a tributary of the Second Songhua River,and its performance was evaluated by comparing the results obtained using isotope-tracer data.The performance of IERDF was also compared with nine baseflow separation techniques belonging to filter,BFI and HYSEP methods.The IERDF was also applied for baseflow separation and calculation of rainfall infiltration recharge coefficient at different locations along the Second Songhua River’s mainstream for the period 2000–2016.The results showed that the minimum smoothing method significantly improved BFImax estimation accuracy.The baseflow process line obtained using IEDRF method was consistent with that obtained using isotope 18 O.The IERDF estimated baseflow also showed stability and reliability when applied in the mainstream of the Second Songhua River.The BFI alone in the river showed an increase from the upstream to the downstream.The proportion of baseflow to total flow showed a decrease with time.The intra-annual variability of BFI was different at different locations of the river due to varying climatic conditions and subsurface characteristics.The highest BFI was observed at the middle reaches of the river in summer due to a water surplus from power generation.The research provided valuable information on baseflow characteristics and runoff mode determination,which can be used for water resources assessment and optimization of economic activity distribution in the region.

A New Approach to State Estimation for Uncertain Linear Systems in a Moving Horizon Estimation Setting

This paper addresses the state estimation problem for linear systems with additive uncertainties in both the state and output equations using a moving horizon approach. Based on the full information estimation setting and the game-theoretic approach to the H∞filtering, a new optimization-based estimation scheme for uncertain linear systems is proposed, namely the H∞-full information estimator, H∞-FIE in short. In this formulation, the set of processed data grows with time as more measurements are received preventing recursive formulations as in Kalman filtering. To overcome the latter problem, a moving horizon approximation to the H∞-FIE is also presented, the H∞-MHE in short. This moving horizon approximation is achieved since the arrival cost is suitably defined for the proposed scheme. Sufficient conditions for the stability of the H∞-MHE are derived. Simulation results show the benefits of the proposed scheme when compared with two H∞filters and the well-known Kalman filter.