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.

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.

State Estimation of Drive-by-Wire Chassis Vehicle Based on Dual Unscented Particle Filter Algorithm

Accurate vehicle dynamic information plays an important role in vehicle driving safety.However,due to the characteristics of high mobility and multiple controllable degrees of freedom of drive-by-wire chassis vehicles,the current mature application of traditional vehicle state estimation algorithms can not meet the requirements of drive-by-wire chassis vehicle state estimation.This paper proposes a state estimation method for drive-by-wire chassis vehicle based on the dual unscented particle filter algorithm,which make full use of the known advantages of the four-wheel drive torque and steer angle parameters of the drive-by-wire chassis vehicle.In the dual unscented particle filter algorithm,two unscented particle filter transfer information to each other,observe the vehicle state information and the tire force parameter information of the four wheels respectively,which reduce the influence of parameter uncertainty and model parameter changes on the estimation accuracy during driving.The performance with the dual unscented particle filter algorithm,which is analyzed in terms of the time-average square error,is superior of the unscented Kalman filter algorithm.The effectiveness of the algorithm is further verified by driving simulator test.In this paper,a vehicle state estimator based on dual unscented particle filter algorithm was proposed for the first time to improve the estimation accuracy of vehicle parameters and states.

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.

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.

High Density 3D Carbon Tube Nanoarray Electrode Boosting the Capacitance of Filter Capacitor

Electric double-layer capacitors(EDLCs)with fast frequency response are regarded as small-scale alternatives to the commercial bulky aluminum electrolytic capacitors.Creating carbon-based nanoarray electrodes with precise alignment and smooth ion channels is crucial for enhancing EDLCs’performance.However,controlling the density of macropore-dominated nanoarray electrodes poses challenges in boosting the capacitance of line-filtering EDLCs.Herein,a simple technique to finely adjust the vertical-pore diameter and inter-spacing in three-dimensional nanoporous anodic aluminum oxide(3D-AAO)template is achieved,and 3D compactly arranged carbon tube(3D-CACT)nanoarrays are created as electrodes for symmetrical EDLCs using nanoporous 3D-AAO template-assisted chemical vapor deposition of carbon.The 3D-CACT electrodes demonstrate a high surface area of 253.0 m^(2) g^(−1),a D/G band intensity ratio of 0.94,and a C/O atomic ratio of 8.As a result,the high-density 3D-CT nanoarray-based sandwich-type EDLCs demonstrate a record high specific areal capacitance of 3.23 mF cm^(-2) at 120 Hz and exceptional fast frequency response due to the vertically aligned and highly ordered nanoarray of closely packed CT units.The 3D-CT nanoarray electrode-based EDLCs could serve as line filters in integrated circuits,aiding power system miniaturization.

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. .

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。

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.

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.

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.

3D robust anisotropic diffusion filtering algorithm for sparse view neutron computed tomography 3D image reconstruction

The most critical part of a neutron computed tomography(NCT) system is the image processing algorithm,which directly affects the quality and speed of the reconstructed images.Various types of noise in the system can degrade the quality of the reconstructed images.Therefore,to improve the quality of the reconstructed images of NCT systems,efficient image processing algorithms must be used.The anisotropic diffusion filtering(ADF) algorithm can not only effectively suppress the noise in the projection data,but also preserve the image edge structure information by reducing the diffusion at the image edges.Therefore,we propose the application of the ADF algorithm for NCT image reconstruction.To compare the performance of different algorithms in NCT systems,we reconstructed images using the ordered subset simultaneous algebraic reconstruction technique(OS-SART) algorithm with different regular terms as image processing algorithms.In the iterative reconstruction,we selected two image processing algorithms,the Total Variation and split Bregman solved total variation algorithms,for comparison with the performance of the ADF algorithm.Additionally,the filtered back-projection algorithm was used for comparison with an iterative algorithm.By reconstructing the projection data of the numerical and clock models,we compared and analyzed the effects of each algorithm applied in the NCT system.Based on the reconstruction results,OS-SART-ADF outperformed the other algorithms in terms of denoising,preserving the edge structure,and suppressing artifacts.For example,when the 3D Shepp–Logan was reconstructed at 25 views,the root mean square error of OS-SART-ADF was the smallest among the four iterative algorithms,at only 0.0292.The universal quality index,mean structural similarity,and correlation coefficient of the reconstructed image were the largest among all algorithms,with values of 0.9877,0.9878,and 0.9887,respectively.

CRBFT:A Byzantine Fault-Tolerant Consensus Protocol Based on Collaborative Filtering Recommendation for Blockchains

Blockchain has been widely used in finance,the Internet of Things(IoT),supply chains,and other scenarios as a revolutionary technology.Consensus protocol plays a vital role in blockchain,which helps all participants to maintain the storage state consistently.However,with the improvement of network environment complexity and system scale,blockchain development is limited by the performance,security,and scalability of the consensus protocol.To address this problem,this paper introduces the collaborative filtering mechanism commonly used in the recommendation system into the Practical Byzantine Fault Tolerance(PBFT)and proposes a Byzantine fault-tolerant(BFT)consensus protocol based on collaborative filtering recommendation(CRBFT).Specifically,an improved collaborative filtering recommendation method is designed to use the similarity between a node’s recommendation opinions and those of the recommender as a basis for determining whether to adopt the recommendation opinions.This can amplify the recommendation voice of good nodes,weaken the impact of cunningmalicious nodes on the trust value calculation,andmake the calculated resultsmore accurate.In addition,the nodes are given voting power according to their trust value,and a weight randomelection algorithm is designed and implemented to reduce the risk of attack.The experimental results show that CRBFT can effectively eliminate various malicious nodes and improve the performance of blockchain systems in complex network environments,and the feasibility of CRBFT is also proven by theoretical analysis.

