Ensemble Filter Research Articles

From Data to Decision: Interpretable Machine Learning for Predicting Flood Susceptibility in Gdańsk, Poland

Flood susceptibility prediction is complex due to the multifaceted interactions among hydrological, meteorological, and urbanisation factors, further exacerbated by climate change. This study addresses these complexities by investigating flood susceptibility in rapidly urbanising regions prone to extreme weather events, focusing on Gdańsk, Poland. Three popular ML techniques, Support Vector Machine (SVM), Random Forest (RF), and Artificial Neural Networks (ANN), were evaluated for handling complex, nonlinear data using a dataset of 265 urban flood episodes. An ensemble filter feature selection (EFFS) approach was introduced to overcome the single-method feature selection limitations, optimising the selection of factors contributing to flood susceptibility. Additionally, the study incorporates explainable artificial intelligence (XAI), namely, the Shapley Additive exPlanations (SHAP) model, to enhance the transparency and interpretability of the modelling results. The models’ performance was evaluated using various statistical measures on a testing dataset. The ANN model demonstrated a superior performance, outperforming the RF and the SVM. SHAP analysis identified rainwater collectors, land surface temperature (LST), digital elevation model (DEM), soil, river buffers, and normalized difference vegetation index (NDVI) as contributors to flood susceptibility, making them more understandable and actionable for stakeholders. The findings highlight the need for tailored flood management strategies, offering a novel approach to urban flood forecasting that emphasises predictive power and model explainability.

Scale-dependent inflation algorithms for ensemble Kalman filters

Abstract Ensemble-based data assimilation methods often suffer sampling errors due to limited ensemble sizes and model errors, which can result in filter divergence. One method to avoid filter divergence is inflation, which inflates ensemble perturbations to increase ensemble spread and account for model errors. The commonly applied inflation methods, including the multiplicative inflation, relax to prior spread (RTPS), and additive inflation, often use a constant inflation parameter. To capture different error growths at different scales, a scale-dependent inflation is proposed here, which applies different inflation magnitudes for variables associated with different scales. Results from the two-scale Lorenz05 model III show that for the ensemble square-root filter (EnSRF) and integrated hybrid ensemble Kalman filter with ensemble mean updated by hybrid background error covariances (IHEnKF-Mean), scale-dependent inflation is superior to constant inflation. Constant inflation overinflates small-scale variables and results in increased small-scale errors, which then propagate to large-scale variables through the coupling between large- and small-scale variables and lead to increased large-scale errors. Scale-dependent inflation applies larger inflation for large-scale variables and imposes no inflation for small-scale variables, since large-scale errors have larger magnitudes than small-scale ones, and small-scale errors grow faster than large-scale ones. But IHEnKF-Ensemble that updates both the ensemble mean and perturbations with hybrid background error covariances is much less sensitive to scale-dependent inflation, compared to EnSRF and IHEnKF-Mean, because updating ensemble perturbations with hybrid background error covariances can play a role similar to the scale-dependent inflation.

Retina Blood Vessels Segmentation and Classification with the Multi-featured Approach.

Segmenting retinal blood vessels poses a significant challenge due to the irregularities inherent in small vessels. The complexity arises from the intricate task of effectively merging features at multiple levels, coupled with potential spatial information loss during successive down-sampling steps. This particularly affects the identification of small and faintly contrasting vessels. To address these challenges, we present a model tailored for automated arterial and venous (A/V) classification, complementing blood vessel segmentation. This paper presents an advanced methodology for segmenting and classifying retinal vessels using a series of sophisticated pre-processing and feature extraction techniques. The ensemble filter approach, incorporating Bilateral and Laplacian edge detectors, enhances image contrast and preserves edges. The proposed algorithm further refines the image by generating an orientation map. During the vessel extraction step, a complete convolution network processes the input image to create a detailed vessel map, enhanced by attention operations that improve modeling perception and resilience. The encoder extracts semantic features, while the Attention Module refines blood vessel depiction, resulting in highly accurate segmentation outcomes. The model was verified using the STARE dataset, which includes 400 images; the DRIVE dataset with 40 images; the HRF dataset with 45 images; and the INSPIRE-AVR dataset containing 40 images. The proposed model demonstrated superior performance across all datasets, achieving an accuracy of 97.5% on the DRIVE dataset, 99.25% on the STARE dataset, 98.33% on the INSPIREAVR dataset, and 98.67% on the HRF dataset. These results highlight the method's effectiveness in accurately segmenting and classifying retinal vessels.

