2 FILTERING, LINEAR SYSTEMS, AND ESTIMATION

3 THE DISCRETE-TIME KALMAN FILTER

4 TIME-INVARIANT FILTERS

5 KALMAN FILTER PROPERTIES

6 COMPUTATIONAL ASPECTS

7 SMOOTHING OF DISCRETE-TIME SIGNALS

8 APPLICATIONS IN NONLINEAR FILTERING

9 INNOVATIONS REPRESENTATIONS, SPECTRAL FACTORIZATION, WIENER AND LEVINSON FILTERING

10 PARAMETER IDENTIFICATION AND ADAPTIVE ESTIMATION

11 COLORED NOISE AND SUBOPTIMAL REDUCED ORDER FILTERS

APPENDIXES

2 Statement of the Optimal Linear Phase FIR Filter Design Problem

3 Filter Sizing

4 Performance Comparsion with other FIR Design Methods

5 Three Methods of Designing FIR Filters

6 Why Does α Depend on the Cuto Frequency?

7 Extension to Non-lowpass Filters

8 Bibliography for "Notes on the Design of Optimal FIR Filters"

9 "Notes on the Design of Optimal FIR Filters" Appendix A

10 "Notes on the Design of Optimal FIR Filters" Appendix B

11 "Notes on the Design of Optimal FIR Filters" Appendix C

Bibliography

Index

Attributions

2 Quantization

3 Discrete-Time Systems

4 FIR Filtering and Convolution

5 z-Transforms

6 Transfer Functions

7 Digital Filter Realizations

8 Signal Processing Applications

9 DFT/FFT Algorithms

10 FIR Digital Filter Design

11 IIR Digital Filter Design

12 Interpolation, Decimation, and Oversampling

13 Appendices

1. Hidden Markov Model Processing

Part II Discrete-Time HMM Estimation

2. Discrete States and Discrete Observations

3. Continuous-Range Observations

4. Continuous-Range States and Observations

5. A General Recursive Filter

6. Practical Recursive Filters

Part III Continuous-Time HMM Estimation

7. Discrete-Range States and Observations

8. Markov Chains in Brownian Motion

Part IV Two-Dimensional HMM Estimation

9. Hidden Markov Random Fields

Part V HMM Optimal Control

10. Discrete-Time HMM Control

11. Risk-Sensitive Control of HMM

12. Continuous-Time HMM Control

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2 Introduction: Fast Fourier Transforms

3 Multidimensional Index Mapping

4 Polynomial Description of Signals

5 The DFT as Convolution or Filtering

6 Factoring the Signal Processing Operators

7 Winograd's Short DFT Algorithms

8 DFT and FFT: An Algebraic View

9 The Cooley-Tukey Fast Fourier Transform Algorithm

10 The Prime Factor and Winograd Fourier Transform Algorithms

11 Implementing FFTs in Practice

12 Algorithms for Data with Restrictions

13 Convolution Algorithms

14 Comments: Fast Fourier Transforms

15 Conclusions: Fast Fourier Transforms

16 Appendix 1: FFT Flowgraphs

17 Appendix 2: Operation Counts for General Length FFT

18 Appendix 3: FFT Computer Programs

19 Appendix 4: Programs for Short FFTs

Bibliography

Index

Attributions

Chapter 2: XtremeDSP Design Considerations

Chapter 3: DSP48 Slice Math Functions

Chapter 4: MAC FIR Filters

Chapter 5: Parallel FIR Filters

Chapter 6: Semi-Parallel FIR Filters

Chapter 7: Multi-Channel FIR Filters

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1 Introduction to Concise Signal Models

