State-space Model Research Articles

Modelling and Forecasting of Exchange Rate Pairs Using the Kalman Filter

ABSTRACTDeveloping and employing practically useful and easy to calibrate models for prediction of exchange rates remains a challenging task, especially for highly volatile emerging market currencies. In this paper, we propose a novel approach for joint prediction of correlated exchange rates for two different currencies with respect to the same base currency. For this purpose, we reformulate a generalized version of a bivariate ARMA model into a state space model and use the Kalman filter for estimation and forecasting of the underlying exchange rates as latent variables. With extensive numerical experiments spanning 18 different exchange rates (across both emerging markets, developing and developed economies), we demonstrate that our approach consistently outperforms univariate ARMA models as well as the random walk model in short term out‐of‐sample prediction for various exchange rate pairs. Our study fills a gap in the empirical finance literature in terms of robust, explainable, accurate, and easy to calibrate models for forecasting correlated exchange rates. The proposed methodology has applications in exchange rate risk management as well as pricing of financial derivatives based on two exchange rates.

SGFM: Conditional Flow Matching for Time Series Anomaly Detection With State Space Models

SGFM: Conditional Flow Matching for Time Series Anomaly Detection With State Space Models

Mathematical Techniques in the Design of Robust Control Systems

Solid control frameworks are exceptionally imperative for making beyond any doubt that energetic frameworks remain steady and work well in a parcel of diverse circumstances and with a parcel of questions. This diagram tells you everything you wish to know about the numerical strategies utilized to form steady control systems. Strong control tries to bargain with issues like unknowns within the system model, stuns from the exterior, and changes within the system's parameters. It does this to form beyond any doubt that the framework keeps working well and remaining steady in spite of these issues. Lyapunov soundness hypothesis and the H-infinity (H∞) optimization strategy are two of the foremost critical arithmetic apparatuses. Lyapunov steadiness hypothesis gives us a way to see at how steady a framework is, and H∞ minimizes the worst-case pick up from unsettling influence to yield. State-space representations are moreover utilized to show and ponder multi-input multi-output (MIMO) frameworks, which makes control plan more organized. When making controls that guarantee steady execution, strategies like Direct Framework Disparities (LMIs) and Riccati conditions are utilized. The thought of unwavering quality limits is additionally displayed to degree how well the framework can handle factors. The solid control plan incorporates frequency-domain apparatuses, such as the Nyquist and Bode plots, to see at how the framework acts at distinctive frequencies. This makes it simpler to form controllers that can bargain with high-frequency occasions. We conversation around progressed strategies like α-synthesis and strong shaft situation that can offer assistance with certain control problems in dubious settings. Down to earth illustrations appear how these scientific strategies can be used, showing how vital they are in numerous building areas, such as the airplane, vehicle, and prepare control industries. The unique emphasizes how imperative these numerical strategies are for making beyond any doubt that solid control frameworks can handle the challenges of the genuine world, which improves system security, execution, and steadfastness in a wide run of circumstances. The abstract's objective with this outline is to provide you a basic idea of the math that's critical to the field of solid control framework plan.

Nonlinear model predictive controller of hydrogenation of dimethyl oxalate for ethylene glycol production

Abstract Ethylene glycol (EG) is a valuable commodity organic intermediate that is produced using the catalyzed gas-phase hydrogenation process of dimethyl oxalate (DMO) from syngas. The reactor process is challenging to control because of its nonlinearity and multivariable condition. Thus, this study proposes the application of Neural Wiener model predictive control (NWMPC) for DMO hydrogenation reactor control. The application of empirical-based MPC, such as NWMPC, is still new in DMO hydrogenation reactor control. In order to simulate the process, the DMO hydrogenation reactor is modeled using Aspen Plus and Aspen Dynamic software. The Neural Wiener (NW) model is developed based on state space and neural network modeling using a Linear-Nonlinear (L-N) identification approach. A validation test is also performed to verify the accuracy of the NW model. Based on the test, the model accuracy is acceptable with the coefficient of determination (R2) of 0.965 for EG output mole fraction (first output) and R2 of 0.936 for product temperature (second output). The NWMPC capability is evaluated with a PID controller to handle a setpoint change in EG output mole fraction and reject disturbance in the feed stream flow rate. The control performance results have demonstrated the superior ability of the NWMPC to handle such scenarios better than PID in terms of controller action speed and profile.

