Correction of microwave pulse reflection by digital filters in superconducting quantum circuits

Reducing the control error is vital for high-fidelity digital and analog quantum operations.In superconducting circuits,one disagreeable error arises from the reflection of microwave signals due to impedance mismatch in the control chain.Here,we demonstrate a reflection cancelation method when considering that there are two reflection nodes on the control line.We propose to generate the pre-distortion pulse by passing the envelopes of the microwave signal through digital filters,which enables real-time reflection correction when integrated into the field-programmable gate array(FPGA).We achieve a reduction of single-qubit gate infidelity from 0.67%to 0.11%after eliminating microwave reflection.Real-time correction of microwave reflection paves the way for precise control and manipulation of the qubit state and would ultimately enhance the performance of algorithms and simulations executed on quantum processors.

AAK Theorem and a Design of Multidimensional BIBO Stable Filters

Rational approximation theory occupies a significant place in signal processing and systems theory. This research paper proposes an optimal design of BIBO stable multidimensional Infinite Impulse Response filters with a realizable (rational) transfer function thanks to the Adamjan, Arov and Krein (AAK) theorem. It is well known that the one dimensional AAK results give the best approximation of a polynomial as a rational function in the Hankel semi norm. We suppose that the Hankel matrix associated to the transfer function has a finite rank.

Performance Evaluation of Two Series Vertical Flow Filters for Wastewater Treatment: A Case Study of the Prototype Installed at Gaston Berger University, Saint-Louis, Senegal

This paper evaluates the efficacy of two sequential vertical flow filters (VFF), FV1 and FV2, implanted with Typha, in a pilot-scale wastewater treatment system. FV1 comprises three cells (FV1a, FV1b, and FV1c), while FV2 consists of two cells (FV2a and FV2b), each designed to reduce various physicochemical and microbiological pollutants from wastewater. Quantitative analyses show significant reductions in electrical conductivity (from 1331 to 1061 μS/cm), biochemical oxygen demand (BOD5 from 655.6 to 2.3 mg/L), chemical oxygen demand (COD from 1240 to 82.2 mg/L), total nitrogen (from 188 to 37.3 mg/L), and phosphates (from 70.9 to 14.6 mg/L). Notably, FV2 outperforms FV1, particularly in decreasing dissolved salts and BOD5 to remarkably low levels. Microbiological assessments reveal a substantial reduction in fecal coliforms, from an initial concentration of 7.5 log CFU/100mL to 3.7 log CFU/100mL, and a complete elimination of helminth eggs, achieving a 100% reduction rate in FV2. The study highlights the impact of design parameters, such as filter material, media depth, and plant species selection, on treatment outcomes. The findings suggest that the judicious choice of these components is critical for optimizing pollutant removal. For instance, different filtration materials show varying efficacies, with silex plus river gravel in FV1c achieving superior pollutant reduction rates. In conclusion, VFFs emerge as a promising solution for wastewater treatment, underscoring the importance of design optimization to enhance system efficiency. Continuous monitoring and adaptation of treatment practices are imperative to ensure water quality, allowing for safe environmental discharge or water reuse. The research advocates for ongoing improvements in wastewater treatment technologies, considering the environmental challenges of the current era. The study concludes with a call for further research to maximize the effectiveness of VFFs in water management.

Data-Based Filters for Non-Gaussian Dynamic Systems With Unknown Output Noise Covariance

This paper proposes linear and nonlinear filters for a non-Gaussian dynamic system with an unknown nominal covariance of the output noise.The challenge of designing a suitable filter in the presence of an unknown covariance matrix is addressed by focusing on the output data set of the system.Considering that data generated from a Gaussian distribution exhibit ellipsoidal scattering,we first propose the weighted sum of norms(SON)clustering method that prioritizes nearby points,reduces distant point influence,and lowers computational cost.Then,by introducing the weighted maximum likelihood,we propose a semi-definite program(SDP)to detect outliers and reduce their impacts on each cluster.Detecting these weights paves the way to obtain an appropriate covariance of the output noise.Next,two filtering approaches are presented:a cluster-based robust linear filter using the maximum a posterior(MAP)estimation and a clusterbased robust nonlinear filter assuming that output noise distribution stems from some Gaussian noise resources according to the ellipsoidal clusters.At last,simulation results demonstrate the effectiveness of our proposed filtering approaches.

