Time-varying State Space Model Research Articles

Experience-dependent modulation of collective behavior in larval zebrafish.

Complex group behavior can emerge from simple inter-individual interactions. Commonly, these interactions are considered static and hardwired and little is known about how experience and learning affect collective group behavior. Young larvae use well described visuomotor transformations to guide interindividual interactions and collective group structure. Here, we use naturalistic and virtual-reality (VR) experiments to impose persistent changes in population density and measure their effects on future visually evoked turning behavior and the resulting changes in group structure. We find that neighbor distances decrease after exposure to higher population densities, and increase after the experience of lower densities. These adaptations develop slowly and gradually, over tens of minutes and remain stable over many hours. Mechanistically, we find that larvae estimate their current group density by tracking the frequency of neighbor-evoked looming events on the retina and couple the strength of their future interactions to that estimate. A time-varying state-space model that modulates agents' social interactions based on their previous visual-social experiences, accurately describes our behavioral observations and predicts novel aspects of behavior. These findings provide concrete evidence that inter-individual interactions are not static, but rather continuously evolve based on past experience and current environmental demands. The underlying neurobiological mechanisms of experience dependent modulation can now be explored in this small and transparent model organism.

Real-time estimation of fuel injection rate and injection volume in high-pressure common rail systems

The injection rate and injection volume are essential parameters for the combustion process, which greatly affect the engine efficiency and emission performance. However, at the current time the injection information cannot be obtained in real time during the actual operation of engine. This paper presents a novel real-time estimation method for the injection rate and injection volume based on the measurable rail pressure. A comprehensive dynamic model is derived by considering both the effect of fuel injection and supply process on the pressure fluctuation. Then a linear time-varying state space model is constructed by choosing three appropriate state variables. On this basis, considering the measurement noise and model uncertainty, a Kalman filter-based estimation method of the injection information is investigated. And the noise covariance matrix Q is optimally designed to adapt to a wide range of operating conditions. The proposed estimation method is validated on the different conditions, and the results show the injection rate estimation errors are within 4.5 %, the injection volume estimation errors are within 4 %. And on the situation with overlap of injection and supply process, the injection rate and injection volume estimation errors are all within 4.5 %.

Dynamic Short Circuit Ratio for Stability Assessment of Grid Connected VSC-HVDC Systems Considering the Impact of Time-Varying Phase Shift

As more renewable resources are integrated into the receiving-end AC grid through VSC-HVDC, the grid connected VSC-HVDC system is facing a critical dynamic stability issue involving multiple-frequency oscillatory behaviors, which mainly stems from the low-system-strength and the time-varying phase shift. This paper proposes a general stability analysis method to measure the dynamic stability of grid connected VSC-HVDC system from the point of view of input to state stability (ISS). A nonlinear time-varying discrete-time state space model (NTDS <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> M) of the grid connected VSC-HVDC system is built considering the impact of the time-varying phase shift. Then, the NTDS <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> M is decomposed into several interconnected subsystems. The general asymptotic gain matrix (GAGM), whose elements are derived from the proposed dissipative-form sum-type inequalities (DSIs), is constructed to quantify the interactions between multiple subsystems. Finally, a general dynamic stability analysis index, called dynamic short circuit ratio (DSCR), is proposed to effectively explain the critical dynamic instability point of the grid connected VSC-HVDC system, based on the spectral radius property of the GAGM. Moreover, the real-time simulations and multiple comparative studies are implemented in this paper to verify the effectiveness of the proposed NTDS <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> M and stability analysis method by using RT-LAB platform.

Noise Covariances Identification by MDM: Weighting, Recursion, and Implementation

The problem of noise covariance matrix identification of stochastic linear time-varying state-space models is addressed. The measurement difference method (MDM) is generalized to time-varying dimensions of the measurement and control. Three MDM identification techniques that differ in weighting used in the underlying least squares method are proposed. The techniques differ in estimate quality and computational complexity. In addition, recursive forms are designed for two techniques. The performance of the proposed techniques is analyzed using two numerical examples. The implementation of techniques is enclosed with the paper.

