File Name: discrete stochastic processes and optimal filtering .zip
In statistics and control theory , Kalman filtering , also known as linear quadratic estimation LQE , 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, by estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. The Kalman filter has numerous applications in technology. A common application is for guidance, navigation, and control of vehicles, particularly aircraft, spacecraft and dynamically positioned ships. Kalman filters also are one of the main topics in the field of robotic motion planning and control and can be used in trajectory optimization.
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Exercises with solutions feature in each chapter to demonstrate the practical application of these ideas using Matlab. Chapter 1. Random vectors. Chapter 2. Gaussian vectors. Chapter 3. Introduction to Discrete Time Processes 93 3.
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This paper is concerned with the optimal Kalman filtering problem for a class of discrete stochastic systems with multiplicative noises and random two-step sensor delays. Three Bernoulli distributed random variables with known conditional probabilities are introduced to characterize the phenomena of the random two-step sensor delays which may happen during the data transmission. By using the state augmentation approach and innovation analysis technique, an optimal Kalman filter is constructed for the augmented system in the sense of the minimum mean square error MMSE. Subsequently, the optimal Kalman filtering is derived for corresponding augmented system in initial instants. Finally, a simulation example is provided to demonstrate the feasibility and effectiveness of the proposed filtering method. The filtering problem has been a mainstream research topic in the control theory due to its wide and important engineering applications such as signal processing, econometrics communication, guidance, navigation, and control of vehicles [ 1 — 4 ].
The locally optimal filter is designed for a class of discrete-time systems subject to stochastic nonlinearity functions, finite-step correlated noises, and missing measurements. The multiplicative noises are employed to describe the random disturbances in the system model. The phenomena of missing measurements occur in a random way and the missing probability is characterized by Bernoulli distributed random variables with known conditional probabilities. Based on the projection theory, a class of Kalman-type locally optimal filter is constructed and the filtering error covariance matrix is minimized in the sense of minimum mean square error principle. Also, by solving the recursive matrix equation, we can obtain the filter gain. Finally, two examples are provided: one is a numerical example to illustrate the feasibility and effectiveness of the proposed filtering scheme; the other is to solve the problem of target estimation for a tracking system considering networked phenomena. The filtering theory is a kind of optimal approach to estimate the state of the target plant based on the measurement output of the observation signals and the certain filtering criteria.
Optimal filtering applied to stationary and non-stationary signals provides the most efficient means of dealing with problems arising from the.
Ogni modulo equivale a 3 crediti ECTS. La descrizione del modulo scarica il pdf riporta le informazioni linguistiche per ogni modulo, suddivise nelle seguenti categorie:. The goal of this module is to introduce the students to the powerful world of statistical digital signal processing. While at the bachelor level digital signal processing is most often taught with deterministic signals, in the real world most interesting signals are stochastic in nature. Hence in more advanced applications, such as prediction or noise removal, the theories presented in this module are essential.
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This course gives thorough knowledge of linear estimation theory. The main theme of the course is optimal linear estimation, Kalman and Weiner filtering, which are systematic methods to solve estimation problems with applications in several technical disciplines, for example in telecommunications, automatic control and signal processing but also in other disciplines, such as econometrics and statistics.
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In the classical approach to optimal filtering, it is assumed that the stochastic model of the physical process is fully known. For instance, in Wiener filtering it is assumed that the power spectra are known with certainty. The implicit assumption is that the parameters of the model can be accurately estimated. When models are complex or parameter estimation is difficult or expensive , this assumption is unwarranted. With uncertain models, the natural solution is to optimize over both the original objective and the model uncertainty, thereby arriving at optimal robust operators , the topic of this book.
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