New Insights in the Biodegradability and the Ecotoxicological Effects of Solar Products Containing Mineral and Chemical UV-Filters on Marine Zoo- and Phytoplanktons: An in silico and in vitro Study

Background: Cosmetic formulations, and particularly solar products which contain mineral and chemical UV-filters, are often suspected of causing harmful effects on marine fauna and flora. After the publication of our work in 2019 concerning the ecotoxicological effects of such formulations on corals (Seriatopora hystrix), we here provide some new information about the biodegradability and the ecotoxicological effects of these products on marine zoo- and phytoplankton. Therefore, we choose to realize in silico and in vitro studies of the biodegradability of several solar products but also to evaluate the ecotoxicological effects of these products on one phytoplankton, i.e. Phaeodactylum tricornutum, and one zooplankton, i.e. Acartia tonsa, of a great importance for sea species survival (notably as sources of food). Materials and methods: Two different approaches were used to study the biodegradability of the tested products: One in silico method and an in vitro one. 2 solar products were involved in the in silico study which consisted in the determination of the degradation factor (DF) of each ingredient of the tested formulas in order to finally obtain their estimated biodegradability percentage. Already available data concerning each ingredient coupled to a computer model developed with one of our partners were used to achieve this study. The in vitro study involved 8 formulas containing UV-filters and was led by following the OECD 301 F guidelines. Ecotoxicological studies of 7 of the formulas containing UV-filters were for their part realized by following the ISO 10253 guidelines for the experiments led with Phaeodactylum tricornutum, and the ISO 14669 guidelines for the experiments led with Acartia tonsa. In these studies, the effect of each tested product on crustaceans’ mortality and algal growth inhibition was assessed. Results: The in silico study predicted that formulas containing chemical UV-filters display a high biodegradability (superior to the threshold value of 60% given by the OECD 301 F guidelines). In the in vitro part of our work, the 8 tested formulas showed a biodegradability slightly inferior to the one predicted in the in silico experiments. Therefore, in order to evaluate if these calculated biodegradability value could have significant harmful effects on zoo- or phytoplankton, we studied the effect of our products regarding the growth inhibition on Phaeodactylum tricornutum and the mortality on Acartia tonsa. In this last part of the study, all the tested products were classified as “non ecotoxic” following an internal classification based on Part 4 entitled “Environmental Hazards” of Globally Harmonized System of Classification and Labelling of Chemicals (GHS), 9th edition (2021). Conclusions: These results are notably in line with those published by our teams in 2019 on the effects of solar cosmetic products on corals and seem to confirm that formulas containing mineral and chemical UV-filters can be daily used without displaying significant noxious effects on marine fauna and flora. .

Natural products and extracts from plants as natural UV filters for sunscreens:A review

Although solar exposure is necessary for human health,phototoxicology induced by excessive UVB and UVA radiation,which involves sunburns,skin aging and even tu-morigenesis,has been widely researched.Sunscreen is one of the most important ways to protect skin from UV phototoxic damage.As well as inorganic and organic UV filters,some natural products or plant extracts with aromatic rings in their structures,such as flavonoids or polyphenols,can absorb UV to reduce sunburn,acting as a natu-ral UV filter;they also show antioxidant or/and anti-inflammatory activity.This could explain why,although there are no officially approval natural commercial sun-filters,more and more commercial sunscreen products containing plant extracts are avail-able on the market.Here we summarize articles focusing on natural UV filters from plant published in the last 6 years,selecting the most significant data in order to better understand the photoprotective activity of natural products and extracts from plants,including their major constituents and main biological effects,methods for evaluating UV radiation resistance,anti-UV radiation experimental models and anti-UV radiation mechanisms.