Bootstrapping State-Space Models: Distribution-Free Estimation in View of Prediction and Forecasting

Linear models, seasonal autoregressive integrated moving average (SARIMA) models, and state-space models have been widely adopted to model and forecast economic data. While modeling using linear models and SARIMA models is well established in the literature, modeling using state-space models has been extended with the proposal of alternative estimation methods to the maximum likelihood. However, maximum likelihood estimation assumes, as a rule, that the errors are normal. This paper suggests implementing the bootstrap methodology, utilizing the model’s innovation representation, to derive distribution-free estimates—both point and interval—of the parameters in the time-varying state-space model. Additionally, it aims to estimate the standard errors of these parameters through the bootstrap methodology. The simulation study demonstrated that the distribution-free estimation, coupled with the bootstrap methodology, yields point forecasts with a lower mean-squared error, particularly for small time series or when dealing with smaller values of the autoregressive parameter in the state equation of state-space models. In this context, distribution-free estimation with the bootstrap methodology serves as an alternative to maximum likelihood estimation, eliminating the need for distributional assumptions. The application of this methodology to real data showed that it performed well when compared to the usual maximum likelihood estimation and even produced prediction intervals with a similar amplitude for the same level of confidence without any distributional assumptions about the errors.

Economic statistical strategies for the transportation industry based on time-varying parametric state space models

Abstract Under the new situation, the speed of economic development continues to accelerate, and under the influence of the modernization process, the transportation industry is more closely linked with the economy. To promote the sustainable development of the transportation industry, it is necessary to establish a scientific and effective economic statistics strategy to achieve steady economic growth. This paper designs a segmented time-varying parametric state space model based on the state space model to construct an economic statistical system for the transportation industry. By integrating and breaking the original design model, the structure, function, and statistical process of the system are optimized. The system is introduced into the transportation industry to analyze the application effect. According to the data, the economic revenue of the railroad transportation industry reached 464.293 billion yuan at the end of 2021, 45.48 times more than that of 10,208.81 billion yuan in 1986, and the market share increased from 23.23% in 2000 to 31.19% in 2021. The market share of waterway transportation industry, on the other hand, rose from 29.07% in 2000 to 32.87% in 2021. The share of capital investment in waterways and civil aviation continues to change in a downward trend from about 11% in the previous period. The economic statistics strategy can improve the economic efficiency of the transportation industry, so that the whole industry can gradually adapt to the current level of economic development and the needs of people’s life.

A time-varying state-space model for real-time temperature predictions in rack-based cooling data centers

Fast-growing data centers (DCs) require efficient cooling systems (such as rack-based cooling architectures) and control strategies to reduce operating costs and guarantee desired indoor conditions. Thus, this study proposed a novel real-time temperature prediction model for rack-based cooling DCs, in order to facilitate advanced control regarding cooling management and workload assignment. Specifically, a data-driven technology was introduced to estimate time-invariant model parameters, in order to avoid the time-consuming physics-based parameters extracting process. The mass conservation relationships were employed to update time-varying flow parameters in real-time to capture the nonlinear behaviors in DCs. Moreover, the proposed control-oriented thermal modeling method can model hot air recirculation and cold air bypass occurring simultaneously for the first time. The performance of the developed time-varying state-space model was validated by CFD simulation data. Additionally, the timeliness of modeling and temperature prediction was also investigated. The results show that the developed model achieves sufficient accuracy with a mean absolute error (MAE) equal to 0.28 °C, even for long prediction horizons and dynamic IT workloads. Also, the developed model has outstanding timeliness for advanced control techniques, in terms of less than 30 min for parameter identification and less than 10 s for temperature prediction.

Measurement Difference Method: A Universal Tool for Noise Identification

This article deals with noise identification of a system described by the linear time-varying state-space model using correlation methods. In particular, the stress is laid on the measurement difference method (MDM) as a universal tool allowing estimation of moments and parameters of the state and measurement noises. The recent results are summarized in a common framework and the full (and weighted) MDM implementation is developed. This implementation provides unbiased and weakly consistent estimate of an arbitrary raw or central moment of the state and measurement noises. The performance of the method is shown in a numerical study.

Novel Unbiased Optimal Receding-Horizon Fixed-Lag Smoothers for Linear Discrete Time-Varying Systems

This paper proposes novel unbiased minimum-variance receding-horizon fixed-lag (UMVRHF) smoothers in batch and recursive forms for linear discrete time-varying state space models in order to improve the computational efficiency and the estimation performance of receding-horizon fixed-lag (RHF) smoothers. First, an UMVRHF smoother in batch form is proposed by combining independent receding-horizon local estimators for two separated sub-horizons. The local estimates and their error covariance matrices are obtained based on an optimal receding horizon filter and the smoother in terms of the unbiased minimum variance; they are then optimally combined using Millman’s theorem. Next, the recursive form of the proposed UMVRHF smoother is derived to improve its computational efficiency and extendibility. Additionally, we introduce a method for extending the proposed recursive smoothing algorithm to a posteriori state estimations and propose the Rauch–Tung–Striebel receding-horizon fixed-lag smoother in recursive form. Furthermore, a computational complexity reduction technique that periodically switches the two proposed recursive smoothing algorithms is proposed. The performance and effectiveness of the proposed smoothers are demonstrated by comparing their estimation results with those of previous algorithms for Kalman and receding-horizon fixed-lag smoothers via numerical experiments.

