Fundamentals of Kalman Filtering: A Practical Approach, Third Edition

Musoff, Howard; Zarchan, Paul

doi:10.2514/4.867200

Cited by 39 publications

(14 citation statements)

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“…In KF, (x t |x t−1 ) and ( y t |x t ) are both assumed to be Gaussians. The KF consists of two steps, namely, a "prediction" step and an "updating" step [24]. Letx t|t−1 be the prior estimate at time t given information available at time t −1, V t|t−1 be the prior estimate of state error covariance,x t be the posterior estimate given observation y t , and V t be the posterior estimate of the state error covariance.…”

Section: Kalman Filtermentioning

confidence: 99%

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Dynamics identification and forecasting of COVID-19 by switching Kalman filters

Zeng

Ghanem

2020

Comput Mech

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The COVID-19 pandemic has captivated scientific activity since its early days. Particular attention has been dedicated to the identification of underlying dynamics and prediction of future trend. In this work, a switching Kalman filter formalism is applied on dynamics learning and forecasting of the daily new cases of COVID-19. The main feature of this dynamical system is its ability to switch between different linear Gaussian models based on the observations and specified probabilities of transitions between these models. It is thus able to handle the problem of hidden state estimation and forecasting for models with non-Gaussian and nonlinear effects. The potential of this method is explored on the daily new cases of COVID-19 both at the state-level and the country-level in the US. The results suggest a common disease dynamics across states that share certain features. We also demonstrate the ability to make short to medium term predictions with quantifiable error bounds.

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Section: Kalman Filtermentioning

confidence: 99%

“…Kalman filter has been demonstrated in a wide range of applications from the navigation and tracking of vehicles and aircraft [24][25][26] to estimation and forecast in economics [27].…”

Section: Kalman Filtermentioning

confidence: 99%

Dynamics identification and forecasting of COVID-19 by switching Kalman filters

Zeng

Ghanem

2020

Comput Mech

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“…In this new approach, we use the framework of the Multiple Model Adaptive Estimator (MMAE) originally proposed in 1965 19 . The MMAE has been shown to be effective in a variety of cases 20,21 and operates by running multiple filters in parallel with a probabilistic framework to switch between the filters. In a typical implementation, the MMAE uses several Kalman filters, each with a different system model.…”

Section: Mmae Svsf-kfmentioning

confidence: 99%

“…We shall consider only the position estimate, so we can treat the innovations as a scalar value. The likelihood function for the i th filter given a scalar innovation input can be expressed as 21 :…”

Section: Mmae Svsf-kfmentioning

confidence: 99%

A multiple model adaptive SVSF-KF estimation strategy

Goodman

Wilkerson

Eggleton

et al. 2019

Signal Processing, Sensor/Information Fusion, and Target Recognition XXVIII

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State estimation strategies play a critical role in obtaining accurate information about the state of dynamic systems as they develop. Such information can be important on its own and critical for precise and predictable control of such systems. The Kalman filter (KF) is a classic algorithm and among the most powerful tools in state estimation. The Kalman filter however can be sensitive to modeling uncertainty and sudden changes in system dynamics. The Smooth Variable Structure Filter (SVSF) is a relatively new estimation strategy that operates on variable structure concepts. In general, the SVSF has the advantage that is can be quite robust to modeling uncertainty and sudden fault conditions. Recent advancements to the SVSF, such as the addition of a covariance formulation, and the derivation of a time varying smoothing boundary layer (VBL), have allowed for combined SVSF-KF strategies. In a typical SVSF-KF approach, the VBL is used to detect the presence of a system fault, and switch from the more optimal KF gain to the more robust SVSF gain. While this approach has been proven effective in several cases, there are circumstances where the VBL will fail to indicate the presence of an ongoing fault. A new form of the SVSF-KF is proposed, based on the framework of the Multiple Model Adaptive Estimator.

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“…One of the principal landmarks in stochastic observer theory is the optimal stochastic estimators formulation or Kalman filter (KF) [ 4 , 5 , 6 ]. These estimators are based in the state space systems and different versions, such as extended KF (EKF) [ 7 , 8 , 9 ], unscented KF (UKF) [ 10 , 11 ], or robust KF (RKF) [ 12 ], generalize its use with nonlinear Gaussian problems as shown in Afshari et al [ 3 ].…”

Section: Introductionmentioning

confidence: 99%

Forecasting Nonlinear Systems with LSTM: Analysis and Comparison with EKF

Caña

Herrero

Molina

2021

Sensors

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Certain difficulties in path forecasting and filtering problems are based in the initial hypothesis of estimation and filtering techniques. Common hypotheses include that the system can be modeled as linear, Markovian, Gaussian, or all at one time. Although, in many cases, there are strategies to tackle problems with approaches that show very good results, the associated engineering process can become highly complex, requiring a great deal of time or even becoming unapproachable. To have tools to tackle complex problems without starting from a previous hypothesis but to continue to solve classic challenges and sharpen the implementation of estimation and filtering systems is of high scientific interest. This paper addresses the forecast–filter problem from deep learning paradigms with a neural network architecture inspired by natural language processing techniques and data structure. Unlike Kalman, this proposal performs the process of prediction and filtering in the same phase, while Kalman requires two phases. We propose three different study cases of incremental conceptual difficulty. The experimentation is divided into five parts: the standardization effect in raw data, proposal validation, filtering, loss of measurements (forecasting), and, finally, robustness. The results are compared with a Kalman filter, showing that the proposal is comparable in terms of the error within the linear case, with improved performance when facing non-linear systems.

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Fundamentals of Kalman Filtering: A Practical Approach, Third Edition

Cited by 39 publications

References 0 publications

Dynamics identification and forecasting of COVID-19 by switching Kalman filters

Dynamics identification and forecasting of COVID-19 by switching Kalman filters

A multiple model adaptive SVSF-KF estimation strategy

Forecasting Nonlinear Systems with LSTM: Analysis and Comparison with EKF

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