Here is the full list of best reference books on Introduction to Linear Filtering and Beyond.
1. “Kalman Filtering Theory” by A V Balakrishnan
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Book Review: This is a very good one semester course book for graduate courses. Knowledge of elementary stochastic process theory is the prerequisite. The book demonstrates the aspects of kalman filtering which can be given a strong mathematical basis. The book contains chapters on state space theory, signal (random process) theory, statistical estimation theory and the mathematical framework on which kalman filtering rests. The book also concludes with chapter on likelihood ratios where the important concept is kalman filter formulation. Discrete time models are considered throughout the book to explain various concepts.


2. “Stochastic Processes and Filtering Theory” by A H Jazwinski
Book Review: The book presents linear as well as nonlinear filtering theory which is very useful to the engineering students. The prerequisites for this book are advanced calculus, ordinary differential equations theory and analysis of matrices. The book presents both theory as well as practical applications. The book models dynamical systems by finite dimensional markov processes and outputs of stochastic difference and differential equations. The author also defines the problems of filtering, prediction and smoothing. The author also demonstrates mathematical solutions to nonlinear filtering problems and presents the development of approximate nonlinear filters.


3. “Optimal Filtering” by B D O Anderson and J B Moore
Book Review: This book contains very detailed information regarding communication systems, digital filtering theory and signal processing. The book is very useful for students studying in the field of control and communications, statistics, economics, bioengineering and operations research. The various topics covered in the book include filtering, linear systems, estimation, discrete time kalman filter, time invariant filters, kalman filter properties, computational aspects and discrete time signal smoothing. Other topcis include nonlinear filtering applications, innovations representations, spectral factorization, parameter identification and adaptive estimation.
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4. “Dynamic Programming and Optimal Control Vol. I” by D Bertsekas
Book Review: The book is focused towards modeling, conceptualization, finite horizon problems, mathematical analysis and computation and provides an uptodate account of approximate large scale dynamic programming and reinforcement learning. This book deals with the far ranging algorithmic methodology of dynamic programming. This book is best suited for optimal control, markovian decision problems, planning and sequential decision making under certainty and discrete optimization. The book demonstrates the method generality and power with many examples and applications pertaining to engineering and operations researchers.


5. “Systems and Control: An Introduction to Linear, Sampled & NonLinear Systems (Advanced Series in Electrical & Computer Engineering)” by Terry Dougherty  
6. “A Concise Introduction to Linear Algebra” by Geza Schay G Za Schay Schay  
7. “Introduction to Linear Algebra” by Lang  
8. “Introduction to Linear Algebra” by Inder K Rana  
9. “Introduction to Linear Optimization and Extensions with MATLAB” by Kwon  
10. “Introduction to Linear Circuit Analysis and Modelling: From DC to RF” by Luis Moura Izzat Darwazeh  
People who are searching for Free downloads of books and free pdf copies of these books – “Kalman Filtering Theory” by A V Balakrishnan, “Stochastic Processes and Filtering Theory” by A H Jazwinski, “Optimal Filtering” by B.D.O. Anderson and J.B. Moore, “Dynamic Programming and Optimal Control Vol. I” by D Bertsekas, “Systems and Control: An Introduction to Linear, Sampled & NonLinear Systems (Advanced Series in Electrical & Computer Engineering)” by Terry Dougherty, “A Concise Introduction to Linear Algebra” by Geza Schay G Za Schay Schay, “Introduction to Linear Algebra” by Lang, “Introduction to Linear Algebra” by Inder K Rana, “Introduction to Linear Optimization and Extensions with MATLAB” by Kwon, “Introduction to Linear Circuit Analysis and Modelling: From DC to RF” by Luis Moura Izzat Darwazeh – we would like to mention that we don’t have free downloadable pdf copies of these good books and one should look for free pdf copies from these Authors only if they have explicitly made it free to download and read them.
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