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.

Optimize Purcell filter design for reducing influence of fabrication variation

To protect superconducting qubits and enable rapid readout, optimally designed Purcell filters are essential. To suppress the off-resonant driving of untargeted readout resonators, individual Purcell filters are used for each readout resonator.However, achieving consistent frequency between a readout resonator and a Purcell filter is a significant challenge. A systematic computational analysis is conducted to investigate how fabrication variation affects filter performance, through focusing on the coupling capacitor structure and coplanar waveguide(CPW) transmission line specifications. The results indicate that the T-type enclosing capacitor(EC), which exhibits lower structural sensitivity, is more advantageous for achieving target capacitance than the C-type EC and the interdigital capacitor(IDC). By utilizing a large-sized CPW with the T-type EC structure, fluctuations in the effective coupling strength can be reduced to 10%, given typical micro-nanofabrication variances. The numerical simulations presented in this work minimize the influence of fabrication deviations, thereby significantly improving the reliability of Purcell filter designs.

Accurate method based on data filtering for quantitative multi-element analysis of soils using CF-LIBS

To obtain more stable spectral data for accurate quantitative analysis of multi-element,especially for the large-area in-situ elements detection of soils, we propose a method for a multielement quantitative analysis of soils using calibration-free laser-induced breakdown spectroscopy(CF-LIBS) based on data filtering. In this study, we analyze a standard soil sample doped with two heavy metal elements, Cu and Cd, with a specific focus on the line of Cu I324.75 nm for filtering the experimental data of multiple sample sets. Pre-and post-data filtering,the relative standard deviation for Cu decreased from 30% to 10%, The limits of detection(LOD)values for Cu and Cd decreased by 5% and 4%, respectively. Through CF-LIBS, a quantitative analysis was conducted to determine the relative content of elements in soils. Using Cu as a reference, the concentration of Cd was accurately calculated. The results show that post-data filtering, the average relative error of the Cd decreases from 11% to 5%, indicating the effectiveness of data filtering in improving the accuracy of quantitative analysis. Moreover, the content of Si, Fe and other elements can be accurately calculated using this method. To further correct the calculation, the results for Cd was used to provide a more precise calculation. This approach is of great importance for the large-area in-situ heavy metals and trace elements detection in soil, as well as for rapid and accurate quantitative analysis.

Unknown Environment Measurement Mapping by Unmanned Aerial Vehicle Using Kalman Filter-Based Low-Cost Estimated Parallel 8-Beam LIDAR

The measurement and mapping of objects in the outer environment have traditionally been conducted using ground-based monitoring systems,as well as satellites.More recently,unmanned aerial vehicles have also been employed for this purpose.The accurate detection and mapping of a target such as buildings,trees,and terrains are of utmost importance in various applications of unmanned aerial vehicles(UAVs),including search and rescue operations,object transportation,object detection,inspection tasks,and mapping activities.However,the rapid measurement and mapping of the object are not currently achievable due to factors such as the object’s size,the intricate nature of the sites,and the complexity of mapping algorithms.The present system introduces a costeffective solution for measurement and mapping by utilizing a small unmanned aerial vehicle(UAV)equipped with an 8-beam Light Detection and Ranging(LiDAR)system.This approach offers advantages over traditional methods that rely on expensive cameras and complex algorithm-based approaches.The reflective properties of laser beams have also been investigated.The system provides prompt results in comparison to traditional camerabased surveillance,with minimal latency and the need for complex algorithms.The Kalman estimation method demonstrates improved performance in the presence of noise.The measurement and mapping of external objects have been successfully conducted at varying distances,utilizing different resolutions.

Optimized online filter stack spectrometer for ultrashort X-ray pulses

Currently,with the advent of high-repetition-rate laser-plasma experiments,the demand for online diagnosis for the X-ray spectrum is increasing because the laser-plasma-generated X-ray spectrum is very important for characterizing electron dynamics and applications.In this study,scintillators and silicon PIN(P-type–intrinsic-N-type semiconductor)diodes were used to construct a wideband online filter stack spectrometer.The X-ray sensor and filter arrangement was optimized using a genetic algorithm to minimize the condition number of the response matrix.Consequently,the unfolding error was significantly reduced based on numerical experiments.The detector responses were quantitatively calibrated by irradiating the scintillator and PIN diode with various nuclides and comparing the measuredγ-ray peaks.A prototype 15-channel spectrometer was developed by integrating an X-ray detector with front-and back-end electronics.The prototype spectrometer could record X-ray pulse signals at a repetition rate of 1 kHz.Furthermore,an optimized spectrometer was employed to record the real-time spectra of laser-driven bremsstrahlung sources.This optimized spectrometer offers a compact solution for spectrum diagnostics of ultrashort X-ray pulses,exhibiting improved accuracy in terms of spectrum measurements and repetition rates,and could be widely used in next-generation high-repetition-rate high-power laser facilities.