一种基于Filter Faster R-CNN的数字PCR液滴检测技术

目的研究液滴数字聚合酶链式反应(ddPCR)液滴检测技术,去除图像中灰尘、气泡、芯片表面的划痕以及微小凹陷等因素产生的异常点对结果的影响,实现高通量、稳定和准确的ddPCR液滴的自动检测。方法提出Filter Faster R-CNN ddPCR液滴检测模型。使用Faster R-CNN生成液滴预测框,之后使用异常点过滤模块(Filter)去除阳性液滴预测框中的异常点。以诺如病毒片段的质粒为模板进行ddPCR实验,建立一个ddPCR数据集,用于模型的训练(2462例,约占78.56%)和测试(672例,约占21.44%)。对异常点过滤模块的3个过滤支路在验证集上进行消融实验,通过与其他ddPCR液滴检测模型进行比较的对比实验以及进行ddPCR的绝对定量实验。结果在少尘和多尘的环境中,Filter Faster R-CNN阳性液滴准确率为98.23%和88.35%,综合指标F1分数分别达到了99.15%和99.14%,高于其他相比较的模型。独立样本T检验的结果证明,相比未添加过滤模块的网络,添加过滤模块后能够显著提示模型在多尘环境中的阳性准确率。在ddPCR绝对定量实验中,将商业化流式检测设备的结果作为标准浓度,绘制了回归线。结果显示,回归线斜率为1.0005,截距为-0.025,决定系数达到了0.9997,二者结果高度一致。结论本文提出了一种基于Filter Faster R-CNN的ddPCR液滴检测技术,为在多种环境条件下的ddPCR实验提供了鲁棒的液滴检测方法。

Underwater four-quadrant dual-beam circumferential scanning laser fuze using nonlinear adaptive backscatter filter based on pauseable SAF-LMS algorithm

The phenomenon of a target echo peak overlapping with the backscattered echo peak significantly undermines the detection range and precision of underwater laser fuzes.To overcome this issue,we propose a four-quadrant dual-beam circumferential scanning laser fuze to distinguish various interference signals and provide more real-time data for the backscatter filtering algorithm.This enhances the algorithm loading capability of the fuze.In order to address the problem of insufficient filtering capacity in existing linear backscatter filtering algorithms,we develop a nonlinear backscattering adaptive filter based on the spline adaptive filter least mean square(SAF-LMS)algorithm.We also designed an algorithm pause module to retain the original trend of the target echo peak,improving the time discrimination accuracy and anti-interference capability of the fuze.Finally,experiments are conducted with varying signal-to-noise ratios of the original underwater target echo signals.The experimental results show that the average signal-to-noise ratio before and after filtering can be improved by more than31 d B,with an increase of up to 76%in extreme detection distance.

Estimating the subsolar magnetopause position from soft X-ray images using a low-pass image filter

The Lunar Environment heliospheric X-ray Imager(LEXI)and Solar wind Magnetosphere Ionosphere Link Explorer(SMILE)missions will image the Earth’s dayside magneto pause and cusps in soft X-rays after their respective launches in the near future,to specify glo bal magnetic reconnection modes for varying solar wind conditions.To suppo rt the success of these scientific missions,it is critical to develop techniques that extract the magnetopause locations from the observed soft X-ray images.In this research,we introduce a new geometric equation that calculates the subsolar magnetopause position(RS)from a satellite position,the look direction of the instrument,and the angle at which the X-ray emission is maximized.Two assumptions are used in this method:(1)The look direction where soft X-ray emissions are maximized lies tangent to the magnetopause,and(2)the magnetopause surface near the subsolar point is almost spherical and thus RSis nea rly equal to the radius of the magneto pause curvature.We create synthetic soft X-ray images by using the Open Geospace General Circulation Model(OpenGGCM)global magnetohydrodynamic model,the galactic background,the instrument point spread function,and Poisson noise.We then apply the fast Fourier transform and Gaussian low-pass filte rs to the synthetic images to re move noise and obtain accurate look angles for the soft X-ray pea ks.From the filte red images,we calculate RS and its accuracy for different LEXI locations,look directions,and solar wind densities by using the OpenGGCM subsolar magnetopause location as ground truth.Our method estimates RS with an accuracy of<0.3 RE when the solar wind density exceeds>10 cm-3.The accuracy improves for greater solar wind densities and during southward interplanetary magnetic fields.The method ca ptures the magnetopause motion during southwa rd interplaneta ry magnetic field turnings.Consequently,the technique will enable quantitative analysis of the magnetopause motion and help reveal the dayside reconnection modes for dynamic solar wind conditions.This technique will suppo rt the LEXI and SMILE missions in achieving their scientific o bjectives.

