Thank you! Estimation + Information Theory. ELEC 3004: Systems 1 June

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1 Estimation + Information Theory 2014 School of Information Technology and Electrical Engineering at The University of Queensland Thank you! ELEC 3004: Systems 1 June

Schedule Week Date Lecture Title 1 2-Mar Introduction 3-Mar Systems Overview 2 9-Mar Signals as Vectors & Systems as Maps 10-Mar [Signals] 3 4 5 6 7 8 9 10 11 12 13 16-Mar Sampling & Data Acquisition

2 Schedule Week Date Lecture Title 1 2-Mar Introduction 3-Mar Systems Overview 2 9-Mar Signals as Vectors & Systems as Maps 10-Mar [Signals] Mar Sampling & Data Acquisition & Antialiasing Filters 17-Mar [Sampling] 23-Mar System Analysis & Convolution 24-Mar [Convolution & FT] 30-Mar Discrete Systems & Z-Transforms 31-Mar [Z-Transforms] 13-Apr Frequency Response & Filter Analysis 14-Apr [Filters] 20-Apr Digital Filters 21-Apr [Digital Filters] 27-Apr Discrete Systems Analysis 28-Apr [Feedback] 4-May Introduction to (Digital) Control 5-May [Digitial Control] 11-May Digital Control Design 12-May [Introduction to State-Space] 18-May State-Space - Analysis 19-May [Stability] 25-May Digital Control Systems: Shaping the Dynamic Response 26-May [Applications in Industry] 1-Jun System Identification & [Summary and Course Review] 2-Jun Estimation + Information Theory ELEC 3004: Systems 1 June Lab 4 ELEC 3004: Systems 1 June

3 Final Exam Review Monday, June 22, 2015 From: 2-4p In Hawken: 50-T105 Tuesday June 9, 2015 From 2-4p In TBA ELEC 3004: Systems 1 June Estimation: Yet another way to beat the noise ELEC 3004: Systems 1 June

Along multiple dimensions ELEC 3004: Systems 1 June 2015 7 State Space We collect our set of uncertain variables into a vector x = [x 1, x 2,, x N ] T

4 Along multiple dimensions ELEC 3004: Systems 1 June State Space We collect our set of uncertain variables into a vector x = [x 1, x 2,, x N ] T The set of values that x might take on is termed the state space There is a single true value for x, but it is unknown ELEC 3004: Systems 1 June

5 State Space Dynamics ELEC 3004: Systems 1 June Measured versus True Measurement errors are inevitable So, add Noise to State... State Dynamics becomes: Can represent this as a Normal Distribution ELEC 3004: Systems 1 June

6 Recovering The Truth Numerous methods Termed Estimation because we are trying to estimate the truth from the signal A strategy discovered by Gauss Least Squares in Matrix Representation ELEC 3004: Systems 1 June Recovering the Truth: Terminology ELEC 3004: Systems 1 June

7 General Problem ELEC 3004: Systems 1 June Duals and Dual Terminology ELEC 3004: Systems 1 June

8 Estimation Process in Pictures ELEC 3004: Systems 1 June Kalman Filter Process ELEC 3004: Systems 1 June

9 KF Process in Equations ELEC 3004: Systems 1 June KF Considerations ELEC 3004: Systems 1 June

10 Ex: Kinematic KF: Tracking Consider a System with Constant Acceleration ELEC 3004: Systems 1 June In Summary KF: The true state (x) is separate from the measured (z) Lets you combine prior controls knowledge with measurements to filter signals and find the truth It regulates the covariance (P) As P is the scatter between z and x So, if P 0, then z x (measurements truth) EKF: Takes a Taylor series approximation to get a local F (and G and H ) ELEC 3004: Systems 1 June

Shannon Information Theory The fundamental problem of communication is that of reproducing at one point, either exactly or approximately, a message selected at another point.

channel A channel, which is the medium over which the signal, carrying the information that composes the message, is sent A receiver, which transforms the signal back into the message intended for

11 Shannon Information Theory The fundamental problem of communication is that of reproducing at one point, either exactly or approximately, a message selected at another point. On the transmission of information over a noisy channel: An information source that produces a message A transmitter that operates on the message to create a signal which can be sent through a channel A channel, which is the medium over which the signal, carrying the information that composes the message, is sent A receiver, which transforms the signal back into the message intended for delivery A destination, which can be a person or a machine, for whom or which the message is intended ELEC 3004: Systems 1 June Shannon and Weaver: Models of Communication Three problems in Communication: The technical problem: how accurately can the message be transmitted? The semantic problem: how precisely is the meaning conveyed? The effectiveness problem: how effectively does the received meaning affect behaviour? Source: ELEC 3004: Systems 1 June

