Theoretical Study of an RF Positioning System Using Phase Synchronized Anchor Nodes

78 Pages·2011·2.53 MB·English

Theoretical Study of an RF Positioning
System Using Phase Synchronized
Anchor Nodes

Author:
Juan Carlos Rodríguez Silva

Universitat Politècnica de Catalunya
Department of Signal Theory and Communications
July 20th 2011
Thesis Director:
Jordi Joan Mallorquí Franquet

Contents
Contents ....................................................................................................................................................... i
List of Figures/Tables ................................................................................................................................ v
1. Introduction ....................................................................................................................................... 1
1.1 Motivation: SABRINA 2.0 ........................................................................................................ 1
1.2 Objectives .................................................................................................................................... 2
2. Background - State of the art ........................................................................................................... 5
2.1 Elements in a Positioning System ............................................................................................ 5
2.2 Estimation Methods .................................................................................................................. 6
2.2.1 RSS Estimation ..................................................................................................................... 6
2.2.2 TOA and TDOA Estimation ............................................................................................... 7
2.2.3 AOA Estimation ................................................................................................................... 8
2.3 Algorithms .................................................................................................................................. 8
2.3.1 Trilateration Algorithm ....................................................................................................... 8
2.3.2 Multilateration Algorithm .................................................................................................. 9
2.3.3 Triangulation Algorithm .................................................................................................. 10
2.4 Examples of Positioning Systems .......................................................................................... 11
2.4.1 Satellite-Based Positioning Systems ................................................................................ 11
2.4.1.1 GLONASS .................................................................................................................. 11
2.4.1.2 GALILEO ................................................................................................................... 11
2.4.1.3 GPS .............................................................................................................................. 12
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2.4.2 Monotone-based System ................................................................................................... 13
2.4.3 Chirp-based System ........................................................................................................... 14
2.4.4 TRX Sentrix – Commercial Example ............................................................................... 15
3. System Design ................................................................................................................................. 17
3.1 Elements to define ................................................................................................................... 17
3.1.1 Design Constraints ............................................................................................................ 17
3.1.2 System Architecture .......................................................................................................... 19
3.1.3 Estimation Technique and Transmitted Signal ............................................................. 20
3.1.4 Sampling Frequencies ....................................................................................................... 20
3.2 Phase Synchronization Scheme ............................................................................................. 21
3.3 Design Calculations ................................................................................................................. 22
3.3.1 Signal Characteristics ........................................................................................................ 22
3.3.1.1 Tx-Rx Chain ............................................................................................................... 22
3.3.1.2 Transmission time delay .......................................................................................... 24
3.3.1.3 Chirp Compression ................................................................................................... 24
3.3.1.4 Signal Broadcast Structure ....................................................................................... 26
3.3.2 Retrieving the Distance Information ............................................................................... 27
3.3.2.1 Time Analysis (TDOA) ............................................................................................. 27
3.3.2.1.1 Hyperbola vs. Hyperboloid ................................................................................ 28
3.3.2.1.2 Straightforward Solution ..................................................................................... 30
3.3.2.1.3 Matrix of Differences ............................................................................................ 31
3.3.2.1.4 Direct Method ....................................................................................................... 33
3.3.2.1.5 Least-Square Method ........................................................................................... 33
3.3.2.1.6 Chan’s Method ...................................................................................................... 33
3.3.2.1.7 Taylor Series Expansion Method ........................................................................ 33
3.3.2.1.8 Steepest Descent Method ..................................................................................... 35
3.3.2.2 Phase Analysis ........................................................................................................... 37
3.3.2.2.1 Phase Ambiguity Equation ................................................................................. 37
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3.3.2.2.2 Relation between phase and distance ................................................................ 38
3.4 Error theory .............................................................................................................................. 39
3.4.1 Systematic Errors ............................................................................................................... 39
3.4.2 Multipath on MIMO channels ......................................................................................... 40
3.4.3 Accuracy of TDOA ............................................................................................................ 40
3.4.3.1 Variance ...................................................................................................................... 41
3.4.3.2 Cramer-Rao Lower Bound ....................................................................................... 41
3.4.3.2.1 Optimized Topology ............................................................................................ 43
3.5 Validation and results ............................................................................................................. 43
3.5.1 Design Equations ............................................................................................................... 43
3.5.2 Taylor Series Expansion (TSE) ......................................................................................... 48
3.5.3 Quantization error ............................................................................................................. 50
3.5.4 Real Implementation Example ......................................................................................... 51
3.6 Summary ................................................................................................................................... 53
4. Implementation ............................................................................................................................... 55
4.1 SABRINA 2.0 ............................................................................................................................ 55
4.2 Positioning System: Feasibility .............................................................................................. 58
4.2.1 Memory: Number of Bits .................................................................................................. 58
4.2.2 Memory: Recording Time ................................................................................................. 59
4.2.3 Processing Time ................................................................................................................. 59
4.3 Position System: Receiver Corrections ................................................................................. 59
4.3.1 Oscillator Phase Correction .............................................................................................. 59
4.3.2 Matched Filter Correction ................................................................................................. 60
4.4 Further Improvements ............................................................................................................ 60
4.4.1 Data Fusion Techniques .................................................................................................... 60
4.4.2 Kalman Filter ...................................................................................................................... 61
5. Conclusions ..................................................................................................................................... 63
Bibliography ............................................................................................................................................. 65
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List of Figures/Tables

