Second-order Autoregressive Model Research Articles

Maneuvering extended target tracking method based on transformer network

This research introduces a new approach to address the challenges related to inaccuracies in shape estimation and motion state tracking during the tracking of maneuvering extended targets. The method combines a novel neural network model with a cubature Kalman filter. Initially, the target’s shape variation is represented using a second-order autoregressive model, and Bayesian filtering is employed for target contour estimation in static environments. Subsequently, the kinematic state tracking of maneuvering targets is enhanced by modifying a neural network model based on Transformer architecture. Through the effective integration of these techniques, precise tracking of maneuvering extended targets is achieved, facilitating accurate estimation of irregular contour information while tracking the targets’ motion state in real-time. The efficacy of the proposed approach is further confirmed through various simulation scenarios, underscoring its suitability for tracking maneuvering extended targets.

Multi-IMUs and GNSS integrated positioning based on second-order autoregressive model

Multi-IMUs and GNSS integrated positioning based on second-order autoregressive model

Estimation of Heritability under Correlated Errors Using the Full-Sib Model

In plant and animal breeding, sometimes observations are not independently distributed. There may exist a correlated relationship between the observations. In the presence of highly correlated observations, the classical premise of independence between observations is violated. Plant and animal breeders are particularly interested to study the genetic components for different important traits. In general, for estimating heritability, a random component in the model must adhere to specific assumptions, such as random components, including errors, having a normal distribution, and being identically independently distributed. However, in many real-world situations, all of the assumptions are not fulfilled. In this study, correlated error structures are considered errors that are associated to estimate heritability for the full-sib model. The number of immediately preceding observations in an autoregressive series that are used to predict the value at the current observation is defined as the order of the autoregressive models. First-order and second-order autoregressive models i.e., AR(1) and AR(2) error structures, have been considered. In the case of the full-sib model, theoretical derivation of Expected Mean sum square (EMS) considering AR(1) structure has been obtained. A numerical explanation is provided for the derived EMS considering AR(1) structure. The predicted mean squares error (MSE) is obtained after including the AR(1) error structures in the model, and heritability is estimated using the resulting equations. It is noticed that correlated errors have a major influence on heritability estimation. Different correlation patterns, such as AR(1) and AR(2), can be inferred to change heritability estimates and MSE values. To attain better results, several combinations are offered for various scenarios.

Rice crop growth analysis using Auto Regressive Models

Time series play a vital role in predicting and forecasting different types of agricultural applications with respect to different types of problems among successive units of observations. Time series forecasting techniques are applied in all areas of statistics, and one of the most important applications includes backscatter generating time-series data using advanced forecasting techniques. Agriculture is a major food sector in the world, and it is also a major income source for low-income people. In this paper, we present two aspects of the rice crop growing time series process. The first one is to identify different types of rice crop growing stages for backscatter datasets, and the second is to make a mathematical time series model for the generation of different data sets. The different operator techniques (DOT) method was introduced to identify different types of rice crop growing stages in a season. We proposed the DOT method for identification of different phenological stages for a short-term crop and adopted first and second-order auto-regressive models for prediction and forecasting of the generating backscatter time series observations. The measures of the quality fit are mean absolute percent error (MAPE), mean percent error (MPE), and mean absolute error (MAE).

On Order Selection of Arima Models for Stationary Normal and Non-Normal Data Structures

The study is aimed at identifying the orders of time series models in stationary and non-stationary non-normal data from different distributions; with a view to determining the best Autoregressive/ Moving Average orders from different time series, ARIMA models were considered for different underline distributions of data. The data is generated under normal uniform and exponential distribution using a second-order autoregressive model. Data were generated in two forms, these are, when stationarity is observed and when it is violated. Each case of data simulated is fitted to different models and the values of AIC, BIC, HQIC, and FPE are computed. The effect of different levels of parameters (0.3, 0.6, and -0.3, -0.6) at the sample size of 20, 40, 60, 80, 100, 120, 140, 160, 180, and 200 which we considered to represent moderate and large sample sizes respectively on the simulated data from the stationary normal and non-normal data. We concluded in general that the selections of the order for the models considered in this study are tied more to the underlying distribution of the series in relation to the Stationarity and non-Stationarity of the series as it will lead to the identification of the proper model. Since the selection are almost identical in the stationary and non-stationary from both normal and non-normal data structure but varies with the variation in the distribution of the series. And it was also observed that for the ARIMA models the order stocked to the principle of parsimony i.e. models with lower-order selected at most of the sample sizes considered. The need to develop a methodology for model selection that combines both objective and subjective techniques is strongly recommended.