Nonlinear and Non‐Gaussian Ensemble Assimilation of MOPITT CO

AbstractSatellite retrievals of carbon monoxide (CO) are routinely assimilated in atmospheric chemistry models to improve air quality forecasts, produce reanalyzes and to estimate emissions. This study applies the quantile‐conserving ensemble filter framework, a novel assimilation algorithm that can deal with non‐Gaussian and modestly nonlinear distributions. Instead of assuming normal distributions like the Ensemble Adjustments Kalman Filter (EAKF), we now apply a bounded normal rank histogram (BNRH) distribution for the prior. The goal is to efficiently estimate bounded quantities such as CO atmospheric mixing ratios and emission fluxes while maintaining the good performance achieved by the EAKF. We contrast assimilating meteorological and MOPITT (Measurement of Pollution in the Troposphere) observations for May 2018. We evaluate the results with the fourth deployment of the NASA Atmospheric Tomography Mission (ATom‐4) airborne field campaign. We also compare simulations with CO tropospheric columns from the network for the detection of atmospheric composition change and surface in‐situ observations from NOAA carbon cycle greenhouse gases. While the differences remain small, the BNRH approach clearly works better than the EAKF in comparison to all observation data sets.

Innovative framework for accurate and transparent forecasting of energy consumption: A fusion of feature selection and interpretable machine learning

The study presents a novel framework integrating feature selection (FS) and machine learning (ML) techniques to forecast inland national energy consumption (EC) in the United Kingdom across all energy sources. This innovative framework strategically combines three FS approaches with five interpretable ML models using Shapley Additive Explanations (SHAP), with the dual goal of enhancing accuracy and transparency in EC predictions. By meticulously selecting the most pertinent features from diverse features—including meteorological conditions, socioeconomic parameters, and historical consumption patterns of different primary fuels—the proposed framework enhances the robustness of the forecasting model. This is achieved through benchmarking three FS approaches: ensemble filter, wrapper, and a hybrid ensemble filter-wrapper. In addition, we introduce a novel ensemble filter FS, synthesizing outcomes from multiple base FS methods to make well-informed decisions about feature retention. Experimental results underscore the efficacy of integrating both wrapper and ensemble filter-wrapper FS approaches with interpretable ML models, ensuring the forecasting process remains comprehensible and interpretable while utilizing a manageable number of features (four to eight). In addition, experimental results indicate that different feature subsets are usually selected for each combined FS approach and ML model. This study not only demonstrates the framework's capability to provide accurate forecasts but also establishes it as a valuable tool for policymakers and energy analysts.

Data assimilation for combustion ignition delay time simulation using schlieren image velocimetry

This study sought to improve the accuracy of simulating spray penetration and combustion ignition delay by means of data assimilation (DA). The simulations were conducted using the Reynolds-averaged Navier–Stokes (RANS) equations and assimilating the schlieren image data. In DA, an ensemble square root filter (EnSRF) was used to build the statistical model, making the simulation results more accurate without any change in the governing equations. Recognizing that the spray-cone injection angle has a large effect on penetration, we created ensemble members with different injection angles. And we applied the two-component velocity distribution calculated via SIV and updated both velocity and temperature by using a DA statistical model derived from RANS ensemble simulations. The ignition delay time is generally known to vary even under the same experimental conditions because it is influenced by many factors. In this study, we attempted the transient DA-assisted RANS simulation to predict the ignition delay time even when the temporal resolution and accuracy of the observation data ware insufficient. Our trials offer an example of how a combination of techniques can be effectively used to assimilate experimental data obtained under restricted conditions.