Magnonic band-pass and band-stop filters with structurally modulated waveguides

Magnonics is a fascinating and emerging field, which mainly studies processing information with spin waves.Magnonic devices with in-plane magnetization have recently been realized. Because of the isotropic propagation, magnonic devices based on perpendicular magnetization are attracting extensive interest. Here, we numerically demonstrate two magnonic filters with out-of-plane magnetization using micromagnetic simulations. The band-pass and the band-stop functions have been realized in two structurally modulated waveguides, respectively. The intensity of spin waves is manipulated when they arrive at the uniformly/non-uniformly magnetized modulators, which results in the variation of transmission coefficients. It is found that the proposed filters can work at multiple frequencies, which can be further adjusted by the external magnetic field. Our designed magnonic devices with Néel-type skyrmion could promote the development of spin wave computing using spin textures.

An improved particle filter indoor fusion positioning approach based on Wi-Fi/PDR/geomagnetic field

The existing indoor fusion positioning methods based on Pedestrian Dead Reckoning(PDR)and geomagnetic technology have the problems of large initial position error,low sensor accuracy,and geomagnetic mismatch.In this study,a novel indoor fusion positioning approach based on the improved particle filter algorithm by geomagnetic iterative matching is proposed,where Wi-Fi,PDR,and geomagnetic signals are integrated to improve indoor positioning performances.One important contribution is that geomagnetic iterative matching is firstly proposed based on the particle filter algorithm.During the positioning process,an iterative window and a constraint window are introduced to limit the particle generation range and the geomagnetic matching range respectively.The position is corrected several times based on geomagnetic iterative matching in the location correction stage when the pedestrian movement is detected,which made up for the shortage of only one time of geomagnetic correction in the existing particle filter algorithm.In addition,this study also proposes a real-time step detection algorithm based on multi-threshold constraints to judge whether pedestrians are moving,which satisfies the real-time requirement of our fusion positioning approach.Through experimental verification,the average positioning accuracy of the proposed approach reaches 1.59 m,which improves 33.2%compared with the existing particle filter fusion positioning algorithms.

Sensor-Based Adaptive Estimation in a Hybrid Environment Employing State Estimator Filters

It is widely acknowledged that navigation is a significant source of between sites.The Global Positioning System(GPS)has numerous navi-gational advancements,and hence it is used widely.GPS navigation can be compromised at any level between position,location,and estimation,to the detriment of the user.Consequently,a navigation system requires the precise location and underpinning tracking of an object without signal loss.The objective of a hybrid environment prediction system is to foresee the location of the user and their territory by employing a variety of sensors for position estimation and monitoring navigation.This article presents a state estimation of the relative position for indoor and outdoor activity solved with a state estimation algorithm utilizing Kalman filter.Also,a comparative study of variants of the Kalman filter,where linearizing current mean and covariance with nonlinear state estimation as an approach of Extended Kalman Filter(EFK)is applied to the collected data.The third comparative aspect uses probability distribution for the selected points with a Sigma Point Kalman Filter(SPKF)for evaluating an accelerometer,gyroscope,and GPS data in hybrid environments for various activities for different data collection scenar-ios from users.The findings of the presented model demonstrate the robust performance of all forms of the Kalman filter algorithm for diverse user-performed activities in totally contaminated indoor and outdoor environ-ments.Experimental findings with various patterns and data,conducted by different subjects using multiple modes of navigation,show that the approach can indeed lead to the intelligent development of sensor-based navigation and monitoring.State estimation and prediction is extraordinarily beneficial for mining applications,autonomous vehicle localization/tracking,and location-based services.This research work demonstrates both EKF-based and SPKF-based sensor fusion to provide an appropriate estimation.

Simulation Model for Passive Harmonic Filters Using Matlab/Simulink: A Case Study

Electrical grid power quality is a global issue. The grid must supply electricity at sinusoidal voltages and currents without frequency or amplitude fluctuations. Harmonics from non-linear loads change the stable reference point voltage waveform and cause other problems. Harmonic reduction is essential for grid health. Electrical and electronic equipment users, manufacturers, and suppliers all contribute. This article presents a case analysis of the plastic processing industry, which has historically struggled with a difficulty related to the fifth harmonic. Unwanted harmonics are reduced by using a single-tuned passive filter, a double-tuned passive filter, and a second-order damped filter. The total harmonic distortion is almost identical, but the second-order damped filter provides the best harmonic mitigation, meeting the requirements of the IEE 519-1992 Standard.