2 Signal Dictionaries and Representations

3 Manifolds

4 Low-Dimensional Signal Models

5 Approximation

6 Compression

7 Dimensionality Reduction

8 Compressed Sensing

Bibliography

Attributions

1.1 Historical Perspective

1.2 Method of Calculation

2 SINGLE STATIONARY SINUSOID PLUS NOISE

2.1 The Model

2.2 The Likelihood Function

2.3 Elimination of Nuisance Parameters

2.4 Resolving Power

2.5 The Power Spectral Density ^p

2.6 Wolf 's Relative Sunspot Numbers

3 THE GENERAL MODEL EQUATION PLUS NOISE

3.1 The Likelihood Function

3.2 The Orthonormal Model Equations

3.3 Elimination of the Nuisance Parameters

3.4 The Bessel Inequality

3.5 An Intuitive Picture

3.6 A Simple Diagnostic Test

4 ESTIMATING THE PARAMETERS

4.1 The Expected Amplitudes (Aj)

4.2 The Second Posterior Moments (AjAk)

4.3 The Estimated Noise Variance h2i

4.4 The Signal-To-Noise Ratio

4.5 Estimating the {w} Parameters

4.6 The Power Spectral Density

5 MODEL SELECTION

5.1 What About \Something Else?"

5.2 The Relative Probability of Model fj

5.3 One More Parameter

5.4 What is a Good Model?

6 SPECTRAL ESTIMATION

6.1 The Spectrum of a Single Frequency

6.1.1 The \Student t-Distribution"

6.1.2 Example { Single Harmonic Frequency

6.1.3 The Sampling Distribution of the Estimates

6.1.4 Violating the Assumptions { Robustness

6.1.5 Nonuniform Sampling

6.2 A Frequency with Lorentzian Decay

6.2.1 The \Student t-Distribution"

6.2.2 Accuracy Estimates

6.2.3 Example { One Frequency with Decay

6.3 Two Harmonic Frequencies

6.3.1 The \Student t-Distribution"

6.3.2 Accuracy Estimates

6.3.3 More Accuracy Estimates

6.3.4 The Power Spectral Density

6.3.5 Example { Two Harmonic Frequencies

6.4 Estimation of Multiple Stationary Frequencies

6.5 The \Student t-Distribution"

6.5.1 Example { Multiple Stationary Frequencies

6.5.2 The Power Spectral Density

6.5.3 The Line Power Spectral Density

6.6 Multiple Nonstationary Frequency Estimation

7 APPLICATIONS

7.1 NMR Time Series

7.2 Corn Crop Yields

7.3 Another NMR Example

7.4 Wolf 's Relative Sunspot Numbers

7.4.1 Orthogonal Expansion of the Relative SunspotNumbers

7.4.2 Harmonic Analysis of the Relative Sunspot Numbers

7.4.3 The Sunspot Numbers in Terms of Harmonically Related Frequencies

7.4.4 Chirp in the Sunspot Numbers

7.5 Multiple Measurements

7.5.1 The Averaging Rule

7.5.2 The Resolution Improvement

7.5.3 Signal Detection

7.5.4 The Distribution of the Sample Estimates

7.5.5 Example { Multiple Measurements

8 SUMMARY AND CONCLUSIONS

8.1 Summary

8.2 Conclusions

A Choosing a Prior Probability

B Improper Priors as Limits

C Removing Nuisance Parameters

D Uninformative Prior Probabilities

E Computing the \Student t-Distribution"