Dynamical Gaussian, lognormal, and reverse lognormal maximum‐likelihood ensemble filter

AbstractWe present a non‐Gaussian ensemble data assimilation method based on the maximum‐likelihood ensemble filter, which allows for any combination of Gaussian, lognormal, and reverse lognormal errors in both the background and the observations. The technique is fully nonlinear, does not require a tangent linear model, and uses a Hessian preconditioner to minimise the cost function efficiently in ensemble space. When the Gaussian assumption is relaxed, the results show significant improvements in the analysis skill within two atmospheric toy models, and the performance of data assimilation systems for (semi)bounded variables is expected to improve.

Filtering dynamical systems using observations of statistics.

We consider the problem of filtering dynamical systems, possibly stochastic, using observations of statistics. Thus, the computational task is to estimate a time-evolving density ρ(v,t) given noisy observations of the true density ρ†; this contrasts with the standard filtering problem based on observations of the state v. The task is naturally formulated as an infinite-dimensional filtering problem in the space of densities ρ. However, for the purposes of tractability, we seek algorithms in state space; specifically, we introduce a mean-field state-space model, and using interacting particle system approximations to this model, we propose an ensemble method. We refer to the resulting methodology as the ensemble Fokker-Planck filter (EnFPF). Under certain restrictive assumptions, we show that the EnFPF approximates the Kalman-Bucy filter for the Fokker-Planck equation, which is the exact solution to the infinite-dimensional filtering problem. Furthermore, our numerical experiments show that the methodology is useful beyond this restrictive setting. Specifically, the experiments show that the EnFPF is able to correct ensemble statistics, to accelerate convergence to the invariant density for autonomous systems, and to accelerate convergence to time-dependent invariant densities for non-autonomous systems. We discuss possible applications of the EnFPF to climate ensembles and to turbulence modeling.

Analyzing the Effectiveness of Ensemble Based Analysis in Wireless Sensor Networks

The usefulness of ensemble-based total time series analysis in Wi-Fi sensor networks is examined in this paper. A device to uses an ensemble approach combines multiple strategies to enhance overall predictive performance. This research assesses various tactics using unique metrics, such as robustness and accuracy. It contrasts the effectiveness of traditional time series methods with ensemble-based total fashions. An experimental approach focusing mostly on exceptional Wi-Fi sensor network scenarios is employed to evaluate the overall effectiveness of the suggested methods. Additionally, this study looks into how changes to community features like energy delivery, conversation range, and node density affect how effective the suggested methods are. The study's findings maintain the capacity to create effective Wi-Fi sensor networks with improved predicted overall performance. The usefulness of ensemble-based time collecting and analysis techniques for wireless sensor networks is investigated in this research. This study primarily looks upon function extraction and seasonality discounting of time series records in WSNs. In this analysis, seasonality is discounted using an ensemble median filter, and feature extraction is accomplished by primary component assessment. To assess the performance of the suggested ensemble technique on every simulated and real-world international WSN fact, multiple experiments are carried out. The findings suggest that the ensemble approach can improve the exceptional time-gathering records within WSNs and reduce seasonality. Furthermore, when compared to single-sensor strategies, the ensemble technique further improves the accuracy of the function extraction system. This work demonstrates the applicability of the ensemble approach for the investigation of time collection data in WSNs

Convergence Analysis of Ensemble Filters for Linear Stochastic Systems with Poisson-Sampled Observations

For continuous-time linear stochastic dynamical systems driven by Wiener processes, we consider the problem of designing ensemble filters when the observation process is randomly time-sampled. We propose a continuous-discrete McKean–Vlasov type diffusion process with additive Gaussian noise in observation model, which is used to describe the evolution of the individual particles in the ensemble. These particles are coupled through the empirical covariance and require less computations for implementation than the optimal ones based on solving Riccati differential equations. Using appropriate analysis tools, we show that the empirical mean and the sample covariance of the ensemble filter converges to the mean and covariance of the optimal filter if the mean sampling rate of the observation process satisfies certain bounds and as the number of particles tends to infinity.