Efficient Prediction of Judicial Case Decisions Based on State Space Modeling

Efficient Prediction of Judicial Case Decisions Based on State Space Modeling

A robust and efficient cubature Kalman filter based on the variational Bayesian method and its application in target tracking

Abstract In this paper, we propose a robust cubature Kalman filter (CKF) for nonlinear state-space models with unknown state and measurement noise covariance matrix. We study situations in which sensors are independent of each other. Therefore, the unknown measurement noise variance is modeled as an unknown inverse gamma (IG) distribution. The Gaussian-Student-t-inverse-Wishart (GSTIW) mixture distribution is used to model the one-step prediction distribution. Modeling generates numerous unknown parameters. Therefore, we adopt the statistical linearization method to linearize the observation function and then estimate the state and parameters separately to reduce the computational burden of estimating unknown parameters, significantly improving the algorithm’s efficiency. Finally, using the variational Bayesian method, a novel and efficient robust CKF based on the IG distribution and GSTIW mixture distributions (IG-GSTIW-CKF) is obtained. Simulation and experimental results show that the proposed method has better estimation accuracy than several advanced algorithms when sensors are independent. In addition, the efficiency of the proposed algorithm is significantly higher than that of other CKF-based methods.

SSDSNet: A Dual-Stream State-Space Network for Efficient Image Denoising with Long-Range Dependency Modeling

Abstract In recent years, significant progress has been made in image denoising, driven by advancements in modern deep neural networks such as Convolutional Neural Networks
(CNNs) and Transformers. However, existing denoising models often face limitations due to inherent local inductive biases or the quadratic computational complexity of their architectures. Recently, Selective Structured State Space Models, exemplified by Mamba, have shown considerable potential in modeling long-range dependencies with linear complexity. Despite this promise, their application in low-level computer vision tasks remains underexplored. In this study, we introduce a straightforward yet effective model, the Dual-Stream State-Space Module (DSSM), specifically designed for image denoising. The DSSM serves as the core component of our model, combining convolutional operations with the
Mamba model to enhance the capability of capturing both local features and global context.
This dual-stream approach leverages the inherent structure of local image patches while effectively modeling long-range dependencies, resulting in feature representations tailored for denoising tasks. Extensive experiments demonstrate the effectiveness of our method. For instance, on the SIDD dataset, our model achieves performance on par with state-of-the-art methods, maintaining a global receptive field while operating with similar computational costs.

Model Predictive Control for Three-Phase, Four-Leg Dynamic Voltage Restorer

Dynamic voltage restores (DVRs) are usually used to mitigate the effect of voltage sag and guarantee sufficient power supply for sensitive loads. However, three-phase voltage cannot be compensated to the desired balance voltage under unbalanced three-phase loads by traditional DVRs with a three-phase, three-leg inverter. To address this problem, a three-phase, four-leg inverter-based DVR is first introduced in this paper, and then the state space model in its continuous form and discrete form are established, respectively. A two-step predictive method is proposed for the prediction of the output voltage in each switching state by the established voltage prediction model. Finite-control-set model predictive control (MPC) is developed to be used in the three-phase, four-leg inverter-based DVR. Its dynamic response is effectively improved by the proposed MPC method under various voltage sag conditions. The proposed DVR control strategy is validated via MATLAB/Simulink-R2022b simulations, which demonstrate its effectiveness in voltage compensation under various sag conditions.

