Signal and Image Processing in Navigational Systems

by Tuzlukov; Vyacheslav

• ISBN13: 9780849315985
• ISBN10: 0849315980
• Format: Hardcover
• Copyright: 2004-11-29
• Publisher: CRC Press

Summary

Classical and modern theories have given us a degree of noise immunity by defining the sufficient statistic of the mean of the likelihood function. The generalized theory moves beyond these limitations to determine the jointly sufficient statistics of the mean and variance of the likelihood function.Signal and Image Processing in Navigational Systems introduces us to the generalized approach, and then delves rigorously into the theory and practical applications of this approach. This volume represents the most in-depth discussion of the generalized approach to date, providing many examples and computer models to demonstrate how this approach raises the upper limits of noise immunity for navigation systems, leading to better detection performances.This book is vital for signal and image processing experts, radar, communications, acoustics, and navigational systems designers, as well as professionals in the fields of statistical pattern recognition, biomedicine, astronomy, and robotics who wish to extend the boundaries of noise immunity and improve qualitative performance of their systems.

Table of Contents

Part I Theory of Fluctuating Target Return Signals in Navigational Systems
Chapter 1 Probability Distribution Density of the Amplitude and Phase of the Target Return Signal	3	(26)
1.1 Two-Dimensional Probability Distribution Density of the Amplitude and Phase	3	(5)
1.2 Probability Distribution Density of the Amplitude	8	(3)
1.3 Probability Distribution Density of the Phase	11	(4)
1.4 Probability Distribution Density Parameters of the Target Return Signal as a Function of the Distribution Law of the Amplitude and Phase of Elementary Signals	15	(11)
1.4.1 Uniform Probability Distribution Density of Phases	22	(2)
1.4.2 "Triangular" Probability Distribution Density of Phases	24	(1)
1.4.3 Gaussian Probability Distribution Density of Phases	25	(1)
1.5 Conclusions	26	(1)
References	27	(2)
Chapter 2 Correlation Function of Target Return Signal Fluctuations	29	(60)
2.1 Target Return Signal Fluctuations	29	(7)
2.1.1 Physical Sources of Fluctuations	29	(1)
2.1.2 The Target Return Signal: A Poisson Stochastic Process	30	(6)
2.2 The Correlation Function and Power Spectral Density of the Target Return Signal	36	(9)
2.2.1 Space-Time Correlation Function	36	(5)
2.2.2 The Power Spectral Density of Nonstationary Target Return Signal Fluctuations	41	(4)
2.3 The Correlation Function with the Searching Signal of Arbitrary Shape	45	(6)
2.3.1 General Statements	45	(1)
2.3.2 The Correlation Function with the Narrow-Band Searching Signal	46	(2)
2.3.3 The Correlation Function with the Pulsed Searching Signal	48	(1)
2.3.4 The Average Correlation Function	49	(2)
2.4 The Correlation Function under Scanning of the Three-Dimensional (Space) Target	51	(12)
2.4.1 General Statements	51	(2)
2.4.2 The Correlation Function with the Pulsed Searching Signal	53	(5)
2.4.3 The Target Return Signal Power with the Pulsed Searching Signal	58	(3)
2.4.4 The Correlation Function and Power of the Target Return Signal with the Simple Harmonic Searching Signal	61	(2)
2.5 The Correlation Function in Angle Scanning of the Two-Dimensional (Surface) Target	63	(12)
2.5.1 General Statements	63	(2)
2.5.2 The Correlation Function with the Pulsed Searching Signal	65	(3)
2.5.3 The Target Return Signal Power with the Pulsed Searching Signal	68	(6)
2.5.4 The Correlation Function and Power of the Target Return Signal with the Simple Harmonic Searching Signal	74	(1)
2.6 The Correlation Function under Vertical Scanning of the Two-Dimensional (Surface) Target	75	(7)
2.7 Conclusions	82	(2)
References	84	(5)
Chapter 3 Fluctuations under Scanning of the Three-Dimensional (Space) Target with the Moving Radar	89	(52)
3.1 Slow and Rapid Fluctuations	89	(14)
3.1.1 General Statements	90	(1)
