Autonomous Ground Systems Improved Relative Positioning for Path Following in Autonomous Convoys Troupe Tabb, Dr. Scott Martin, Dr. David Bevly, & Jeff Ratowski DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited. 8/9/2018
Autonomous Ground Motivation Systems Autonomous vehicle convoying requires precise path following independent of maintaining a constant line-of-sight between vehicles. – Cameras, radar, and lidar are effective sensors but must ”see” their targets. DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited. 8/9/2018 2
Autonomous Ground Solution Systems • The Global Positioning System (GPS) can be utilized to assist these sensors when vehicles are in view and provide precise relative positioning when the line-of- sight is blocked. 8/9/2018 DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited. 3
Autonomous Ground Systems Multi-Antenna Dynamic Base Real-Time Kinematic Positioning (DRTK) A differential GPS technique for centimeter level positioning 8/9/2018 DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited. 4
Autonomous Ground Conventional DRTK Systems • The conventional method differences measurements from two receivers, resolves integer ambiguities, and provides a relative position vector. – An extension of Real-Time Kinematic (RTK) positioning – No need for a static base station with a surveyed global position – Provides centimeter level relative position between antennas – Does not provide centimeter level global position 8/9/2018 DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited. 5
Autonomous Ground GPS Measurement Models Systems Single-Differenced Pseudorange 𝜠𝝇 = 𝒔 𝒔,𝒄 + 𝒅𝒄 𝒔,𝒄 + 𝜽 𝒔,𝒄 𝒔 𝒔,𝒄 - True distance between rover and base 𝒅𝒄 𝒔,𝒄 - Clock bias between rover and base scaled by 𝒅 the speed of light to be expressed in meters 𝜽 𝒔,𝒄 - Noise on measurement increased by differencing Single-Differenced Carrier Phase 𝜠𝝌 = 𝒔 𝒔,𝒄 + 𝒅𝒄 𝒔,𝒄 + 𝝁𝑶 𝒔,𝒄 + 𝜽 𝒔,𝒄 𝝁𝑶 𝒔,𝒄 - Integer ambiguity term scaled by the respective wavelength 𝝁 of carrier to be expressed in meters 8/9/2018 DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited. 6