Improved gray wolf particle filtering and high‐fidelity second‐order autoregressive equivalent modeling for intelligent state of charge prediction of lithium‐ion batteries

The rapid development of new energy vehicles puts forward higher requirements for the lithium-ion batteries model construction, high-efficiency condition monitoring and collaborative estimation. An improved high-fidelity second-order autoregressive model is proposed and constructed, and the autoregressive model is integrated with the second-order equivalent circuit model, which can achieve an accurate and reliable description of the batteries internal dynamic change process. To achieve the accurate expression of the battery's external characteristics and internal state, the forgetting factor is combined with the recursive least square algorithm to improve the parameter identification accuracy and optimality while reducing the space complexity of the algorithm. A novel gray wolf particle filtering algorithm is proposed, which eliminates the particles severe degradation in traditional algorithms and enhances the ability of particles to resist degradation. The algorithm superiority and generalization are verified under complex working conditions. The experimental results show that the accuracy of the high-fidelity second-order autoregressive model can reach 99%, which can well simulate the complex chemical reaction process inside the lithium-ion battery. Experimental simulation is performed under constant current conditions. Compared with the extended Kalman filter, unscented Kalman filter, and particle filter algorithms, the gray wolf particle filter algorithm has reduced the root mean square error by 3.39%, 0.90%, and 2.84%, and the mean absolute error has reduced by 1.95%, 0.51%, and 2.22%. Under dynamic stress test conditions, the root mean square error is reduced by 1.54%, 0.33%, and 0.78%, and the average absolute error is reduced by 1.4%, 0.22%, and 0.76%. In addition, when tested under different environmental conditions, although the improved algorithm has a relatively long running time, the estimation accuracy of the algorithm is greatly improved and the execution efficiency is high. The improved algorithm provides a theoretical basis for the reliability and stability of the onboard operation of lithium-ion batteries. Highlights A novel lithium-ion battery high-fidelity second-order autoregressive equivalent model is proposed. The gray wolf particle filter is employed to improve the observation accuracy. A recursive calculation method is derived by the time-based parameters.

Survey Expectations and Learning

In this paper, we evaluate a model that describes real-time inflation data together with the inflation expectations measured by the Survey of Professional Forecasters (SPF). We work with a second-order autoregressive model in which the agents learn over time the intercept and persistence coefficients based on real-time data. To model the process of revisions in real time data, we allow for news and noise disturbances. In contrast to the usual time-varying parameter vector autoregression, we use non-linear Kalman filter techniques to estimate the time-varying coefficients of the underlying inflation process. We identify systematic changes in the persistence of the inflation process and in the long-run expected inflation rate that are implied by the model. The inflation forecasts implied by the model are then compared with the SPF forecasts. As we cannot reject the hypothesis that the SPF forecasts are produced based on our model, we re-estimate the model using Survey nowcasts and forecasts as additional observables. This augmented model does not change the nature and magnitude of the time variation in the coefficients of the autoregressive model, but it does help to reduce the uncertainty in the estimates. Overall, the estimated time-variation confirms our results on the perceived inflation process present in estimated DSGE models with learning (Slobodyan and Wouters, 2012a, 2012b).