SFFNet: Shallow Feature Fusion Network Based on Detection Framework for Infrared Small Target Detection

Infrared small target detection (IRSTD) is the process of recognizing and distinguishing small targets from infrared images that are obstructed by crowded backgrounds. This technique is used in various areas, including ground monitoring, flight navigation, and so on. However, due to complex backgrounds and the loss of information in deep networks, infrared small target detection remains a difficult undertaking. To solve the above problems, we present a shallow feature fusion network (SFFNet) based on detection framework. Specifically, we design the shallow-layer-guided feature enhancement (SLGFE) module, which guides multi-scale feature fusion with shallow layer information, effectively mitigating the loss of information in deep networks. Then, we design the visual-Mamba-based global information extension (VMamba-GIE) module, which leverages a multi-branch structure combining the capability of convolutional layers to extract features in local space with the advantages of state space models in the exploration of long-distance information. The design significantly extends the network’s capacity to acquire global contextual information, enhancing its capability to handle complex backgrounds. And through the effective fusion of the SLGFE and VMamba-GIE modules, the exorbitant computation brought by the SLGFE module is substantially reduced. The experimental results on two publicly available infrared small target datasets demonstrate that the SFFNet surpasses other state-of-the-art algorithms.

Optimizing inverted pendulum control: Integrating neural network adaptability

This study explores the implementation and efficacy of a neural network controller for an inverted pendulum system, contrasting it with traditional state feedback control. Initially, state feedback control exhibited limitations in managing complex system dynamics. Subsequently, a neural network controller was developed, trained using datasets from both uncontrolled and refined state space models. The refined model yielded lower training loss and superior control performance. This research demonstrates the neural network controllers enhanced adaptability and precision, offering significant improvements over traditional methods in controlling dynamic systems like inverted pendulums.

Multi-timescale modeling and order reduction towards stability analysis of isolated microgrids

Microgrids incorporate a significant proportion of renewable energy sources and power electronic converters in the energy conversion process, creating a sustainable and clean energy infrastructure. However, the multi-timescale dynamics of microgrids are interactively coupled under a nonlinear structure, which makes it difficult to gain insight into the instability mechanisms without a high-fidelity reduced-order model that preserves the main dynamic behaviors of the system. For the isolated AC microgrid dominated by voltage source inverters (VSI), a detailed state-space model of the system, including the inverter, network, and load, is first developed. Based on this model, the eigenvalue analysis is carried out, and a participation factor analysis tool is also utilized to identify the relevant dynamics that have a strong impact on the system's dominant mode. Furthermore, to simplify the system modeling process without losing essential dynamic interactions, a novel multi-timescale coupled reduced-order model is proposed using a transfer function-based order reduction method, which retains the open-loop gain characteristics to preserve the critical couplings between fast inner loop dynamics and slow droop control dynamics. Finally, the accuracy of the reduced-order model is verified by comparing it with the detailed model and the conventional singular perturbation reduced-order model through eigenvalue distribution and time-domain simulation analysis.

DUALITY: DETECTABILITY VERSUS STABILIZABILITY IN THE STOCHASTIC CONTEXT

The aim of this paper is to extend to the stochastic framework the well known duality relation between the detectability property and the stabilizability property of a finite dimensional, linear time invariant, deterministic system. We consider continuous time linear stochastic systems having the state space representation described by a system of Itˆo differential equations with periodic coefficients possibly subject to some stochastic perturbations modeled by a standard homogeneous Markov process with a finite number of states. It will be seen that in the case when the given system is affected by jump Markov perturba tions a state space representation of the dual triple may be rigorously defined if and only if the transition probability matrix of the Markov process is double stochastic (in the sense that the sums of all elements from its each row and each column are equal 1).