3.1.2 The Fluctuations in the Radar Range	91	(10)
3.1.2.1 The Square Waveform Target Return Signal without Frequency Modulation	95	(1)
3.1.2.2 The Gaussian Target Return Signal without Frequency Modulation	95	(1)
3.1.2.3 The Smoothed Target Return Signal without Frequency Modulation	96	(2)
3.1.2.4 The Square Waveform Target Return Signal with Linear-Frequency Modulation	98	(3)
3.1.2.5 The Gaussian Target Return Signal with Linear-Frequency Modulation	101	(1)
3.1.3 The Doppler Fluctuations	101	(2)
3.2 The Doppler Fluctuations of a High-Deflected Radar Antenna	103	(16)
3.2.1 The Power Spectral Density for an Arbitrary Directional Diagram	103	(8)
3.2.2 The Power Spectral Density for the Gaussian Directional Diagram	111	(1)
3.2.3 The Power Spectral Density for the Sinc-Directional Diagram	112	(4)
3.2.4 The Power Spectral Density for Other Forms of the Directional Diagram	116	(3)
3.3 The Doppler Fluctuations in the Arbitrarily Deflected Radar Antenna	119	(9)
3.3.1 General Statements	119	(3)
3.3.2 The Gaussian Directional Diagram	122	(4)
3.3.3 Determination of the Power Spectral Density	126	(2)
3.4 The Total Power Spectral Density with the Pulsed Searching Signal	128	(8)
3.4.1 General Statements	128	(1)
3.4.2 Interperiod Fluctuations in the Glancing Radar Range	129	(1)
3.4.3 Interperiod Fluctuations in the Fixed Radar Range	129	(6)
3.4.4 Irregularly Moving Radar	135	(1)
3.5 Conclusions	136	(1)
References	137	(4)
Chapter 4 Fluctuations under Scanning of the Two-Dimensional (Surface) Target by the Moving Radar	141	(1)
4.1 General Statements	141	(2)
4.2 The Continuous Searching Nonmodulated Signal	143	(5)
4.3 The Pulsed Searching Signal with Stationary Radar	148	(71)
4.3.1 General Statements	148	(3)
4.3.2 The Arbitrary Vertical-Coverage Directional Diagram: The Gaussian Pulsed Searching Signal	151	(1)
4.3.3 The Arbitrary Vertical-Coverage Directional Diagram: The Square Waveform Pulsed Searching Signal	152	(2)
4.3.4 The Gaussian Vertical-Coverage Directional Diagram: The Square Waveform Pulsed Searching Signal	154	(6)
4.4 The Pulsed Searching Signal with the Moving Radar: The Aspect Angle Correlation Function	160	(1)
4.4.1 General Statements	160	(2)
4.4.2 The Arbitrary Vertical-Coverage Directional Diagram: The Gaussian Pulsed Searching Signal	162	(3)
4.4.3 The Gaussian Vertical-Coverage Directional Diagram: The Gaussian Pulsed Searching Signal	165	(2)
4.4.4 The Wide-Band Vertical-Coverage Directional Diagram: The Square Waveform Pulsed Searching Signal	167	(3)
4.5 The Pulsed Searching Signal with the Moving Radar: The Azimuth Correlation Function	170	(1)
4.5.1 General Statements	170	(4)
4.5.2 The High-Deflected Radar Antenna	174	(2)
4.5.3 The Low-Deflected Radar Antenna	176	(2)
4.6 The Pulsed Searching Signal with the Moving Radar: The Total Correlation Function and Power Spectral Density of the Target Return Signal Fluctuations	178	(1)
4.6.1 General Statements	178	(1)
4.6.2 The Gaussian Directional Diagram: The Gaussian Pulsed Searching Signal	179	(5)
4.6.3 The Gaussian Directional Diagram: The Square Waveform Pulsed Searching Signal	184	(4)
4.6.4 The Pulsed Searching Signal with Low Pulse Period-to-Pulse Duration Ratio	188	(1)
4.7 Short-Range Area of the Radar Antenna	189	(4)
4.8 Vertical Scanning of the Two-Dimensional (Surface) Target	193	(1)
4.8.1 The Intraperiod Fluctuations in Stationary Radar	193	(5)
4.8.2 The Interperiod Fluctuations with the Vertically Moving Radar	198	(4)
4.8.3 The Interperiod Fluctuations with the Horizontally Moving Radar	202	(6)
4.9 Determination of the Power Spectral Density	208	(4)
4.10 Conclusions	212	(2)
References	214	(5)
Chapter 5 Fluctuations Caused by Radar Antenna Scanning	219	(36)
5.1 General Statements	219	(7)
5.1.1 The Correlation Function under Space Scanning	219	(3)
5.1.2 The Correlation Function under Surface Scanning	222	(3)
5.1.3 The General Power Spectral Density Formula	225	(1)
5.2 Line Scanning	226	(17)
5.2.1 One-Line Circular Scanning	226	(7)
5.2.2 Multiple-Line Circular Scanning	233	(2)