Classification of Breast Cancer using Ensemble Filter Feature Selection with Triplet Attention Based Efficient Net Classifier

In medical imaging, the effective detection and classification of Breast Cancer (BC) is a current research important task because of the still existing difficulty to distinguish abnormalities from normal breast tissues due to their subtle appearance and ambiguous margins and distinguish abnormalities from the normal breast. Moreover, BC detection based on an automated detection model is needed, because manual diagnosis faces problems due to cost and shortage of skilled manpower, and also takes a very long time. Using deep learning and ensemble feature selection techniques, in this paper, a novel framework is introduced for classifying BC from histopathology images. The five primary steps of the suggested framework are as follows: 1) to make the largest original dataset and then deep learning model with data augmentation to improve the learning. 2) The best features are selected by an Ensemble Filter Feature selection Method (EFFM) which combines the best feature subsets to produce the final feature subsets. 3) Then the pruned Convolution Neural Network (CNN) model is utilized to extract the optimal features. 4) Finally, the classification is done through the Triplet Attention based Efficient Network (TAENet) classifier. The suggested model produces a 98% accuracy rate after being trained and tested on two different histopathology imaging datasets including images from four different data cohorts. Subsequently, the suggested strategy outperforms the conventional ones since the ensemble filter habitually acquires the best features, and experimental results demonstrate the importance of the proposed approach

Design of multi-ensemble hybrid filtering approach for removal of heart sound from lung auscultations

Successful lung sound extraction from lung auscultations requires precise filters. Lung auscultations include heart and lung sounds. Therefore, the filter design should identify heart sound characteristics. These include periodicity, pitch, frequency, amplitude, etc. Auscultation acquisition sensors are inefficient, so these signals have noise. To get a clean auscultation signal, ambient noise, periodic noise, DC offsets, baseline errors, harmonic noise, etc. must be addressed separately. Data cleaning must maintain a high peak-signal-to-noise ratio without removing desirable signal information. Heart sound patterns are extracted from input auscultations using filter banks on these signals. After heart sound extraction, the output sound sample should only contain lung sounds. Still, heart sound harmonics corrupt output lung sound due to similarities between heart and lung sound patterns. This lowers lung-sound extraction quality and automatic lung-based disease identification efficiency levels. This article proposes a 2-level multi-ensemble filtering model with 43 filters that analyze 15 other parameters to denoise and extract lung sound from lung auscultations to eliminate these drawbacks. Combining LMS, NLMS, and RLS is used for denoising process. For heart sound identification, an ensemble of Savitzky-Golay, FIR equiripple, Butterworth, Chebyshev, Elliptic, and wavelet filters is used. This selective combination of filters improves PSNR by 20% compared to sole filter performance, while signal entropy, crest factor, root mean squared error, kurtosis, etc. also improves for different scenarios.

A Regional multi-Air Pollutant Assimilation System (RAPAS v1.0) for emission estimates: system development and application

