Littérature scientifique sur le sujet « Skewed Kalman filter »

Abstract The ensemble Kalman filter provides an easy-to-use, flexible, and efficient option for data assimilation problems. One of its attractive features in land surface applications is its ability to provide distributional information about variables, such as soil moisture, that can be highly skewed or even bimodal. The ensemble Kalman filter relies on normality approximations that improve its efficiency but can also compromise the accuracy of its distributional estimates. The effects of these approximations can be evaluated by comparing the conditional marginal distributions and moments estimated by the ensemble Kalman filter with those obtained from a sequential importance resampling (SIR) particle filter, which gives exact solutions for large ensemble sizes. Comparisons for two land surface examples indicate that the ensemble Kalman filter is generally able to reproduce nonnormal soil moisture behavior, including the skewness that occurs when the soil is either very wet or very dry. Its conditional mean estimates are very close to those generated by the SIR filter. Its higher-order conditional moments are somewhat less accurate than the means. Overall, the ensemble Kalman filter appears to provide a good approximation for nonlinear, nonnormal land surface problems, despite its dependence on normality assumptions.

Longitudinal assessments are crucial in evaluating the disease state and trajectory in patients with neurodegenerative diseases. Neuropsychological outcomes measured over time often have a non-linear trajectory with autocorrelated residuals and a skewed distribution. We propose the adjusted local linear trend model, an extended state-space model in lieu of the commonly used linear mixed-effects model in modeling longitudinal neuropsychological outcomes. Our contributed model has the capability to utilize information from the stochasticity of the data while accounting for subject-specific trajectories with the inclusion of covariates and unequally spaced time intervals. The first step of model fitting involves a likelihood maximization step to estimate the unknown variances in the model before parsing these values into the Kalman filter and Kalman smoother recursive algorithms. Results from simulation studies showed that the adjusted local linear trend model is able to attain lower bias, lower standard errors, and high power, particularly in short longitudinal studies with equally spaced time intervals, as compared to the linear mixed-effects model. The adjusted local linear trend model also outperforms the linear mixed-effects model when data is missing completely at random, missing at random, and, in certain cases, even in data with missing not at random.

Travel time reliability plays a key role in bus scheduling and service quality. Owing to various stochastic factors, buses often suffer from traffic congestion, delay and bunching, which leads to disturbances of travel time. Automatic vehicle location (AVL) could record the spatiotemporal information of buses, making it possible to understand the status of bus service. In this paper, we specifically analyze the statistical characteristics of travel time based on historic AVL data. Moreover, a Kalman filter-LSTM deep learning is proposed to estimate bus travel time. Numerical tests indicate that the travel time of bus routes shows a left-skewed and right-tail pattern with a good fit of the lognormal distribution. The bus service reliability fluctuates largely in the peak hours, especially the morning peak. Bus bunching and large bus time headway easily occur, and once it occurs, it will continue until destination. The Kalman filter-LSTM model outperforms the ensemble learning methods to predict travel time. This study could provide implications for transit schedule optimization to improve the bus service quality.

This paper proposes a fast and robust dynamic state estimation technique based on model transformation method using the proposed hybrid technique. The proposed hybrid method is the combination of Unscented Kalman Filter (UKF) and Gradient Boosting Decision Tree (GBDT), hence commonly referred to as the UKF–GBDT technique. The proposed model transformation approach is accomplished by taking the active power generator measured as input variable and derived frequency as rate of change of frequency measurements of phasor measurement units (PMU) as dynamic generator output variable model. The proposed hybrid technique is also formulated to deal with data quality issues, and the rate of change of frequency and frequency measurements may be skewed in the presence of rigorous disruption or communication problems. This permits to obtain discrete-time linear dynamic equations in state space based on the linear Kalman filter (LKF). With this proper control, this model alleviates filter divergence problems, which can be a severe issue if the nonlinear model is utilized in greatly strained operating system conditions, and gives quick estimate of rotor speeds together with angles through transient modes if only the transient stability with control is concerned. In the case of long-term dynamics, the outcome of governor’s response in long-term system dynamics is offset together with mechanical power at rotor speed and the state vector angles for joint evaluation. At last, the performance of the proposed method is simulated in MATLAB/Simulink and the performance is compared to the existing methods like UKF, GBDT and ANN. The proposed technique is simulated under three case studies like IEEE 14-, 30- and 118-bus systems.