5.2.3 Line Segment Scanning	235	(6)
5.2.4 Line Circular Scanning with Various Directional Diagrams under Transmitting and Receiving Conditions	241	(2)
5.3 Conical Scanning	243	(6)
5.3.1 Three-Dimensional (Space) Target Tracking	243	(5)
5.3.2 Two-Dimensional (Surface) Target Tracking	248	(1)
5.4 Conical Scanning with Simultaneous Rotation of Polarization Plane	249	(2)
5.5 Conclusions	251	(1)
References	252	(3)
Chapter 6 Fluctuations Caused by the Moving Radar with Simultaneous Radar Antenna Scanning	255	(26)
6.1 General Statements	255	(4)
6.1.1 The Correlation Function in the Scanning of the Three-Dimensional (Space) Target	255	(3)
6.1.2 The Correlation Function in the Scanning of the Two-Dimensional (Surface) Target	258	(1)
6.2 The Moving Radar with Simultaneous Radar Antenna Line Scanning	259	(11)
6.2.1 Scanning of the Three-Dimensional (Space) Target: The Gaussian Directional Diagram	259	(6)
6.2.2 Scanning of the Two-Dimensional (Surface) Target: The Gaussian Directional Diagram	265	(1)
6.2.3 Short-Range Area: The Gaussian Directional Diagram	265	(2)
6.2.4 The Sinc2-Directional Diagram	267	(3)
6.3 The Moving Radar with Simultaneous Radar Antenna Conical Scanning	270	(7)
6.3.1 The Instantaneous Power Spectral Density	270	(3)
6.3.2 The Averaged Power Spectral Density	273	(4)
6.4 Conclusions	277	(1)
References	278	(3)
Chapter 7 Fluctuations Caused by Scatterers Moving under the Stimulus of the Wind	281	(32)
7.1 Deterministic Displacements of Scatterers under the Stimulus of the Layered Wind	281	(8)
7.1.1 The Radar Antenna Is Deflected in the Horizontal Plane	285	(1)
7.1.2 The Radar Antenna Is Deflected in the Vertical Plane	286	(1)
7.1.3 The Radar Antenna Is Directed along the Line of the Moving Radar	287	(1)
7.1.4 The Stationary Radar	288	(1)
7.2 Scatterers Moving Chaotically (Displacement and Rotation)	289	(12)
7.2.1 Amplitudes of Elementary Signals Are Independent of the Displacements of Scatterers	291	(2)
7.2.2 The Velocity of Moving Scatterers Is Random but Constant	293	(2)
7.2.3 The Amplitude of the Target Return Signal Is Functionally Related to Radial Displacements of Scatterers	295	(1)
7.2.4 Chaotic Rotation of Scatterers	296	(2)
7.2.5 Simultaneous Chaotic Displacements and Rotations of Scatterers	298	(3)
7.3 Simultaneous Deterministic and Chaotic Motion of Scatterers	301	(7)
7.3.1 Deterministic and Chaotic Displacements of Scatterers	301	(3)
7.3.2 Chaotic Rotation of Scatterers and Rotation of the Polarization Plane	304	(2)
7.3.3 Chaotic Displacements of Scatterers and Rotation of the Polarization Plane	306	(2)
7.4 Conclusions	308	(2)
References	310	(3)
Chapter 8 Fluctuations under Scanning of the Two-Dimensional (Surface) Target with the Continuous Frequency-Modulated Signal	313	(62)
8.1 General Statements	313	(4)
8.2 The Linear Frequency-Modulated Searching Signal	317	(7)
8.3 The Asymmetric Saw-Tooth Frequency-Modulated Searching Signal	324	(26)
8.3.1 Sloping Scanning	329	(11)
8.3.2 Vertical Scanning and Motion	340	(5)
8.3.3 Vertical Scanning: The Velocity Vector Is Outside the Directional Diagram	345	(5)
8.4 The Symmetric Saw-Tooth Frequency-Modulated Searching Signal	350	(8)
8.5 The Harmonic Frequency-Modulated Searching Signal	358	(8)
8.6 Phase Characteristics of the Transformed Target Return Signal under Harmonic Frequency Modulation	366	(4)
8.7 Conclusions	370	(2)
References	372	(3)
Chapter 9 Fluctuations under Scanning of the Three-Dimensional (Space) Target by the Continuous Signal with a Frequency that Varies with Time	375	(26)
9.1 General Statements	375	(3)
9.2 The Nontransformed Target Return Signal	378	(14)
9.2.1 The Searching Signal with Varying Nonperiodic Frequency	378	(5)
9.2.2 The Periodic Frequency-Modulated Searching Signal	383	(5)
9.2.3 The Average Power Spectral Density with the Periodic Frequency-Modulated Searching Signal	388	(4)
9.3 The Transformed Target Return Signal	392	(5)
9.3.1 Nonperiodic and Periodic Frequency-Modulated Searching Signals	392	(2)