Local effects of non-pharmaceutical interventions on mitigation of COVID-19 spread through decreased human mobilities in Japan: a prefecture-level mediation analysis

To control the COVID-19 epidemic, the Japanese government and the local governments have repeatedly implemented non-pharmaceutical interventions (NPIs) throughout 2020–2022. Using Bayesian state-space mediation models, we examined the effect of repeated NPIs on infection spread mitigation, mediated by human mobility changes in each prefecture during three epidemic phases: from April 1, 2020 to February 28, 2021; from March 1, 2021 to December 16, 2021; and from December 17, 2021 to December 31, 2022. In the first phase, controlling downtown populations at nighttime was effective in mitigating the infection spread in almost all prefectures. In the second and third phases, the effect was not clear, especially in metropolitan prefectures. Controlling visitors from the central prefectures of metropolitan areas was effective in mitigating infection spread in the surrounding prefectures during all phases. These results suggest that the local spread of infection can be mitigated by focusing on nighttime human mobility control in downtown areas before the epidemic spreads widely and transmission routes become more diverse, and that the geospatial spread of infection can be prevented by controlling the flows of people from large cities to other areas.

An Enhanced State-Space Modeling for Detecting Abnormal Aging in VRLA Batteries

The knowledge of battery aging is an indicator that allows controlling the performance of large battery banks. State of Health (SOH) is typically the metric used, encompassing all possible mechanisms in a percentage indicator, with the Coulomb Counting as the most common method. Hence, an in-depth study of aging based on known models provides proper information for correctly managing batteries. This article proposes an aging-sensitive 3-RC-array-equivalent electrical circuit model to characterize the behavior of batteries throughout their useful life, identifying parametric changes as complementary information to the state of health. This model was validated based on experimental tests with 2 V and 6 Ah VRLA batteries aged according to the manufacturer’s recommended use. The results reveal a proportionality through capacity degradation. Then, a control group of batteries was subjected to overcharge and over-discharge conditions. The information given by Coulomb Counting SOH and the proposed method were evaluated. The proposed method provides additional information to the SOH, enhancing the distinguishing capability between typical aging performance and misused aging performance, resulting in a useful tool capable of identifying the aging associated with parametric changes in a time-invariant system where aging is treated as an imminent multiplicative fault.

Active vibration control for rotating machines with current-controlled electrodynamic actuators and velocity feedback of the machine feet based on a generalized mathematical formulation

AbstractA theoretical analysis regarding active vibration control of rotating machines with current-controlled electrodynamic actuators between machine feet and steel frame foundation and with velocity feedback of the machine feet vibrations is presented. First, a generalized mathematical formulation is derived based on a state-space description which can be used for different kinds of models (1D, 2D, and 3D models). It is shown that under special boundary conditions, the control parameters can be directly implemented into the stiffness and damping matrices of the system. Based on the generalized mathematical formulation, an example of a rotating machine—described by a 2D model—with journal bearings, flexible rotor, current-controlled electrodynamic actuators, steel frame foundation, and velocity feedback of the machine feet vibrations is presented where the effectiveness of the described active vibration control system is demonstrated.

An integrated approach for decomposing time series data into trend, cycle and seasonal components

ABSTRACT This study presents a methodology for decomposing time series data into trend, seasonal, and cyclical components using the moving linear model approach by Kyo and Kitagawa (Journal of Business Cycle Research, 19(3): 373-397, 2023). Our approach integrates seasonal adjustment and decomposition into a single framework. We evaluated our approach with two case studies: examining daily COVID-19 case data and the Index of Industrial Production (IIP) in Japan, comparing the results to seasonally adjusted IIP data. Performance metrics included the discrimination power index and the variance of the adjusted cyclical component. Our findings show that our method effectively extracts business cycle information, achieving higher discrimination power and greater adjusted variance compared to seasonally adjusted IIP data, highlighting the superior performance of our integrated seasonal adjustment method. We compared the proposed approach with a state-space modelling method by introducing an overall stability as a new indicator. The results demonstrated the stability of the estimations obtained with our proposed method.