Abstract. Top-down atmospheric inversion infers surface–atmosphere fluxes from spatially distributed observations of atmospheric composition in order to quantify anthropogenic and natural emissions. In this study, we developed a Regional multi-Air Pollutant Assimilation System (RAPAS v1.0) based on the Weather Research and Forecasting–Community Multiscale Air Quality (WRF–CMAQ) modeling system model, the three-dimensional variational (3D-Var) algorithm, and the ensemble square root filter (EnSRF) algorithm. This system can simultaneously assimilate hourly in situ CO, SO2, NO2, PM2.5, and PM10 observations to infer gridded emissions of CO, SO2, NOx, primary PM2.5 (PPM2.5), and coarse PM10 (PMC) on a regional scale. In each data assimilation window, we use a “two-step” scheme, in which the emissions are inferred first and then input into the CMAQ model to simulate initial conditions (ICs) of the next window. The posterior emissions are then transferred to the next window as prior emissions, and the original emission inventory is only used in the first window. Additionally, a “super-observation” approach is implemented to decrease the computational costs, observation error correlations, and influence of representative errors. Using this system, we estimated the emissions of CO, SO2, NOx, PPM2.5, and PMC in December and July 2016 over China using nationwide surface observations. The results show that compared to the prior emissions (2016 Multi-resolution Emission Inventory for China – MEIC 2016)), the posterior emissions of CO, SO2, NOx, PPM2.5, and PMC in December 2016 increased by 129 %, 20 %, 5 %, 95 %, and 1045 %, respectively, and the emission uncertainties decreased by 44 %, 45 %, 34 %, 52 %, and 56 %, respectively. With the inverted emissions, the RMSE of simulated concentrations decreased by 40 %–56 %. Sensitivity tests were conducted with different prior emissions, prior uncertainties, and observation errors. The results showed that the two-step scheme employed in RAPAS is robust in estimating emissions using nationwide surface observations over China. This study offers a useful tool for accurately quantifying multi-species anthropogenic emissions at large scales and in near-real time.

Hybrid Assimilation of Snow Cover Improves Land Surface Simulations over Northern China

Abstract Ensemble data assimilation (DA) is an efficient approach to reduce snow simulation errors by combining observation and land surface modeling. However, there is a small spread between ensemble members of simulated snowpack, which typically occurs for a long time with 100% snow cover fraction (SCF) or snow-free conditions. Here, we apply a hybrid DA method, in which direct insertion (DI) is a supplement of the ensemble square root filter (EnSRF), to assimilate the spaceborne SCF into a land surface model, driven by China Meteorological Administration Land Data Assimilation System high-resolution climate forcings over northern China during the snow season in 2021/22. Compared to the open-loop experiment (without SCF assimilation), the root-mean-square error (RMSE) of SCF is reduced by 6% through the original EnSRF and is even lower (by 14%) in the combined DI and EnSRF (EnSRFDI) experiment. The results reveal the ability of both EnSRF and EnSRFDI to improve the SCF estimation over regions where the snow cover is low, while only EnSRFDI is able to efficiently reduce the RMSE over areas with high SCF. Moreover, the SCF assimilation is also observed to improve the snow depth and soil temperature simulations, with the Kling–Gupta efficiency (KGE) increasing at 60% and 56%–70% stations, respectively, particularly under conditions with near-freezing temperature, in which reliable simulations are typically challenging. Our results demonstrate that the EnSRFDI hybrid method can be applied for the assimilation of spaceborne observational snow cover to improve land surface simulations and snow-related operational products. Significance Statement Due to the small spread between the seasonal snowpack of ensemble simulations, ensemble snow cover fraction (SCF) data assimilation (DA) proves to be ineffective. Therefore, we apply a hybrid method that combines the direct insertion (DI) and ensemble square root filter (EnSRF) to assimilate the spaceborne SCF into a land surface model (LSM) driven by high-resolution climate forcings. Our results reveal the applicability of the EnSRFDI to further improve snow cover simulations over regions with high SCF. Furthermore, the DA experiments were validated through a large number of in situ observations from the China Meteorological Administration. The uncertainties of snow depth and soil temperature simulations are also slightly reduced by the SCF DAs, particularly over regions with a poor LSM performance.

An economical assimilation scheme for radar reflectivity in non‐convective region to suppress spurious precipitation

AbstractIncreasing convection information in initial field and weakening spurious convection information are hot topics in numerical weather prediction. How to economically assimilate radar reflectivity in the non‐convective region (NCR) is the focus of this study. This study proposes a new assimilation scheme for the two‐dimensional (2D) composite reflectivity in NCR through the ensemble square‐root filter method. A single‐column observation test and two convective cases are studied to verify the assimilation effect. Three experiments are designed for each test, including a control experiment (Exp_CTL) that only assimilates convective reflectivity and two assimilation experiments that assimilate reflectivity in NCR (one assimilates 3D weak reflectivity [Exp_RF] and the other assimilates 2D composite reflectivity [Exp_CRF]) based on the Exp_CTL. The results of real‐case studies show that the new scheme has two clear advantages. One is that it can save approximately three quarters of the assimilation workload. The other is that the new scheme has the most significant effect on weakening spurious convection and decreasing the false alarm ratios of precipitation and reflectivity.