This paper deals with the application of SLAM algorithms on experimental four wheel vehicle Car4. The first part shows the basic functioning of SLAM including a description of the extended Kalman filter, which is one of its main components. Then there is a brief list of software tools available to solve this problem in the environment of MATLAB and an overview of sensors used in this work. The second part presents methodology and results of the testing of individual sensors and their combinations to calculate odometry and scan the surrounding space. It also shows the process of applying SLAM algorithms on Car4 vehicle using the selected sensors and the results of testing of the entire system in practice.

Questa tesi riguarda la modellizzazione di serie storiche generate da processi latenti, utilizzando modelli "state-space". Vengono proposti nuovi modelli e metodologie per poi applicarli ad una varietà di casi tipici presenti in finanza ed economia. La tesi è suddivisa in sei capitoli. Il primo capitolo presenta le motivazioni della ricerca, i suoi obiettivi e la presentazione dei contenuti. Il secondo capitolo approfondisce il concetto di modelli "state-space", riporta e discute le procedure di filtraggio più comuni, e chiarisce alcune definizioni, proprietà e concetti matematici che verranno usati nei capitoli successivi. Nel Capitolo 3 viene proposto un nuovo modello "state-space" per tener conto delle asimmetrie ("skewness") nelle osservazioni, nel quale l'assunzione di normalità non è più necessaria. La distribuzione normale viene, infatti, sostituita con la distribuzione "close skew-normal" che è più flessibile ed include la distribuzione normale. Imponendo una struttura auto-regressiva all'equazione di stato e un errore di misura distribuito secondo una "close skew-normal", si costruisce una versione "skewed" del noto filtro di Kalman. Quindi, nel Capitolo 4 si considera la metodologia di filtraggio robusta proposta da Calvet, Czellar and Ronchetti (2015, "Robust Filtering", Journal of the American Statistical Association) con una distribuzione t di Student per ottenere previsioni accurate che tengono conto di valori anomali e di errori di specificazione, sia per i modelli "finite state-space" sia "infinite state-space". Il Capitolo 5 presenta i fondamenti per la costruzione di modelli a volatilità stocastica con errori "close skew-normal" nelle osservazioni. Infine, il Capitolo 6 riassume il contributo della tesi e discute possibili future estensioni della ricerca.
This thesis is concerned with the modelling of time series driven by unobservable processes using state space models. New models and methodologies are proposed and applied on a variety of real life examples arising from finance and economics. The dissertation is comprised of six chapters. The first chapter motivates the thesis, provides the objectives and discusses the outline of the dissertation contents. In the second chapter, we define the concept of state space modelling, review some popular filtering procedures and recall some important definitions, properties and mathematical concepts that will be used in the subsequent chapters. In Chapter three, we propose a new state-space model that accounts for asymmetry, relaxing the assumption of normality and exploiting the close skew-normal distribution which is more flexible and extends the Gaussian distribution. By allowing a stationary autoregressive structure in the state equation, and a close skew-normal distributed measurement error, we also construct a skewed version of the well known Kalman filter. Then in Chapter four, we adapt the robust filtering methodology of Calvet, Czellar and Ronchetti (2015, "Robust Filtering", Journal of the American Statistical Association) to build a robust filter with Student-t observation density that provides accurate state inference accounting for outliers and misspecification; this for both finite and infinite state-space models. In the fifth chapter, we provide the foundations for the construction of stochastic volatility models with close skew-normal errors in the observation equation. The summary of the thesis, future works and possible extensions appear in Chapter six.

Clock synchronization between any two nodes in a Wireless Sensor Network (WSNs) is generally accomplished through exchanging messages and adjusting clock offset and skew parameters of each node’s clock. To cope with unknown network message delays, the clock offset and skew estimation schemes have to be reliable and robust in order to attain long-term synchronization and save energy. A joint clock offset and skew estimation scheme is studied and developed based on the Gaussian Mixture Kalman Particle Filter (GMKPF). The proposed estimation scheme is shown to be a more flexible alternative than the Gaussian Maximum Likelihood Estimator (GMLE) and the Exponential Maximum Likelihood Estimator (EMLE), and to be a robust estimation scheme in the presence of non-Gaussian/nonexponential random delays. This study also includes a sub optimal method called Maximum Likelihood-like Estimator (MLLE) for Gaussian and exponential delays. The computer simulations illustrate that the scheme based on GMKPF yields better results in terms of Mean Square Error (MSE) relative to GMLE, EMLE, GMLLE, and EMLLE, when the network delays are modeled as non-Gaussian/non-exponential distributions or as a mixture of several distributions.