Pan-Mamba: Effective pan-sharpening with state space model

Pan-sharpening involves integrating information from low-resolution multi-spectral and high-resolution panchromatic images to generate high-resolution multi-spectral counterparts. While recent advancements in the state space model, particularly the efficient long-range dependency modeling achieved by Mamba, have revolutionized computer vision community, its untapped potential in pan-sharpening motivates our exploration. Our contribution, Pan-Mamba, represents a novel pan-sharpening network that leverages the efficiency of the Mamba model in global information modeling. In Pan-Mamba, we customize two core components: channel swapping Mamba and cross-modal Mamba, strategically designed for efficient cross-modal information exchange and fusion. The former initiates a lightweight cross-modal interaction through the exchange of partial panchromatic and multi-spectral channels, while the latter facilities the information representation capability by exploiting inherent cross-modal relationships. Through extensive experiments across diverse datasets, our proposed approach surpasses state-of-the-art methods, showcasing superior fusion results in pan-sharpening. To the best of our knowledge, this work is the first attempt in exploring the potential of the Mamba model and establishes a new frontier in the pan-sharpening techniques. The source code is available at https://github.com/alexhe101/Pan-Mamba.

Symbolic state-space exploration meets statistical model checking

Efficient reachability analysis, as well as statistical model checking have been proposed for the evaluation of Hybrid Petri nets with general transitions (HPnGs). Both have different (dis-)advantages. The performance of statistical simulation suffers in large models and the number of required simulation runs to achieve a relatively small confidence interval increases considerably. The approach introduced for analytical reachability analysis of HPnGs, however, becomes infeasible for a large number of random variables. To overcome these limitations, this paper applies statistical model checking (SMC) for a stochastic variant of the Signal Temporal Logic (STL) to a pre-computed symbolic state-space representation of HPnGs, i.e., the Parametric Location Tree (PLT), which has previously been used for model checking HPnGs. Furthermore, we define how to reduce the PLT for a given state-based and path-based STL property, by introducing a three-valued interpretation of a given STL property for every location of the PLT. This paper applies learning in the presence of nondeterminism and considers four different scheduler classes. The proposed improvement is especially useful if a large number of training runs is necessary to optimize the probability that a given STL property holds. A case study on a water tank model shows the feasibility of the approach, as well as improved computation times, when applying the above-mentioned reduction for varying time bounds. We validate our results with existing analytical and simulation tools, as applicable for different types of schedulers.

A Dynare toolbox for social learning expectations

Social learning (SL) is a behavioral model in which expectations and the resulting aggregate dynamics stem from the interactions of a large number of heterogeneous agents. Nonetheless, this framework has so far lacked a parsimonious development with a general-solution method. This paper bridges this gap and introduces a Dynare toolbox to solve any linear state-space model with SL expectations, opening up a wide range of potential applications. As an illustration, optimal monetary policy rules are studied in a microfounded New Keynesian (NK) model under SL and rational expectations (RE).

ACMamba: A State Space Model-Based Approach for Multi-Weather Degraded Image Restoration

In computer vision, eliminating the effects of adverse weather conditions such as rain, snow, and fog on images is a key research challenge. Existing studies primarily focus on image restoration for single weather types, while methods addressing image restoration under multiple combined weather conditions remain relatively scarce. Furthermore, current mainstream restoration networks, mostly based on Transformer and CNN architectures, struggle to achieve an effective balance between global receptive field and computational efficiency, limiting their performance in practical applications. This study proposes ACMamba, an end-to-end lightweight network based on selective state space models, aimed at achieving image restoration under multiple weather conditions using a unified set of parameters. Specifically, we design a novel Visual State Space Module (VSSM) and a Spatially Aware Feed-Forward Network (SAFN), which organically combine the local feature extraction capabilities of convolutions with the long-range dependency modeling capabilities of selective state space models (SSMs). This combination significantly improves computational efficiency while maintaining a global receptive field, enabling effective application of the Mamba architecture to multi-weather image restoration tasks. Comprehensive experiments demonstrate that our proposed approach significantly outperforms existing methods for both specific and multi-weather tasks across multiple benchmark datasets, showcasing its efficient long-range modeling potential in multi-weather image restoration tasks.