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E-raamat: Signal and Image Processing in Navigational Systems

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Signal and Image Processing in Navigational SystemsSuurem pilt
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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.
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
Tuzlukov, Vyacheslav
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