Nonlinear Filtering With Sample-Based Approximation Under Constrained Communication:Progress, Insights and Trends

The nonlinear filtering problem has enduringly been an active research topic in both academia and industry due to its ever-growing theoretical importance and practical significance.The main objective of nonlinear filtering is to infer the states of a nonlinear dynamical system of interest based on the available noisy measurements. In recent years, the advance of network communication technology has not only popularized the networked systems with apparent advantages in terms of installation,cost and maintenance, but also brought about a series of challenges to the design of nonlinear filtering algorithms, among which the communication constraint has been recognized as a dominating concern. In this context, a great number of investigations have been launched towards the networked nonlinear filtering problem with communication constraints, and many samplebased nonlinear filters have been developed to deal with the highly nonlinear and/or non-Gaussian scenarios. The aim of this paper is to provide a timely survey about the recent advances on the sample-based networked nonlinear filtering problem from the perspective of communication constraints. More specifically, we first review three important families of sample-based filtering methods known as the unscented Kalman filter, particle filter,and maximum correntropy filter. Then, the latest developments are surveyed with stress on the topics regarding incomplete/imperfect information, limited resources and cyber security.Finally, several challenges and open problems are highlighted to shed some lights on the possible trends of future research in this realm.

Novel Double-Damped Tuned AC Filters in HVDC Systems

This paper presents a performance analysis of novel doubledampedtuned alternating current (AC) filters in high voltage direct current(HVDC) systems. The proposed double-damped tuned AC filters offer theadvantages of improved performance of HVDC systems in terms of betterpower quality, high power factor, and lower total harmonic distortion (THD).The system under analysis consists of an 878 km long HVDC transmissionline connecting converter stations at Matiari and Lahore, two major cities inPakistan. The main focus of this research is to design a novel AC filter usingthe equivalent impedance method of two single-tuned and double-dampedtuned AC filters. Additionally, the impact of the damping resistor on the ACchannel is examined. TheTHDof theHVDCsystem with and without currentAC filters was also compared in this research and a double-damped tuned ACfilter was proposed. The results of the simulation represent that the proposeddouble-damped tuned AC filter is far smaller in size, offers better powerquality, and has a much lower THD compared to the AC filters currently inplace in the converter station. The simulation analysis was carried out utilizingpower systems computer-aided design (PSCAD) software.

Imaging assessment of photosensitizer emission induced by radionuclide-derived Cherenkov radiation using charge-coupled device optical imaging and long-pass filters

BACKGROUND Radionuclides produce Cherenkov radiation(CR),which can potentially activate photosensitizers(PSs)in phototherapy.Several groups have studied Cherenkov energy transfer to PSs using optical imaging;however,cost-effectively identifying whether PSs are excited by radionuclide-derived CR and detecting fluorescence emission from excited PSs remain a challenge.Many laboratories face the need for expensive dedicated equipment.AIM To cost-effectively confirm whether PSs are excited by radionuclide-derived CR and distinguish fluorescence emission from excited PSs.METHODS The absorbance and fluorescence spectra of PSs were measured using a microplate reader and fluorescence spectrometer to examine the photo-physical properties of PSs.To mitigate the need for expensive dedicated equipment and achieve the aim of the study,we developed a method that utilizes a chargecoupled device optical imaging system and appropriate long-pass filters of different wavelengths(manual sequential application of long-pass filters of 515,580,645,700,750,and 800 nm).Tetrakis(4-carboxyphenyl)porphyrin(TCPP)was utilized as a model PS.Different doses of copper-64(^(64)CuCl_(2))(4,2,and 1 mCi)were used as CR-producing radionuclides.Imaging and data acquisition were performed 0.5 h after sample preparation.Differential image analysis was conducted by using ImageJ software(National Institutes of Health)to visually evaluate TCPP fluorescence.RESULTS The maximum absorbance of TCPP was at 390-430 nm,and the emission peak was at 670 nm.The CR and CRinduced TCPP emissions were observed using the optical imaging system and the high-transmittance long-pass filters described above.The emission spectra of TCPP with a peak in the 645-700 nm window were obtained by calculation and subtraction based on the serial signal intensity(total flux)difference between^(64)CuCl_(2)+TCPP and^(64)CuCl_(2).Moreover,the differential fluorescence images of TCPP were obtained by subtracting the^(64)CuCl_(2)image from the^(64)CuCl_(2)+TCPP image.The experimental results considering different^(64)CuCl_(2)doses showed a dosedependent trend.These results demonstrate that a bioluminescence imaging device coupled with different longpass filters and subtraction image processing can confirm the emission spectra and differential fluorescence images of CR-induced TCPP.CONCLUSION This simple method identifies the PS fluorescence emission generated by radionuclide-derived CR and can contribute to accelerating the development of Cherenkov energy transfer imaging and the discovery of new PSs.