Figure 1. Trilateration situation ............................................................................................................... 8
Figure 2. Multilateration System Architecture. ..................................................................................... 9
Figure 3. Triangulation Situation .......................................................................................................... 10
Figure 4. GPS (Left) and Galileo (Right) Constellations. .................................................................... 12
Figure 5. Phase Model in Wang's System ............................................................................................. 13
Figure 6. Wang's System Timing Sequence.......................................................................................... 14
Figure 7. Chirp System Example Architecture. ................................................................................... 15
Figure 8. TRX Systems' Sentrix .............................................................................................................. 15
Figure 9. Helikite Picture showed in their website. ............................................................................ 18
Figure 10. General System Architecture. .............................................................................................. 19
Figure 11. Simplified Phase Synchronization Scheme. ....................................................................... 21
Figure 12. Tx - Rx Chain. ........................................................................................................................ 22
Figure 13. Compressed Chirp Expression. ........................................................................................... 25
Figure 14. Time Structure of intervals for baseband Chirps. ............................................................. 26
Figure 15. General Hyperbola. ............................................................................................................... 28
Figure 16. Hyperboloid revolution axes and coplanar cut ............................................................... 29
Figure 17. One Sheet (Left) and Two Sheets (Right) hyperboloids ................................................... 30
Figure 18. Estimated location using the Matrix of differences (Left); Detail showing the interval
of ambiguity (Right). ............................................................................................................................... 32
Figure 19. Particular example when the measured TDOA is 0. ........................................................ 32
Figure 20. Flux Diagram for HOA implementation............................................................................ 36
Figure 21. Unwrapped vs. Wrapped phase. ........................................................................................ 37
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Figure 22. Spatial step when measuring the phase. ............................................................................ 37
Figure 23. From left to right: Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron ...... 43
Figure 24. Error magnitude variations vs. Bw and sampling frequency. (a) is the one at the top
and (c) the one at the bottom. ................................................................................................................ 45
Figure 25. Magnitude of the Error vs. Variation of Sampling frequency ........................................ 46
Figure 26. fdp of TDOA Measurements, each color representing a range difference. ................... 47
Figure 27. 10 iterations of the fdp of TDOA Measurements. ............................................................. 47
Figure 28. Measured Distance Differences (Left). Sample Difference in meters (Right). .............. 47
Figure 29. UAV Nominal Trajectory. .................................................................................................... 48
Figure 30. Noisy Measurements of TDOA ........................................................................................... 49
Figure 31. Estimated Trajectory vs. Nominal Trajectory .................................................................... 49
Figure 32. Detail of the first 10 positions of the trajectory (Estimated vs. Real). ............................ 49
Figure 33. Error in 3D (Top left). XY plane cut (Top Right). XZ plane cut (Bottom Right). Error
Magnitude Evolution (Bottom Left). ..................................................................................................... 50
Figure 34. CEP comparison: optimal vs. original (left). Original topology (center). Optimized
topology (Right). ...................................................................................................................................... 51
Figure 35. RF Positioning System Simulation Tool v2.1 ..................................................................... 52
Figure 36. Simplified scheme of SABRINA .......................................................................................... 55
Figure 37. SABRINA 2.0 RF Architecture ............................................................................................. 56
Figure 38. Top view of the SMT-941 + SMT351T + SMT111 Board ................................................... 57
Figure 39. DDR2 Memory Bank connections. ...................................................................................... 58
Figure 40. MLX90360 degrees of freedom. ........................................................................................... 61

Table 1. Contrast of the possible Schemes. ........................................................................................... 20
Table 2. Design Parameters and Variables. .......................................................................................... 46

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