9.3.2 The Average Power Spectral Density with the Periodic Frequency-Modulated Searching Signal	394	(3)
9.4 Conclusions	397	(2)
References	399	(2)
Chapter 10 Fluctuations Caused by Variations in Frequency from Pulse to Pulse	401	(20)
10.1 Three-Dimensional (Space) Target Scanning	401	(13)
10.1.1 Nonperiodic Variations in the Frequency of the Searching Signal	401	(4)
10.1.2 The Interperiod Fluctuations	405	(2)
10.1.3 The Average Power Spectral Density	407	(3)
10.1.4 Periodic Frequency Modulation	410	(4)
10.2 Two-Dimensional (Surface) Target Scanning	414	(3)
10.3 Conclusions	417	(1)
References	418	(3)
Part II Generalized Approach to Space-Time Signal and Image Processing in Navigational Systems
Chapter 11 Foundations of the Generalized Approach to Signal Processing in Noise	421	(36)
11.1 Basic Concepts	421	(4)
11.2 Criticism	425	(2)
11.3 Initial Premises	427	(1)
11.4 Likelihood Ratio	428	(5)
11.5 The Engineering Interpretation	433	(3)
11.6 Generalized Detector	436	(13)
11.6.1 The Case of the Slow Fluctuations	443	(3)
11.6.2 The Case of the Rapid Fluctuations	446	(3)
11.7 Conclusions	449	(2)
References	451	(6)
Chapter 12 Theory of Space-Time Signal and Image Processing in Navigational Systems	457	(70)
12.1 Basic Concepts of Navigational System Functioning	457	(6)
12.2 Basics of the Generalized Approach to Signal and Image Processing in Time	463	(9)
12.2.1 The Signal with Random Initial Phase	466	(3)
12.2.2 The Signal with Stochastic Amplitude and Random Initial Phase	469	(3)
12.3 Basics of the Generalized Approach to Space-Time Signal and Image Processing	472	(20)
12.4 Space-Time Signal Processing and Pattern Recognition Based on the Generalized Approach to Signal Processing	492	(7)
12.5 Peculiarities of Optical Signal Formation	499	(10)
12.6 Peculiarities of the Formation of the Earth's Surface Radar Image	509	(4)
12.7 Foundations of Digital Image Processing	513	(6)
12.8 Conclusions	519	(4)
References	523	(4)
Chapter 13 Implementation Methods of the Generalized Approach to Space-Time Signal and Image Processing in Navigational Systems	527	(1)
13.1 Synthesis of Quasioptimal Space-Time Signal and Image Processing Algorithms Based on the Generalized Approach to Signal Processing	527	(58)
13.1.1 Criterial Correlation Functions	529	(2)
13.1.2 Difference Criterial Functions	531	(1)
13.1.3 Spectral Criterial Functions	532	(1)
13.1.4 Bipartite Criterial Functions	533	(3)
13.1.5 Rank Criterial Functions	536	(1)
13.2 The Quasioptimal Generalized Image Processing Algorithm	536	(19)
13.3 The Classical Generalized Image Processing Algorithm	555	(6)
13.4 The Difference Generalized Image Processing Algorithm	561	(1)
13.5 The Generalized Phase Image Processing Algorithm	562	(3)
13.6 The Generalized Image Processing Algorithm: Invariant Moments	565	(2)
13.7 The Generalized Image Processing Algorithm: Amplitude Ranking	567	(3)
13.8 The Generalized Image Processing Algorithm: Gradient Vector Sums	570	(3)
13.9 The Generalized Image Processing Algorithm: Bipartite Functions	573	(1)
13.10 The Hierarchical Generalized Image Processing Algorithm	574	(3)
13.11 The Generalized Image Processing Algorithm: The Use of the Most Informative Area	577	(1)
13.12 The Generalized Image Processing Algorithm: Coding of Images	578	(2)
13.13 The Multichannel Generalized Image Processing Algorithm	580	(1)
13.14 Conclusions	581	(1)
References	582	(3)
Chapter 14 Object Image Preprocessing	585	(16)
14.1 Object Image Distortions	585	(1)
14.2 Geometrical Transformations	585	(10)
14.2.1 The Perspective Transformation	586	(3)
14.2.2 Polynomial Estimation	589	(3)
14.2.3 Transformations of Brightness Characteristics	592	(3)
14.3 Detection of Boundary Edges	595	(3)
14.4 Conclusions	598	(1)
References	599	(2)
Appendix I Classification of Stochastic Processes	601	(12)
References	612	(1)
Appendix II The Power Spectral Density of the Target Return Signal with Arbitrary Velocity Vector Direction of the Moving Radar in Space and with the Presence of Roll and Pitch Angles	613	(8)
References	620	(1)
Notation Index	621	(10)
Index	631