A time-domain approach to the total ozone time series and a test of its predictability within a univariate framework

ABSTRACT The present study reports a univariate predictive model for Total Ozone (TO) concentration derived from Ozone Monitoring Instrument (OMI)/Aura observations. Using the Markovian approach through proper discretization method it has been observed that the second-order Markov Chain can represent the time series of TO Concentration. Considering daily data spanning from 2015 to 2019, consisting of 1593 daily TO concentration data. Identifying second order as the most suitable Markov Chain we have considered a second-order autoregressive model for univariate prediction of the time series. Finally, the prediction of TO concentration available from satellite remote sensing has been assessed statistically for its prediction accuracy. The prediction accuracy has been assessed through Willmott’s Indices and Pearson Correlation Coefficient.

Low-dimensional representations of Ni\xf1o 3.4 evolution and the spring persistence barrier

The El Niño-Southern Oscillation (ENSO) is the dominant mode of climate variability on interannual time scales, and its temporal evolution can be summarized using the Niño 3.4 index. Here we used EOF analysis to construct low-dimensional representations of the 12-month evolution of Niño 3.4 during different times of the year. The leading EOF explains more than 90% of the variance of the Niño 3.4 evolution from June to May, which means that the differences in evolution from one year to another are essentially differences in amplitude. Two EOFs explained 94% or more of the evolution variance for other 12-month periods of the year. The two-dimensional nature of the Niño 3.4 trajectories is a direct expression of the spring persistence barrier since the first EOF describes wintertime ENSO events, and the second EOF describes independent behavior during the antecedent spring. A periodic second-order autoregressive (AR2) model reproduced the observed properties, but a first-order model did not. Niño 3.4 EOFs in ocean-atmosphere coupled model forecasts matched observed EOFs with varying levels of fidelity depending on model and time of year. Forecast models with more accurate climatological covariance also have lower mean-squared error (MSE). Low-dimensional EOF-based statistical corrections reduced forecast MSE.

Resilience in the Decision-Making of an Artificial Autonomous System on the Stock Market

This paper presents the design of a resilience mechanism for supporting investment decision-making processes performed by artificial autonomous systems. In the field of Psychology, resilience is understood as the capacity of people to overcome adversity. Resilience has been determined to be a permanent necessary element for the life of an individual. In addition, different levels of intelligence, analysis capacities, and degrees of autonomy have been progressively incorporated within information systems that are oriented to support decision-making processes, such as those for stock markets. Particularly, the inclusion of affective criteria or variables within decision-making systems represents a promising line of action. However, to the best of our knowledge, there are no proposals that suggest the inclusion of a psychological approach to resilience within an autonomous decision-making system for stock markets. Specifically, the incorporation of a psychological approach to resilience allows the autonomous system to face special difficult investment scenarios (e.g., an economic shock) and prevent the system from achieving a permanent negative performance. Thus, psychological resilience can enable an artificial autonomous system to adapt its decision-making processes according to uncertain investment environments. Our proposal conducts experiments using official data from the Standard & Poor's 500 Index. The results are promising and are based on a second-order autoregressive model. The test results suggest that the use of a resilience mechanism within an artificial autonomous system can contain and recover the affective dimensions of the system when it faces adverse decision scenarios.

Environmental variability and density dependence in the temporal Taylor’s law

Taylor’s law (TL) is an empirical rule describing the approximate relationship between the variance and the mean of population density: log10(variance) ≈ log10(a) + b × log10(mean). Although TL has been verified in various ecological systems, essential questions remain unanswered. Why is TL so widely observed? What mechanisms or processes generate TL? Why do most observed slopes b fall in the limited range 1 <b < 2? Density-dependent movement of individuals among populations has been proposed as a mechanism that leads to TL with slopes 1 <b < 2. We used the Gompertz model (a second-order autoregressive model of the logarithm of population density) to analyze the temporal TL of gray-sided vole populations. Our extensive simulations using various combinations of model parameters for environmental variability and density dependence demonstrated that sustainable populations could obey TL in the absence of density-dependent movement among populations, and identified the parameter combinations that produced slopes 1 <b < 2. When environmental variability was low and density dependence was intermediate, simulated data sets showed higher probabilities for 1 <b < 2, but the probability was not very high. In general, slopes became steeper (b increased) as environmental variability increased and as density dependence coefficients decreased. In the Gompertz model, both environmental variability and density dependence cause population density to vary, and on the logarithmic scale of population density, those effects are symmetric above and below the equilibrium density. However, effects of the variability are higher above the equilibrium density on the natural scale of population density, and thus the mean of population density increases with increasing population variability. Therefore, the temporal TL can be formed when population density is measured in the natural scale. In sustainable populations well described by the Gompertz model, the slope b can be determined by the interplay of environmental variability and density dependence.