2 Probability

2.1 Introduction

2.2 Spinning pointers and flipping coins

2.3 Probability spaces

2.4 Discrete probability spaces

2.5 Continuous probability spaces

2.6 Independence

2.7 Elementary conditional probability

2.8 Problems

3 Random variables, vectors, and processes

3.1 Introduction

3.2 Random variables

3.3 Distributions of random variables

3.4 Random vectors and random processes

3.5 Distributions of random vectors

3.6 Independent random variables

3.7 Conditional distributions

3.8 Statistical detection and classification

3.9 Additive noise

3.10 Binary detection in Gaussian noise

3.11 Statistical estimation

3.12 Characteristic functions

3.13 Gaussian random vectors

3.14 Simple random processes

3.15 Directly given random processes

3.16 Discrete time Markov processes

3.17 ⋆Nonelementary conditional probability

3.18 Problems

4 Expectation and averages

4.1 Averages

4.2 Expectation

4.3 Functions of random variables

4.4 Functions of several random variables

4.5 Properties of expectation

4.6 Examples

4.7 Conditional expectation

4.8 ⋆Jointly Gaussian vectors

4.9 Expectation as estimation

4.10 ⋆Implications for linear estimation

4.11 Correlation and linear estimation

4.12 Correlation and covariance functions

4.13 ⋆The central limit theorem

4.14 Sample averages

4.15 Convergence of random variables

4.16 Weak law of large numbers

4.17 ⋆Strong law of large numbers

4.18 Stationarity

4.19 Asymptotically uncorrelated processes

4.20 Problems

5 Second-order theory

5.1 Linear filtering of random processes

5.2 Linear systems I/O relations

5.3 Power spectral densities

5.4 Linearly filtered uncorrelated processes

5.5 Linear modulation

5.6 White noise

5.7 ⋆Time averages

5.8 ⋆Mean square calculus

5.9 ⋆Linear estimation and filtering

5.10 Problems

6 A menagerie of processes

6.1 Discrete time linear models

6.2 Sums of iid random variables

6.3 Independent stationary increment processes

6.4 ⋆Second-order moments of isi processes

6.5 Specification of continuous time isi processes

6.6 Moving-average and autoregressive processes

6.7 The discrete time Gauss–Markov process

6.8 Gaussian random processes

6.9 The Poisson counting process

6.10 Compound processes

6.11 Composite random processes

6.12 ⋆Exponential modulation

6.13 ⋆Thermal noise

6.14 Ergodicity

6.15 Random fields

6.16 Problems

Appendix A Preliminaries

A.1 Set theory

A.2 Examples of proofs

A.3 Mappings and functions

A.4 Linear algebra

A.5 Linear system fundamentals

A.6 Problems

Appendix B Sums and integrals

B.1 Summation

B.2 ⋆Double sums

B.3 Integration

B.4 ⋆The Lebesgue integral

Appendix C Common univariate distributions

Appendix D Supplementary reading

References

Index

2 Models for Dynamic Systems

3 Stability

4 On-Line Parameter Estimation

5 Parameter Identifiers and Adaptive Observers

6 Model Reference Adaptive Control

7 Adaptive Pole Placement Control

8 Robust Adaptive Laws

9 Robust Adaptive Control Schemes

1 Introduction and Motivation

2 Introduction to Path Planning and Obstacle Avoidance

2.1 Holonomicity

2.2 Configuration Space

2.3 The Minkowski-Sum

2.4 Voronoi Methods

2.5 Bug Methods

2.6 Potential Methods

3 Estimation - A Quick Revision

3.1 Introduction

3.2 What is Estimation?

3.2.1 Defining the problem

3.3 Maximum Likelihood Estimation

3.4 Maximum A-Posteriori - Estimation

3.5 Minimum Mean Squared Error Estimation

3.6 Recursive Bayesian Estimation

4 Least Squares Estimation

4.1 Motivation

4.1.1 A Geometric Solution

4.1.2 LSQ Via Minimisation

4.2 Weighted Least Squares

4.2.1 Non-linear Least Squares

4.2.2 Long Baseline Navigation - an Example

5 Kalman Filtering -Theory, Motivation and Application

5.1 The Linear Kalman Filter

5.1.1 Incorporating Plant Models - Prediction

5.1.2 Joining Prediction to Updates

5.1.3 Discussion

5.2 Using Estimation Theory in Mobile Robotics

5.2.1 A Linear Navigation Problem - “Mars Lander”

5.2.2 Simulation Model

5.3 Incorporating Non-Linear Models - The Extended Kalman Filter

5.3.1 Non-linear Prediction

5.3.2 Non-linear Observation Model

5.3.3 The Extended Kalman Filter Equations

6 Vehicle Models and Odometry

6.1 Velocity Steer Model

6.2 Evolution of Uncertainty

6.3 Using Dead-Reckoned Odometry Measurements

6.3.1 Composition of Transformations

7 Feature Based Mapping and Localisation

7.1 Introduction

7.2 Features and Maps

7.3 Observations

7.4 A Probabilistic Framework

7.4.1 Probabilistic Localisation

7.4.2 Probabilistic Mapping

7.5 Feature Based Estimation for Mapping and Localising

7.5.1 Feature Based Localisation

7.5.2 Feature Based Mapping

7.6 Simultaneous Localisation and Mapping - SLAM

7.6.1 The role of Correlations

8 Multi-modal and other Methods

8.1 Montecarlo Methods - Particle Filters

8.2 Grid Based Mapping

9 In Conclusion

10 Miscellaneous Matters

10.1 Drawing Covariance Ellipses

10.2 Drawing High Dimensional Gaussians

11 Example Code

11.1 Matlab Code For Mars Lander Example

11.2 Matlab Code For Ackerman Model Example

11.3 Matlab Code For EKF Localisation Example

11.4 Matlab Code For EKF Mapping Example

11.5 Matlab Code For EKF SLAM Example

11.6 Matlab Code For Particle Filter Example

1.1 Historical Uses of Wind

1.2 History of Wind Electric Generation

1.3 Horizontal Axis Wind Turbine Research

1.4 Darrieus Wind Turbines

1.5 Innovative Wind Turbines

1.6 California Wind farms

2 Wind Characteristics

2.1 Meteorology of Wind

2.2 World Distribution of Wind

2.3 Wind Speed Distribution in the United States

2.4 Atmospheric Stability

2.5 Wind Speed Variation With Height

2.6 Wind Speed Statistics

2.7 Weibull Statistics

2.8 Determining the Weibull Parameters

2.9 Rayleigh and Normal Distributions

2.10 Distribution of Extreme Winds

2.11 Problems

3 Wind Measurements

3.1 Eolian Features

3.2 Biological Indicators

3.3 Rotational Anemometers

3.4 Other Anemometers

3.5 Wind Direction

3.6 Wind Measurements with Balloons

3.7 Problems

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I. Introduction

II. Simple Transformer Manipulations

III. Two-phase Transformer Connections

IV. Three-phase Transformation System

V. Three-phase Transformer Difficulties

VI. Three-phase Two-phase Systems and Transformation

VII. Six-phase Transformation and Operation

VIII. Methods of Cooling Transformers

IX. Construction, Installation and Operation of Large Transformers

X. Auto Transformers

XI. Con.stant-current Transformers and Operation

XII. Series Transformers and Their Operation

XIII. Regulators and Compensators

XIV. Transformer Testing in Practice

XV. Transformer Specifications

Appendix

Index