Recursive Optimal Finite Impulse Response Filter and Its Application to Adaptive Estimation

In this paper, the recursive form of an optimal finite impulse response filter is proposed for discrete time-varying state-space models. The recursive form of the finite impulse response filter is derived by employing finite horizon Kalman filtering with optimally estimated initial conditions. The horizon initial state and its error covariance on the horizon are optimally estimated by using recent finite measurements, in the sense of maximum likelihood estimation, then initiating the finite horizon Kalman filter. The optimality and unbiasedness of the proposed filter are proved by comparison with the conventional optimal finite impulse response filter in batch form. Moreover, an adaptive FIR filter is also proposed by applying the adaptive estimation scheme to the proposed recursive optimal FIR filter as its application. To evaluate the performance of the proposed algorithms, a computer simulation is performed to compare the conventional Kalman filter and adaptive Kalman filters for the gas turbine aircraft engine model.

Univariate and Multivariate Time Series Modeling using a Harmonic Decomposition Methodology

This paper contributes by developing an univariate and multivariate harmonic decomposition methodology to model time series.The models are stated in a state space representation derived from a Fourier series analysis to describe an arbitrary signal. The frequency values of the harmonic content are used to define state variables in order to describe a signal through a time-varying linear state space model, which serves to synthesize an optimal state observer (Kalman-Bucy filter). Once the observer converges and the states (harmonics) become constant, the observer model can be used to predict the signal, i.e., a time series forecasting can be performed.The preocedure can be developed for the univariate or multivariate case of time series modeling, where in the last one, a statistical analysis is used to determine which variables should be taken into account to obtain a more accurate model. The proposed modeling approach is successfully applied for the modeling and forecast of the time series of electrical power demand and a wind/solar profile.

A Time-Varying State-Space Model for Real-Time Temperature Predictions in Rack-Based Cooling Data Centers

A Time-Varying State-Space Model for Real-Time Temperature Predictions in Rack-Based Cooling Data Centers

DynaNet: Neural Kalman Dynamical Model for Motion Estimation and Prediction.

Dynamical models estimate and predict the temporal evolution of physical systems. State-space models (SSMs) in particular represent the system dynamics with many desirable properties, such as being able to model uncertainty in both the model and measurements, and optimal (in the Bayesian sense) recursive formulations, e.g., the Kalman filter. However, they require significant domain knowledge to derive the parametric form and considerable hand tuning to correctly set all the parameters. Data-driven techniques, e.g., recurrent neural networks, have emerged as compelling alternatives to SSMs with wide success across a number of challenging tasks, in part due to their impressive capability to extract relevant features from rich inputs. They, however, lack interpretability and robustness to unseen conditions. Thus, data-driven models are hard to be applied in safety-critical applications, such as self-driving vehicles. In this work, we present DynaNet, a hybrid deep learning and time-varying SSM, which can be trained end-to-end. Our neural Kalman dynamical model allows us to exploit the relative merits of both SSM and deep neural networks. We demonstrate its effectiveness in the estimation and prediction on a number of physically challenging tasks, including visual odometry, sensor fusion for visual-inertial navigation, and motion prediction. In addition, we show how DynaNet can indicate failures through investigation of properties, such as the rate of innovation (Kalman gain).

Robust state estimation for uncertain linear discrete systems with d‐step state delay

This paper discusses the state estimation problems of an uncertain linear discrete time-varying state space model with d-step state delay. Based on the principle of minimising the expectation of estimation errors and the method of state augmentation, a robust state estimation algorithm is proposed. Specially, this estimator retains the form of Kalman-like filter and the characteristics of fast recursive calculation. Moreover, the conditions of bounded estimation error covariance and the proof of asymptotic unbiasedness of the filter are given. Finally, numerical examples are used to verify the effectiveness and the wide applicability of this estimator.

