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Multisensor Precise Positioning for Automated and Connected Vehicles
Published in Hussein T. Mouftah, Melike Erol-Kantarci, Sameh Sorour, Connected and Autonomous Vehicles in Smart Cities, 2020
Mohamed Elsheikh, Aboelmagd Noureldin
The Kalman filter [29] is a recursive Bayesian filter that estimates the system states with the aid of some measurements from the system observables. The Kalman filter combines the state prediction from the system model and the updates from the measurements to generate the output solution. This combination depends on the covariance matrices of the prediction and measurement models which represent the uncertainty about each one of them. The Kalman filter outputs are the estimated system states accompanied by the statistical information about the covariance of these estimates. The advantage of Kalman filter, compared to other techniques such as least squares, is the utilization of the information about the deterministic and statistical properties of the system states in addition to the independent measurement updates.
Advanced Control Systems
Published in Arthur G.O. Mutambara, Design and Analysis of Control Systems, 2017
In this section, the principles and concepts of estimation are introduced. An estimator is a decision rule that takes as an argument a sequence of observations and computes a value for the parameter or state of interest. The Kalman filter is a recursive linear estimator that successively calculates a minimum variance estimate for a state that evolves over time, on the basis of periodic observations that are linearly related to this state. The Kalman filter estimator minimizes the mean squared estimation error and is optimal with respect to a variety of important criteria under specific assumptions about process and observation noise. The development of linear estimators can be extended to the problem of estimation for nonlinear systems. The Kalman filter has found extensive applications in such fields as aerospace navigation, robotics and process control.
Introduction
Published in Maurizio Mazzoleni, Improving Flood Prediction Assimilating Uncertain Crowdsourced Data into Hydrological and Hydraulic Models, 2017
Among data assimilation techniques the Kalman filter is one of the most used methods to assimilate, in an efficient recursive way, observed noisy data into dynamic systems (Kalman, 1960). However, one limitation of the Kalman filter is that it is optimal only for linear dynamic systems. For this reason, different variants of the Kalman filter, such as the extended Kalman filter (Madsen and Cañizares, 1999; Aubert et al., 2003), unscented Kalman filter, ensemble Kalman filter (Reichle, 2000; Evensen, 2003; Komma et al., 2008; Mendoza et al., 2012; Noh et al., 2013; Rafieeinasab et al., 2014) and recursive ensemble Kalman filter (McMillan et al., 2013) have been proposed and applied in hydrologic modelling. Madsen and Cañizares (1999) compared the performance of EKF and EnKF in coastal area modelling. Although the study showed that the EnKF does not fail in the case of strong non-linear dynamics, it was found to be very time consuming. Application of Kalman filtering methods to hydrodynamic modelling has been explored by Verlaan and Heemink (1995) and Verlaan (1998).
Unknown input observer design for linear time-invariant multivariable systems based on a new observer normal form
Published in International Journal of Systems Science, 2022
Helmut Niederwieser, Markus Tranninger, Richard Seeber, Markus Reichhartinger
Kalman filter based state estimators, such as for example the classical Kalman filter (Kalman, 1960; Kalman & Bucy, 1961) in the case of linear systems and the extended Kalman filter (Sorenson, 1985) as well as the unscented Kalman filter (Julier & Uhlmann, 1997; Wan & Van Der Merwe, 2000) in the case of nonlinear systems, allow to model unknown inputs as a Gaussian process noise with zero mean. High-gain observers (Khalil & Praly, 2014) suppress the influence of unknown inputs by means of a linear output injection with high gain. However, high-gain observers as well as the previously mentioned Kalman filter based methods are not exact even in the theoretical case without any measurement noise and model uncertainties. In contrast to the aforementioned linear methods, sliding mode based observers allow for a theoretically exact estimation of the state variables in the presence of a wide range of input uncertainties, e.g. unknown inputs with bounded amplitude or bounded derivatives (Bejarano & Fridman, 2010; De Loza et al., 2013; Fridman et al., 2006; Koshkouei & Zinober, 2004; Li & Zhang, 2018; Shtessel et al., 2014; Utkin et al., 1999).
Unknown Resistive Torque Estimation of a Rotary Drilling System Based on Kalman Filter
Published in IETE Journal of Research, 2022
R. Riane, M. Kidouche, R. Illoul, M. Z. Doghmane
Kalman estimator, also known as linear quadratic estimation, is an algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone. The Kalman filter has numerous applications in technology; a common application is for guidance, navigation, and control of vehicles, particularly aircraft and spacecraft [18–23]. Due to the short time delay between issuing commands and receiving sensory feedback, the use of Kalman filter supports a realistic model for making estimates of the current state of the system and issuing updated commands. The algorithm mechanism is composed of two-step processes. In the prediction step, Kalman filter produces estimations of the current state variables, along with their uncertainties. Once the outcome of the next measurement (necessarily corrupted with some amount of error, including random noise) is observed, these estimates are updated using a weighted average, with more weight being given to estimates with higher certainty. The algorithm is recursive; it can be run in real time, using only the present input measurements and the previously calculated state and its uncertainty matrix; no additional past information is required. Using Kalman filter does not assume that the errors are Gaussian [24]. However, the filter yields better results in the special case where all errors are Gaussian.
Speed sensorless control of seven phase asynchronous motor drive system using extended Kalman filter
Published in International Journal of Electronics Letters, 2022
Estimation of motor speed using motor terminal voltages and current has many rewards over using speed measurement devices. Such as reduction of the drive cost. It is reasonable for antagonistic environments, reduced maintenance, and increased robustness and reliability of the drive system. EKF used to estimate the motor speed of IM. The main advantage of the Kalman filter is its facility to introduce the superiority of the estimate (i.e., the variance), and its moderately low complexity. Nevertheless, its main weakness is that it provides precise results only for Gaussian and linear models. Extended Kalman filter (EKF) is suitable. (Arulampalam et al. (2002); Tanvir & Merabet, 2020). For non-Gaussian and non-linear models. Kalman filter is an authoritative adaptive filtering process that is constructed based on the state space depiction of a dynamic system, consisting of a system state changeover equation and a measurement equation. One of the critical features of constructing a Kalman filter is the strategy of these two equations K1,K2.