Global trends in the awareness of sepsis: insights from search engine data between 2012 and 2017

BackgroundSepsis is an established global health priority with high mortality that can be curtailed through early recognition and intervention; as such, efforts to raise awareness are potentially impactful and increasingly common. We sought to characterize trends in the awareness of sepsis by examining temporal, geographic, and other changes in search engine utilization for sepsis information-seeking online.MethodsUsing time series analyses and mixed descriptive methods, we retrospectively analyzed publicly available global usage data reported by Google Trends (Google, Palo Alto, CA, USA) concerning web searches for the topic of sepsis between 24 June 2012 and 24 June 2017. Google Trends reports aggregated and de-identified usage data for its search products, including interest over time, interest by region, and details concerning the popularity of related queries where applicable. Outlying epochs of search activity were identified using autoregressive integrated moving average modeling with transfer functions. We then identified awareness campaigns and news media coverage that correlated with epochs of significantly heightened search activity.ResultsA second-order autoregressive model with transfer functions was specified following preliminary outlier analysis. Nineteen significant outlying epochs above the modeled baseline were identified in the final analysis that correlated with 14 awareness and news media events. Our model demonstrated that the baseline level of search activity increased in a nonlinear fashion. A recurrent cyclic increase in search volume beginning in 2012 was observed that correlates with World Sepsis Day. Numerous other awareness and media events were correlated with outlying epochs. The average worldwide search volume for sepsis was less than that of influenza, myocardial infarction, and stroke.ConclusionsAnalyzing aggregate search engine utilization data has promise as a mechanism to measure the impact of awareness efforts. Heightened information-seeking about sepsis occurs in close proximity to awareness events and relevant news media coverage. Future work should focus on validating this approach in other contexts and comparing its results to traditional methods of awareness campaign evaluation.

A DC offset removal algorithm based on AR model

ABSTRACTThis work proposes an auto-regressive (AR) model-based algorithm that can eliminate the adverse influence of the exponentially decaying DC offset in the phasor estimation process using discrete Fourier transform (DFT). The proposed algorithm comprises three stages: DFT, AR model implementation, and compensation. First, DFT can eliminate all harmonic components and estimate the phasor of the fundamental frequency component. Second, the AR model is used to calculate the error caused by the exponentially decaying DC offset in the phasor value estimated by DFT. A second-order AR model that uses three successively estimated phasor values is utilized. Finally, the phasor of the fundamental frequency component can be accurately estimated by compensating the error caused by the exponentially decaying DC offset. The performance of the proposed algorithm is evaluated for a-phase to ground fault on a 154 kV 25 km overhead transmission line. Electromagnetic Transients Program is used to generate fault signals...

Dyna

To look human, digital full-body avatars need to have soft-tissue deformations like those of real people. We learn a model of soft-tissue deformations from examples using a high-resolution 4D capture system and a method that accurately registers a template mesh to sequences of 3D scans. Using over 40,000 scans of ten subjects, we learn how soft-tissue motion causes mesh triangles to deform relative to a base 3D body model. Our Dyna model uses a low-dimensional linear subspace to approximate soft-tissue deformation and relates the subspace coefficients to the changing pose of the body. Dyna uses a second-order auto-regressive model that predicts soft-tissue deformations based on previous deformations, the velocity and acceleration of the body, and the angular velocities and accelerations of the limbs. Dyna also models how deformations vary with a person's body mass index (BMI), producing different deformations for people with different shapes. Dyna realistically represents the dynamics of soft tissue for previously unseen subjects and motions. We provide tools for animators to modify the deformations and apply them to new stylized characters.

