This module covers the Kalman filter model and derivation. It provides insights into the mathematical foundations of the filter and its significance in estimation tasks.
This module introduces the fundamental concepts of estimation and the importance of signals in various applications. Topics include the definitions of signals, their characteristics, and an overview of the entire course structure.
This module delves into probability theory, covering essential concepts such as probability distributions, Bayes' theorem, and conditional probabilities. Understanding these concepts is crucial for analyzing random processes.
This module focuses on random variables, including their types, properties, and significance in statistical analysis. Key discussions include discrete and continuous random variables and their applications in estimation.
This module explains the function of random variables and joint density functions. It covers how to calculate joint probabilities and their applications in multi-dimensional random processes.
This module discusses mean and variance, critical statistical measures in estimation. Students will learn how to compute these values and understand their significance in analyzing random processes.
This module introduces random vectors and processes, elucidating their role in statistical analysis. Students will examine the concepts of covariance, correlation, and how these affect system performance.
This module explores the interaction between random processes and linear systems. It discusses how random inputs affect system outputs, emphasizing system stability and performance analysis.
This module presents numerical problems related to estimation techniques. Students will work through practical examples to enhance their understanding of theoretical concepts applied in real-world scenarios.
This module covers miscellaneous topics related to random processes. It provides a broader context for understanding various estimation techniques and their applications in different fields.
This module focuses on linear signal models, examining their structure and application in estimation. Students will learn how to model real-world signals using linear approaches.
This module discusses linear mean square error estimation. It covers various estimation methods and their effectiveness in minimizing errors in signal processing applications.
This module examines auto-correlation and power spectrum estimation. Students will learn techniques to analyze the periodicity and frequency content of signals using statistical methods.
This module revisits the Z-transform, focusing on its importance in linear systems analysis. Topics include properties of eigenvectors and eigenvalues and their applications in estimation.
This module introduces the concept of innovation in estimation theory, discussing its role in predicting outcomes and refining estimates based on new information.
This module covers least squares estimation and optimal IIR filters. Students will learn how to apply these techniques to minimize estimation errors in dynamic systems.
This module introduces adaptive filters, which adjust their parameters based on incoming data. Students will learn key algorithms and their applications in real-time signal processing.
This module focuses on state estimation, discussing techniques to estimate the internal states of dynamic systems. Key methods include the use of Kalman filters for optimal results.
This module covers the Kalman filter model and derivation. It provides insights into the mathematical foundations of the filter and its significance in estimation tasks.
This module continues the derivation of the Kalman filter, focusing on practical implementation aspects. Students will explore various applications and scenarios where Kalman filters are utilized.
This module discusses the properties of estimators, including bias, consistency, and efficiency. Students will learn how to evaluate different estimators and their effectiveness in practical applications.
This module covers the time-invariant Kalman filter, discussing its applications in various control systems. It emphasizes the importance of understanding time-invariance in estimation processes.
This module presents a case study of the Kalman filter, applying theoretical knowledge to a practical scenario. Students will analyze results and refine their understanding of the filter's performance.
This module introduces system identification concepts. Students will learn how to create mathematical models based on observed data and the significance of these models in control systems.
This module focuses on linear regression and recursive least squares. Students will learn techniques to estimate parameters in linear models and the advantages of recursive algorithms.
This module covers various variants of least squares estimation, examining different approaches and their applications in practice. Students will compare strengths and weaknesses of each method.
This module discusses the least squares estimation method, providing a foundation for understanding its mathematical principles and practical implementations in data fitting processes.
This module focuses on model order selection and residual tests, emphasizing their importance in ensuring model accuracy. Students will learn how to assess models through statistical tests.
This module addresses practical issues in identification, including noise, outliers, and data limitations. Students will explore solutions to enhance model reliability and accuracy.
This module covers estimation problems in instrumentation and control systems. Students will explore various case studies, applying theoretical knowledge to solve real-world challenges.
This concluding module summarizes the course content, reinforcing key concepts and techniques learned throughout the course. Students will reflect on their learning and prepare for future applications.