Dual-Branch Fourier-Mixing Transformer Network for Hyperspectral Target Detection

In recent years, transformers have shown great potential in hyperspectral image processing and have also been gradually applied in hyperspectral target detection (HTD). Nonetheless, applying a typical transformer to HTD remains challenging. The heavy computation burden of the multi-head self-attention (MSA) in transformers limits its efficient HTD, while the limited ability to extract local spectral features can reduce the discrimination of the learned spectral features. To further explore the potential of transformers for HTD, for balance of representation ability and computational efficiency, we propose a dual-branch Fourier-mixing transformer network for hyperspectral target detection (DBFTTD). First, this work explores a dual-branch Fourier-mixing transformer network. The transformer-style network replaces the MSA sublayer in the transformer with a Fourier-mixing sublayer, which shows advantages in improving computational efficiency and learning valuable spectral information effectively for HTD. Second, this work proposes learnable filter ensembles in the Fourier domain that are inspired by ensemble learning to improve detection performance. Third, a simple but efficient dropout strategy is proposed for data augmentation. Sufficient and balanced training samples are constructed for training the dual-branch network, and training samples for balanced learning can further improve detection performance. Experiments on four data sets indicate that our proposed detector is superior to the state-of-the-art detectors.

Simplified Kalman smoother and ensemble Kalman smoother for improving reanalyses

Abstract. The paper presents a simplification of the Kalman smoother that can be run as a post-processing step using only minimal stored information from a Kalman filter analysis, which is intended for use with large model products such as the reanalyses of the Earth system. A simple decay assumption is applied to cross-time error covariances, and we show how the resulting equations relate formally to the fixed-lag Kalman smoother and how they can be solved to give a smoother analysis along with an uncertainty estimate. The method is demonstrated in the Lorenz (1963) idealised system which is applied to both an extended and ensemble Kalman filter and smoother. In each case, the root mean square errors (RMSEs) against the truth, for both assimilated and unassimilated (independent) data, of the new smoother analyses are substantially smaller than for the original filter analyses, while being larger than for the full smoother solution. Up to 70 % (40 %) of the full smoother error reduction, with respect to the extended (ensemble) filters, respectively, is achieved. The uncertainties derived for the new smoother also agree remarkably well with the actual RMSE values throughout the assimilation period. The ability to run this smoother very efficiently as a post-processor should allow it to be useful for really large model reanalysis products and especially for ensemble products that are already being developed by various operational centres.

Improving Vortex Position Accuracy with a New Multiscale Alignment Ensemble Filter

Abstract A multiscale alignment (MSA) ensemble filtering method was introduced by Ying to reduce nonlinear position errors effectively during data assimilation. The MSA method extends the traditional ensemble Kalman filter (EnKF) to update states from large to small scales sequentially, during which it leverages the displacement vectors derived from the large-scale analysis increments to reduce position errors at smaller scales through warping of the model grid. This study stress tests the MSA method in various scenarios using an idealized vortex model. We show that the MSA improves filter performance as number of scales (Ns) increases in the presence of nonlinear position errors. We tuned localization parameters for the cross-scale EnKF updates to find the best performance when assimilating an observation network. To further reduce the scale mismatch between observations and states, a new option called MSA-O is introduced to decompose observations into scale components during assimilation. Cycling DA experiments show that the MSA-O consistently outperforms the traditional EnKF at equal computational cost. A more challenging scenario for the MSA is identified when the large-scale background flow and the small-scale vortex are incoherent in terms of their errors, making the displacement vectors not effective in reducing vortex position errors. Observation availability for the small scales also limits the use of large Ns for the MSA. Potential remedies for these issues are discussed.