Modelo compatible de altura dominante - índice de sitio para táscate (Juniperus deppeana Steud.)

El objetivo de este trabajo fue determinar la calidad de estación de táscate (Juniperusdeppeana Steud.), a través del método de índice de sitio, en la región de San Dimas, Durango. La base de datos proviene de 43 análisis troncales de árboles derribados en actividades de aprovechamiento. Los modelos de Chapman-Richards y de Schumacher, mediante los procedimientos de diferencias algebraicas y diferencias algebraicas generalizadas, se probaron para determinar el índice de sitio; además, se modeló la estructura del error con un modelo autorregresivo de segundo orden para corregir la dependencia de errores longitudinales presentes. Los resultados mostraron que el modelo de Chapman-Richards en diferencias algebraicas generalizadas presentó el mejor ajuste de acuerdo con el coeficiente de determinación ajustado (R2 adj = 0.98) y la raíz del cuadrado medio del error (RCME = 0.46 m). La representación gráfica de las curvas de calidad generadas con este modelo, sobrepuestas a las alturas observadas, corroboraron la bondad de ajuste del modelo seleccionado. La ecuación obtenida con la metodología de diferencias algebraicas generalizadas estima directamente la altura dominante y el índice de sitio a cualquier altura y edad de referencia.

Experimental feasibility study of estimation of the normalized central blood pressure waveform from radial photoplethysmogram.

The feasibility of a novel system to reliably estimate the normalized central blood pressure (CBPN) from the radial photoplethysmogram (PPG) is investigated. Right-wrist radial blood pressure and left-wrist PPG were simultaneously recorded in five different days. An industry-standard applanation tonometer was employed for recording radial blood pressure. The CBP waveform was amplitude-normalized to determine CBPN. A total of fifteen second-order autoregressive models with exogenous input were investigated using system identification techniques. Among these 15 models, the model producing the lowest coefficient of variation (CV) of the fitness during the five days was selected as the reference model. Results show that the proposed model is able to faithfully reproduce CBPN (mean fitness = 85.2% ± 2.5%) from the radial PPG for all 15 segments during the five recording days. The low CV value of 3.35% suggests a stable model valid for different recording days.

Adaptive frequency estimation of three-phase power systems

The frequency of a three-phase power system can be estimated by identifying the parameter of a second-order autoregressive (AR2) linear predictive model for the complex-valued αβ signal of the system. Since, in practice, both input and output of the AR2 model are observed with noise, the recursive least-squares (RLS) estimate of the system frequency using this model is biased. We show that the estimation bias can be evaluated and subtracted from the RLS estimate to yield a bias-compensated RLS (BCRLS) estimate if the variance of the noise is known a priori. Moreover, in order to simultaneously compensate for the noise on both input and output of the AR2 model, we utilize the concept of total least-square (TLS) estimation and calculate a recursive TLS (RTLS) estimate of the system frequency by employing the inverse power method. Unlike the BCRLS algorithm, the RTLS algorithm does not require the prior knowledge of the noise variance. We prove mean convergence and asymptotic unbiasedness of the BCRLS and RTLS algorithms. Simulation results show that the RTLS algorithm outperforms the RLS and BCRLS algorithms as well as a recently-proposed widely-linear TLS-based algorithm in estimating the frequency of both balanced and unbalanced three-phase power systems.

Overcompensation and phase effects in a cyclic common vole population: between first and second-order cycles.