Today s Lecture is Brought To You By the Number 5 ELEC 3004: Systems 1 June 2015 23 SECATs: Let s look back at the topic list from Lecture 1 The course is has a huge mandate: It is really 3 ½ courses

12 Today s Lecture is Brought To You By the Number 5 ELEC 3004: Systems 1 June SECATs: Let s look back at the topic list from Lecture 1 The course is has a huge mandate: It is really 3 ½ courses in one! Linear Systems Signal Processing Controls & Digital Controls It is b r o a d!! There is a logic to it They share the same mathematical nature (poles & zeros) The math is common to more than just circuits! ELEC 3004: Systems 1 June

13 Lots of Stuff To Cover Systems Controllability and state transfer Signal Abstractions Discrete Time Observability and state estimation Signals as Vectors / Systems as Maps Continuous Time And that, of course, Linear Systems and Their Properties Laplace Transformation Linear Systems are Cool! LTI Systems Feedback and Control Autonomous Linear Dynamical Systems Additional Applications Convolution Linear Functions FIR & IIR Systems Linear Algebra Review Frequency domain Least Squares Fourier Transform (CT) Least Squares Problems Fourier Transform (DT) Least Squares Applications Matrix Decomposition and Linear Even and Odd Signals Algebra Likelihood Regularized Least Squares Causality Least-squares Impulse Response Least-squares applications Root Locus Orthonormal sets of vectors Bode Functions Eigenvectors and diagonalization Linear dynamical systems with inputs Left-hand Plane and outputs Symmetric matrices, quadratic forms, matrix norm, and SVD Frequency Response ELEC 3004: Systems 1 June Yes, this is Hard! Why? Breath Books, books, everywhere, yet we re all on Wikipedia!! Authors tend to be too generalizable Assumptions: Numerous conditions that need to be remembered Tacit Details: The need for examples (but these are few and always seem the same) Time consuming ELEC 3004: Systems 1 June

14 SECaTs: Some Lessons in the Works for Next Year I shall only use my own slides Less is more! Smaller assignments More time for Examples Better organization Better tutorials More examples!! I get that. But, we ve come a long way To make this happen I need your support! ELEC 3004: Systems 1 June Next Time in Linear Systems. Week Date Lecture Title 1 2-Mar Introduction 3-Mar Systems Overview 9-Mar Signals as Vectors & Systems as Maps 2 10-Mar [Signals] Mar Sampling & Data Acquisition & Antialiasing Filters 17-Mar [Sampling] 23-Mar System Analysis & Convolution 24-Mar [Convolution & FT] 30-Mar Discrete Systems & Z-Transforms 31-Mar [Z-Transforms] 13-Apr Frequency Response & Filter Analysis 14-Apr [Filters] 20-Apr Digital Filters 21-Apr [Digital Filters] 27-Apr Discrete Systems Analysis 28-Apr [Feedback] 4-May Introduction to (Digital) Control 5-May [Digitial Control] 11-May Digital Control Design 12-May [Introduction to State-Space] 18-May State-Space - Analysis 19-May [Stability] 25-May Digital Control Systems: Shaping the Dynamic Response 26-May [Applications in Industry] 13 1-Jun System Identification & [Summary and Course Review] 2-Jun Estimation + Information Theory We re at the End. It s (the) final! Thank you folks! ELEC 3004: Systems 1 June

15 Now Finally Some Philosophy (I am a Dr of it!!!) Systems: Signals, Controls A Fundamental Yearn! National Geographic. Mount Everest at night (the lights along the apex are the headlamps of other mountaineers) We keep moving forward, opening new doors, and doing new things because we're curious and curiosity keeps leading us down new paths. -Walt Disney ELEC 3004: Systems 1 June

Digital Filters IIR (& Their Corresponding Analog Filters) Week Date Lecture Title

http://elec3004.com Digital Filters IIR (& Their Corresponding Analog Filters) 2017 School of Information Technology and Electrical Engineering at The University of Queensland Lecture Schedule: Week Date