A two-stage hybrid biomarker selection method based on ensemble filter and binary differential evolution incorporating binary African vultures optimization

BackgroundIn the field of genomics and personalized medicine, it is a key issue to find biomarkers directly related to the diagnosis of specific diseases from high-throughput gene microarray data. Feature selection technology can discover biomarkers with disease classification information.ResultsWe use support vector machines as classifiers and use the five-fold cross-validation average classification accuracy, recall, precision and F1 score as evaluation metrics to evaluate the identified biomarkers. Experimental results show classification accuracy above 0.93, recall above 0.92, precision above 0.91, and F1 score above 0.94 on eight microarray datasets.MethodThis paper proposes a two-stage hybrid biomarker selection method based on ensemble filter and binary differential evolution incorporating binary African vultures optimization (EF-BDBA), which can effectively reduce the dimension of microarray data and obtain optimal biomarkers. In the first stage, we propose an ensemble filter feature selection method. The method combines an improved fast correlation-based filter algorithm with Fisher score. obviously redundant and irrelevant features can be filtered out to initially reduce the dimensionality of the microarray data. In the second stage, the optimal feature subset is selected using an improved binary differential evolution incorporating an improved binary African vultures optimization algorithm. The African vultures optimization algorithm has excellent global optimization ability. It has not been systematically applied to feature selection problems, especially for gene microarray data. We combine it with a differential evolution algorithm to improve population diversity.ConclusionCompared with traditional feature selection methods and advanced hybrid methods, the proposed method achieves higher classification accuracy and identifies excellent biomarkers while retaining fewer features. The experimental results demonstrate the effectiveness and advancement of our proposed algorithmic model.

A theoretical analysis of one-dimensional discrete generation ensemble Kalman particle filters

Despite the widespread usage of discrete generation Ensemble Kalman particle filtering methodology to solve nonlinear and high dimensional filtering and inverse problems, little is known about their mathematical foundations. As genetic-type particle filters (a.k.a. sequential Monte Carlo), this ensemble-type methodology can also be interpreted as mean-field particle approximations of the Kalman-Bucy filtering equation. In contrast with conventional mean-field type interacting particle methods equipped with a globally Lipschitz interacting drift-type function, Ensemble Kalman filters depend on a nonlinear and quadratic-type interaction function defined in terms of the sample covariance of the particles. Most of the literature in applied mathematics and computer science on these sophisticated interacting particle methods amounts to designing different classes of useable observer-type particle methods. These methods are based on a variety of inconsistent but judicious ensemble auxiliary transformations or include additional inflation/localisationtype algorithmic innovations, in order to avoid the inherent time-degeneracy of an insufficient particle ensemble size when solving a filtering problem with an unstable signal. To the best of our knowledge, the first and the only rigorous mathematical analysis of these sophisticated discrete generation particle filters is developed in the pioneering articles by Le Gland-Monbet-Tran and by Mandel-Cobb-Beezley, which were published in the early 2010s. Nevertheless, besides the fact that these studies prove the asymptotic consistency of the Ensemble Kalman filter, they provide exceedingly pessimistic meanerror estimates that grow exponentially fast with respect to the time horizon, even for linear Gaussian filtering problems with stable one dimensional signals. In the present article we develop a novel self-contained and complete stochastic perturbation analysis of the fluctuations, the stability, and the long-time performance of these discrete generation ensemble Kalman particle filters, including time-uniform and non-asymptotic mean-error estimates that apply to possibly unstable signals. To the best of our knowledge, these are the first results of this type in the literature on discrete generation particle filters, including the class of genetic-type particle filters and discrete generation ensemble Kalman filters. The stochastic Riccati difference equations considered in this work are also of interest in their own right, as a prototype of a new class of stochastic rational difference equation.