Analysis of inflation influencing factor system based on M-F model and fuzzy statistical test

When the new model is used to comprehensively study the dynamic influencing factors of inflation, the conclusions drawn can reflect economic conditions more truly, and can provide more practical policy recommendations for macroeconomic management. According to the machine learning algorithm and the current situation of inflation, this paper constructs an analysis model of the factors affecting inflation based on the M-F model. Moreover, by analyzing the linkage relationship between exchange rate and interest rate under the current economic background, based on the M-F-D model of machine learning, this paper conducts an empirical test on the linkage effect of interest rate and exchange rate since my country’s exchange rate reform. In addition, this paper selects 10 macroeconomic indicators related to inflation from the macroeconomic data and uses the time-varying parameter state space model to conduct a comprehensive analysis. The research results show that the model constructed in this paper has a certain effect in the research of inflationary factors.

Dynamic Underwater Acoustic Channel Tracking for Correlated Rapidly Time-Varying Channels

In this work, we focus on the model-mismatch problem for model-based subspace channel tracking in the correlated underwater acoustic channel. A model based on the underwater acoustic channel's correlation can be used as the state-space model in the Kalman filter to improve the underwater acoustic channel tracking compared that without a model. Even though the data support the assumption that the model is slow-varying and uncorrelated to some degree, to improve the tracking performance further, we can not ignore the model-mismatch problem because most channel models encounter this problem in the underwater acoustic channel. Therefore, in this work, we provide a dynamic time-variant state-space model for underwater acoustic channel tracking. This model is tolerant to the slight correlation after decorrelation. Moreover, a forward-backward Kalman filter is combined to further improve the tracking performance. The performance of our proposed algorithm is demonstrated with the same at-sea data as that used for conventional channel tracking. Compared with the conventional algorithms, the proposed algorithm shows significant improvement, especially in rough sea conditions in which the channels are fast-varying.

A Dynamic Analysis of the Optimal Scale of Fiscal Social Security Expenditure in Jilin Province ——Based on Time-varying Parameter State Space Model

A Dynamic Analysis of the Optimal Scale of Fiscal Social Security Expenditure in Jilin Province ——Based on Time-varying Parameter State Space Model

Predictive Coupled Control of the Road Train Longitudinal and Lateral Motion on a Curved Path

In this paper, we consider the problem of a road train path-following on a curved path with an optimal velocity. To solve the problem, we propose a control algorithm based on the coupled model predictive control strategy. Model predictive control assumes the computation of a control sequence by solving an optimal control problem on a finite horizon for a current state of a nonlinear time-varying system. We use the truck steering angle and road train acceleration as control inputs. We describe the road train longitudinal and lateral dynamics using an implicit nonlinear model in continuous time. To derive a discrete linear time-varying state-space prediction model describing the deviations of system dynamics from a reference path we use the Euler method to discretize the original system and compute analytical formulae for its Jacobian by MATLAB Symbolic Math Toolbox. We calculate the reference path and corresponding reference values of the state vector applying the well-known geometric techniques, which utilize the path coordinates and its curvature information. We take the reference values of a truck and a semitrailer yaw angles to be equal. Thus, the reference value of the jackknifing angle is zero. The calculations of reference velocity take into account its skid and rollover limits. To validate the proposed path-following algorithm on the road train we design a simulation model in Simulink. The paper presents the simulation results of testing the movement of a road train along a given path for various values of the reference speed. We show that the algorithm provides high enough reference path-following accuracy, vehicle reference speed tracking, and low values of the jackknifing angle on the speed values up to 18 m/s and curvature radii down to 250 m. The proposed algorithm can be used in ADAS-systems and autonomous vehicles development.

Longitudinal Modelling and Control of In-Wheel-Motor Electric Vehicles as Multi-Agent Systems

This paper deals with longitudinal motion control of electric vehicles (EVs) driven by in-wheel-motors (IWMs). It shows that the IWM-EV is fundamentally a multi-agent system with physical interaction. Three ways to model the IWM-EV are proposed, and each is applicable to certain control objectives. Firstly, a nonlinear model with hierarchical structure is established, and it can be used for passivity-based motion control. Secondly, a linearized model with rank-1 interconnection matrix is presented for stability analysis. Thirdly, a time-varying state-space model is proposed for optimal control using linear quadratic regulator (LQR). The proposed modellings contribute the new understanding of IWM-EV dynamics from the view point of multi-agent-system theory. By choosing the suitable control theory for each model, the complexity level of system design is maintained constant, no matter what the number of IWMs installed to the vehicle body. The effectiveness of three models and their design approaches are discussed by several examples with Matlab/Carsim co-simulator.

An Extended Taylor Rule and its Applicability in China - An Empirical Analysis Based on Time-Varying Parameters State-Space Model

An Extended Taylor Rule and its Applicability in China - An Empirical Analysis Based on Time-Varying Parameters State-Space Model