A dual adaptive unscented Kalman filter algorithm for SINS-based integrated navigation system

In this study, the problem of measuring noise pollution distribution by the intertial-based integrated navigation system is effectively suppressed. Based on nonlinear inertial navigation error modeling, a nested dual Kalman filter framework structure is developed. It consists of unscented Kalman filter (UKF)master filter and Kalman filter slave filter. This method uses nonlinear UKF for integrated navigation state estimation. At the same time, the exact noise measurement covariance is estimated by the Kalman filter dependency filter. The algorithm based on dual adaptive UKF (Dual-AUKF) has high accuracy and robustness, especially in the case of measurement information interference. Finally, vehicle-mounted and ship-mounted integrated navigation tests are conducted. Compared with traditional UKF and the Sage-Husa adaptive UKF (SH-AUKF), this method has comparable filtering accuracy and better filtering stability. The effectiveness of the proposed algorithm is verified.

Recursive Filtering for Stochastic Systems With Filter-and-Forward Successive Relays

In this paper,the recursive filtering problem is considered for stochastic systems over filter-and-forward successive relay(FFSR)networks.An FFSR is located between the sensor and the remote filter to forward the measurement.In the successive relay,two cooperative relay nodes are adopted to forward the signals alternatively,thereby existing switching characteristics and inter-relay interferences(IRI).Since the filter-and-forward scheme is employed,the signal received by the relay is retransmitted after it passes through a linear filter.The objective of the paper is to concurrently design optimal recursive filters for FFSR and stochastic systems against switching characteristics and IRI of relays.First,a uniform measurement model is proposed by analyzing the transmission mechanism of FFSR.Then,novel filter structures with switching parameters are constructed for both FFSR and stochastic systems.With the help of the inductive method,filtering error covariances are presented in the form of coupled difference equations.Next,the desired filter gain matrices are further obtained by minimizing the trace of filtering error covariances.Moreover,the stability performance of the filtering algorithm is analyzed where the uniform bound is guaranteed on the filtering error covariance.Finally,the effectiveness of the proposed filtering method over FFSR is verified by a three-order resistance-inductance-capacitance circuit system.

Bayesian Filtering for High-Dimensional State-Space Models With State Partition and Error Compensation

In the era of exponential growth of data availability,the architecture of systems has a trend toward high dimensionality,and directly exploiting holistic information for state inference is not always computationally affordable.This paper proposes a novel Bayesian filtering algorithm that considers algorithmic computational cost and estimation accuracy for high-dimensional linear systems.The high-dimensional state vector is divided into several blocks to save computation resources by avoiding the calculation of error covariance with immense dimensions.After that,two sequential states are estimated simultaneously by introducing an auxiliary variable in the new probability space,mitigating the performance degradation caused by state segmentation.Moreover,the computational cost and error covariance of the proposed algorithm are analyzed analytically to show its distinct features compared with several existing methods.Simulation results illustrate that the proposed Bayesian filtering can maintain a higher estimation accuracy with reasonable computational cost when applied to high-dimensional linear systems.

Dynamic Event-Triggered Quadratic Nonfragile Filtering for Non-Gaussian Systems:Tackling Multiplicative Noises and Missing Measurements

This paper focuses on the quadratic nonfragile filtering problem for linear non-Gaussian systems under multiplicative noises,multiple missing measurements as well as the dynamic event-triggered transmission scheme.The multiple missing measurements are characterized through random variables that obey some given probability distributions,and thresholds of the dynamic event-triggered scheme can be adjusted dynamically via an auxiliary variable.Our attention is concentrated on designing a dynamic event-triggered quadratic nonfragile filter in the well-known minimum-variance sense.To this end,the original system is first augmented by stacking its state/measurement vectors together with second-order Kronecker powers,thus the original design issue is reformulated as that of the augmented system.Subsequently,we analyze statistical properties of augmented noises as well as high-order moments of certain random parameters.With the aid of two well-defined matrix difference equations,we not only obtain upper bounds on filtering error covariances,but also minimize those bounds via carefully designing gain parameters.Finally,an example is presented to explain the effectiveness of this newly established quadratic filtering algorithm.