The book starts with a theoretical study of the relationship between phase frequency functions on a two-dimensional plane. This is followed by explanations of detection methods using unambiguous phase parameters. The analysis demonstrates how difference change rates work with parameters for measuring phase difference and wavelength integers. In addition, there is a jump phenomenon between the difference term of phase difference and the difference value of the wavelength integer, that can be used to mathematically compute the distance between these parameters respectively.
The results in this work have interesting implications for location measurement with a lack of phase ambiguity. The methods show a framework for converting signal processing models for passive location detection systems for unambiguous phase difference calculations. It also provides an effective solution to the problem of how to eliminate the influence of the measurement error of the wavelength integer difference on the positioning accuracy.
Key Features:
- Sequentially presents theoretical frameworks to build the reader's knowledge for better understanding the topics
- Presents a unique method for measuring the motion parameters on a moving platform based on unambiguous phase difference measurement parameters.
- Summarizes phase difference location methods, including direction finding and ranging
- Discusses passive methods of phase difference localization by means of virtual observation
- Includes references for further reading
Table of Contents
Chapter 1 The General Solution of the Phase Difference Positioning Equation
1.1 Introduction
1.2. The Uncertainty of Phase Shift Ranging
1.3. Phase Difference Detection of Path Difference
1.4. Fundamental Solutions of Asymmetrical Onedimensional Double-Base Arrays
1.5. Linear Solutions of One-Dimensional Symmetric Double-Base Array
1.5.1. Benchmark the Midpoint of the Array
1.5.2. Benchmark the Left End of the Array
1.5.3. Benchmark the Right End of the Array
Conclusion
References
Chapter 2 Internal Characteristics of Double-Base Array
2.1 Introduction
2.2. Single Base Midpoint Direction Finding Formula
2.2.1. Overview
2.2.2. Formula Simplification Method
2.2.3. Path Difference Approximation
2.2.4. Trigonometric Method
2.2.5. Geometric Projection
2.2.5.1. Compensation Angle
2.2.5.2. Projection of Baseline on Path Difference
2.2.5.3. Expansion of the Projection Formula
2.2.5.4. Approximate Simplification
2.2.5.5. Analog Calculation
2.2.6. Summary
2.3. the Arithmetic Series Relationship Between Adjacent Path Differences
2.3.1. Overview
2.3.2. the Difference Function of the Path Difference?
2.3.3. Geometric Diagram of Tolerances
2.3.4. Physical Characteristics
2.3.4.1. Approximate Simplification of the Ranging Solution
2.3.4.2. Movement Time Difference of Detection Platform
2.3.4.3. Acceleration Characteristic -- Relationship To the Doppler Rate of Change
2.3.4.4. Speed Characteristic -- Relationship To the Phase Difference Rate of Change
2.3.5. Summary
2.4. Median Relation Among Three Arrival Angles
2.4.1. Overview
2.4.2. the Median Relationship Based on the Tangent Function
2.4.3. the Median Relationship Based on the Sine Function
2.4.4. Mean Relation Among Three Arrival Angle
2.4.5. Mutual Offset Characteristics of Calculated Deviations
2.5. Median Relation Among Three Radial Distances
2.5.1. Overview
2.5.2. Approximate Results
2.5.3. Rigorous Derivation
2.5.4. Summary
Conclusion
References
Chapter 3 Path Difference and Its Difference Function
3.1 Introduction
3.2. Multi-Channel Phase Difference Detection of Phase Difference 3.2.1. Overview
3.2.2.1. Difference Approximation
3.2.3. the Phase Difference Rate
3.3. Difference Function of Path Difference
3.3.1. Overview
3.3.2. Decomposition of a Phase Change Function
3.3.3. Change Rule
3.3.4. Correction of Phase Jump
3.3.5. Validation
3.3.6. Summary
3.4. Error Analysis
3.4.1. Analyse
3.4.2. Summary
3.5. Non-Fuzzy Phase Difference Measurement of Path Difference
Conclusion
References
Chapter 4 Unambiguous Phase Difference Measurement of Positioning Parameters
4.1. Unambiguous Phase Difference Measurement of Doppler Parameters
4.1.2. Fuzzy - Free Solution of Doppler Shift
4.1.2.1. Definition
4.1.2.2. Function Relation Between Frequency Shift and Phase Shift Change Rate