Population cycles in voles are often thought to be generated by one-year delayed density dependence on the annual population growth rate. In common voles, however, it has been suggested by Turchin (2003) that some populations exhibit first-order cycles, resulting from strong overcompensation (i.e. carrying capacity overshoots in peak years, with only an effect of the current year abundance on annual growth rates). We focus on a common vole (Microtus arvalis) population from western France that exhibits 3-year cycles. Several overcompensating nonlinear models for populations dynamics are fitted to the data, notably those of Hassell, and Maynard-Smith and Slatkin. Overcompensating direct density dependence (DD) provides a satisfactory description of winter crashes, and one-year delayed density dependence is not responsible for the crashes, thus these are not classical second-order cycles. A phase-driven modulation of direct density dependence maintains a low-phase, explaining why the cycles last three years instead of two. Our analyses suggest that some of this phase dependence can be expressed as one-year delayed DD, but phase dependence provides a better description. Hence, modelling suggests that cycles in this population are first-order cycles with a low phase after peaks, rather than fully second-order cycles. However, based on the popular log-linear second-order autoregressive model, we would conclude only that negative delayed density dependence exists. The additive structure of this model cannot show when delayed DD occurs (here, during lows rather than peaks). Our analyses thus call into question the automated use of second-order log-linear models, and suggests that more attention should be given to non-(log)linear models when studying cyclic populations. From a biological viewpoint, the fast crashes through overcompensation that we found suggest they might be caused by parasites or food rather than predators, though predators might have a role in maintaining the low phase and spatial synchrony.

Northern Hemisphere temperature reconstruction during the last millennium using multiple annual proxies

Previous studies have either exclusively used annual tree-ring data or have combined tree-ring series with other, lower temporal resolution proxy series. Both approaches can lead to sig- nificant uncertainties, as tree-rings may underestimate the amplitude of past temperature varia- tions, and the validity of non-annual records cannot be clearly assessed. In this study, we assembled 45 published Northern Hemisphere (NH) temperature proxy records covering the past millennium, each of which satisfied 3 essential criteria: the series must be of annual resolution, span at least a thousand years, and represent an explicit temperature signal. Suitable climate archives included ice cores, varved lake sediments, tree-rings and speleothems. We reconstructed the average annual land temperature series for the NH over the last millennium by applying 3 different recon- struction techniques: (1) principal components (PC) plus second-order autoregressive model (AR2), (2) composite plus scale (CPS) and (3) regularized errors-in-variables approach (EIV). Our recon- struction is in excellent agreement with 6 climate model simulations (including the first 5 models derived from the fifth phase of the Coupled Model Intercomparison Project (CMIP5) and an earth system model of intermediate complexity (LOVECLIM), showing similar temperatures at multi- decadal timescales; however, all simulations appear to underestimate the temperature during the Medieval Warm Period (MWP). A comparison with other NH reconstructions shows that our results are consistent with earlier studies. These results indicate that well-validated annual proxy series should be used to minimize proxy-based artifacts, and that these proxy series contain sufficient information to reconstruct the low-frequency climate variability over the past millennium.

Antedependence models for nonstationary categorical longitudinal data with ignorable missingness: likelihood‐based inference

Time index-ordered random variables are said to be antedependent (AD) of order (p1 ,p2 , … ,pn ) if the kth variable, conditioned on the pk immediately preceding variables, is independent of all further preceding variables. Inferential methods associated with AD models are well developed for continuous (primarily normal) longitudinal data, but not for categorical longitudinal data. In this article, we develop likelihood-based inferential procedures for unstructured AD models for categorical longitudinal data. Specifically, we derive maximum likelihood estimators (MLEs) of model parameters; penalized likelihood criteria and likelihood ratio tests for determining the order of antedependence; and likelihood ratio tests for homogeneity across groups, time invariance of transition probabilities, and strict stationarity. We give closed-form expressions for MLEs and test statistics, which allow for the possibility of empty cells and monotone missing data, for all cases save strict stationarity. For data with an arbitrary missingness pattern, we derive an efficient restricted expectation-maximization algorithm for obtaining MLEs. We evaluate the performance of the tests by simulation. We apply the methods to longitudinal studies of toenail infection severity (measured on a binary scale) and Alzheimer's disease severity (measured on an ordinal scale). The analysis of the toenail infection severity data reveals interesting nonstationary behavior of the transition probabilities and indicates that an unstructured first-order AD model is superior to stationary and other structured first-order AD models that have previously been fit to these data. The analysis of the Alzheimer's severity data indicates that the antedependence is second order with time-invariant transition probabilities, suggesting the use of a second-order autoregressive cumulative logit model.