4.1.2.3. Relation Between Frequency Shift and Phase Difference
4.1.2.4. Non-Fuzzy Solution of Frequency Shift
4.1.3. Unambiguous Phase Difference Measurement of Frequency Difference
4.1.3.1. Derivation
4.1.3.2. Validation
4.3.3.3. Measurement Error
4.1.4. Unambiguous Phase Difference Measurement of Doppler Change Rate
4.1.4.1. Overview
4.1.4.2. Based on the Function Between the Frequency Shift and the Radial Distance Change Rate
4.1.4.3. Based on the Functional Relationship Between Frequency Shift and Phase Difference
4.1.4.4. Unambiguous Representation
4.1.4.5. Relative Calculation Error
4.1.4.6. Error Analysis
4.1.4.7. Summary
4.2. Unambiguous Phase Difference Measurement of Motion Parameters
4.2.2. Relative Angular Velocity
4.2.2.1. Overview
4.2.2.2. the Derivation of the Formula
4.2.2.3. a Relation Between the Frequency Difference and Angular Velocity
4.2.2.4. Unambiguous Solution
4.2.2.5. Analog Calculation
4.2.2.6. Error Analysis
4.2.2.7. Summary
4.2.3. Radial Acceleration
4.2.3.1. Overview
4.2.3.2. Derived
4.2.3.3. Estimation of Detection Accuracy
4.2.3.4. Summary
4.3. Orthogonal Velocity Component
References
Chapter 5 Unambiguous Phase Difference Direction Finding Based on Short Baseline Array
5.1 Introduction
5.2. Unambiguous Phase Difference Direction Finding Based on Virtual Short Baseline
5.2.1. Overview
5.2.2. Approximate Direction Finding Based on Phase Interference
5.2.2.1. Plane Wave Hypothesis
5.2.2.2. Difference Approximation
5.2.3. Proof of Formula
5.2.4. Array Construction
5.2.5. Locating Datum
5.2.6. Virtual Direction-Finding Formula
5.2.7. Phase Jump
5.2.8. Correction of Jump
5.2.9. Relative Calculation Error
5.2.9.1. Data
5.2.9.2. Baseline Length
5.2.9.3. Proportional Coefficient
5.2.9.4. Broadband Variation Characteristics
5.2.10. the Error Analysis
5.2.11. Compound Measurement -- Improvement of Direction - Finding Accuracy
5.2.11.1. Overview
5.2.11.2. Geometric Similarity
5.2.11.3. Composite Solution
5.2.12. Composite Array -- Reduce Direction-Finding Error
5.2.13. Summary
5.3. the Effect of the Wavelength Number Difference
5.3.1. Overview
5.3.2. the Solution To the Wavenumber Difference
5.3.3. Rms Measurement Error
5.3.4. Virtual Direction-Finding Formula
5.4. Orthogonal Phase Difference Direction-Finding Method Based on Equivalent Simulation
5.4.2. Normalization
5.4.3. Geometric Interpretation
5.4.4. Orthogonal Array
5.4.5. Maximum Direction Finding
5.4.6. Simulation Calculation
5.4.7. the Error Analysis
5.4.8. Summary
5.5. Airborne Direction-Finding Method Based on Doppler-Phase Measurement
5.5.1. Overview
5.5.2. Ratio of Doppler Frequency Shift Change Rate
5.5.3. Integer Value of Radial Distance
5.5.4. Df Equation Based on Doppler Shift-Phase Difference
5.5.5. Summary
References
Chapter 6 Unambiguous Phase Difference Ranging for Short Baseline Double-Base Symmetric Array
6.1 Fundamental Formula
6.2. Approximate Solution
6.2.1. A More Regular Representation
6.3. Ranging Based on Phase Change Rate
6.4. Ranging Based on Doppler Rate of Change
6.4.1. Direct Solution
6.4.2. Indirect Solution
6.5. Ranging Based on Radial Acceleration
6.6. Relative Calculation Error
6.7. Error Analysis
Conclusion
References
Chapter 7 Error Conversion Factor Between Angle and Phase Measurements
7.1. Overview
7.2. Total Differential Analysis of Measurement Error
7.2.1. the Transformation From Phase Difference To Angle -- Single-Base Array
7.2.2. the Transformation From Phase Difference To Angle -- Virtual Short Baseline
7.2.3. Analysis
7.3. High Order Direction Finding Method
7.3.1. Overview
7.3.2. Variable Transformation
7.3.3. Decrease Order Deduction
7.3.4. Evolution of Layout
7.3.5. Error Analysis
7.4. Virtual Extension of Baseline Length of Bi-Station Direction- Finding Array
7.4.1. Overview
7.4.2. Virtual Extensions Based on Angles Only
7.4.3. a Virtual Extension
7.4.3.1. Derivation
7.4.3.2. Error Analysis
7.4.3.3. Mathematical Explanation
7.4.4. Secondary Virtual Extensions
7.4.4.1. Geometrical Relationship
7.4.4.2. Virtual Ranging Solution
7.4.4.3. Error Analysis
7.4.5. Summary
7.5. Passive Ranging Formula for Two Detection Platforms With Different Motion Directions
7.5.1. Overview
7.5.2. Plane Geometric Models
7.5.3. Positioning Equation
7.5.4. Simulation Verification
7.5.5. Error Analysis
7.5.6. Summary
Author
- Tao Yu