Autonomous Ground Process Systems 1. Relative carrier phase ambiguities are estimated as decimals (float solution). (Sub-meter precision) 2. The float solution estimates are intelligently rounded to integer values using the LAMBDA method 3. The high precision relative position vector (HPRPV) is calculated between the two receivers. (Centimeter precision) 8/9/18 DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited. 7
Autonomous Ground Hardware Configuration Systems 8/9/2018 DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited. 8
Autonomous Ground Fixed-Baseline RTK Systems • Adding a measurement of the fixed baseline between two antennas. – Low-precision estimates are constrained to a circle with radius equal to baseline magnitude – RTK measured baseline variance 0.01 𝑑𝑛 2 𝒚 𝒔,𝒄 𝒛 𝒔,𝒄 𝒜 𝒔,𝒄 𝑰 = 𝟏 𝟏 𝟐𝒚𝒏 𝝇 𝒄 𝝇 𝒄 𝝇 𝒄 𝟑 𝟑 𝟑 𝝇 𝒄 = 𝒚 𝒔,𝒄 + 𝒛 𝒔,𝒄 + 𝒜 𝒔,𝒄 8/9/2018 DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited. 9
Autonomous Ground DRTK with Known Baseline Systems States Measurements 𝒚 𝒔,𝒄 𝑴𝟐 Observation Matrix ∆𝝇 𝒔,𝒄 𝒚 𝒔,𝒄 𝑴𝟑 ∆𝝇 𝒔,𝒄 𝒋 𝒋 𝒋 𝒃 𝒚 𝒃 𝒛 𝒃 𝒜 −𝟐 𝟏 𝒏𝒚𝒏 𝒛 𝒔,𝒄 𝑴𝟐 𝒜 = 𝜠𝝌 𝒔,𝒄 𝒋 𝒋 𝒋 𝒛 𝒔,𝒄 𝒃 𝒚 𝒃 𝒛 𝒃 𝒜 −𝟐 𝞵𝑱 𝒏𝒚𝒏 𝑰 = 𝑴𝟐 𝒜 𝒔,𝒄 𝜠𝝌 𝒔,𝒄 𝒚 𝒔,𝒄 𝒛 𝒔,𝒄 𝒜 𝒔,𝒄 𝟏 𝟏 𝟐𝒚𝒏 𝒜 𝒔,𝒄 |𝒔 𝒔,𝒄 | 𝝇 𝒄 𝝇 𝒄 𝝇 𝒄 𝒅𝒄 𝒔,𝒄 𝒀 = State Covariance Measurement Noise Covariance 𝒅𝒄 𝒔,𝒄 𝟑 𝑸 𝒚 𝟏 ⋯ 𝟏 𝟑 𝝉 𝒔 𝑬𝑴𝑴 + 𝝉 𝒄 𝑬𝑴𝑴 𝟏 𝟏 𝟐 𝑶 𝒔,𝒄 ⋮ ⋱ ⋮ 𝑸 𝟏 = 𝟑 𝟑 . 𝑺 = 𝟏 𝝉 𝒔 𝑸𝑴𝑴 + 𝝉 𝒄 𝑸𝑴𝑴 𝟏 𝒏 𝟏 ⋯ 𝑸 𝑶 𝟏 . 𝟑 𝟏 𝟏 𝝉 𝒔𝒖𝒍 . 𝒏 𝑶 𝒔,𝒄 8/9/2018 DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited. 10
Autonomous Ground State Transition & Process Noise Systems 𝜸 𝟏 𝟑𝒚𝟑 𝟏 𝟑𝒚𝟑 𝟏 𝟑𝒚𝟑 𝟏 𝟑𝒚𝒏 𝟏 𝟑𝒚𝟑 𝜸 𝟏 𝟑𝒚𝟑 𝟏 𝟑𝒚𝟑 𝟏 𝟑𝒚𝒏 𝜸 = 𝟐 ∆𝒖 𝟏 𝟑𝒚𝟑 𝟏 𝟑𝒚𝟑 𝜸 𝟏 𝟑𝒚𝟑 𝟏 𝟑𝒚𝒏 𝝔 = 𝟏 𝟐 𝟏 𝟑𝒚𝟑 𝟏 𝟑𝒚𝟑 𝟏 𝟑𝒚𝟑 𝜸 𝟏 𝟑𝒚𝒏 𝟏 𝒏𝒚𝟑 𝟏 𝒏𝒚𝟑 𝟏 𝒏𝒚𝟑 𝟏 𝒏𝒚𝟑 𝑱 𝒏𝒚𝒏 𝑹 𝒚 𝟏 𝟑𝒚𝟑 𝟏 𝟑𝒚𝟑 𝟏 𝟑𝒚𝟑 𝟏 𝟑𝒚𝒏 𝟏 𝟑𝒚𝟑 𝑹 𝒛 𝟏 𝟑𝒚𝟑 𝟏 𝟑𝒚𝟑 𝟏 𝟑𝒚𝒏 𝑹 = 𝟏 𝟑𝒚𝟑 𝟏 𝟑𝒚𝟑 𝑹 𝒜 𝟏 𝟑𝒚𝟑 𝟏 𝟑𝒚𝒏 𝟏 𝟑𝒚𝟑 𝟏 𝟑𝒚𝟑 𝟏 𝟑𝒚𝟑 𝑹 𝒅𝒄 𝟏 𝟑𝒚𝒏 𝟏 𝒏𝒚𝟑 𝟏 𝒏𝒚𝟑 𝟏 𝒏𝒚𝟑 𝟏 𝒏𝒚𝟑 𝑹 𝑶 8/9/2018 DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited. 11
Autonomous Ground Multi-Antenna DRTK Systems Vector addition provides additional measurements 𝑴𝟐 𝝇 𝟐𝟒 𝝌 𝟑𝟒 = 𝝌 𝟐𝟒 − 𝝌 𝟐𝟑 𝑴𝟑 𝝇 𝟐𝟒 𝑴𝟐 𝝇 𝟐𝟒 Carrier Measurement Model 𝑴𝟑 𝝌 𝟐𝟒 = 𝝌 𝟑𝟒 +𝒔 𝟐𝟑 + 𝝁𝑶 𝟐𝟑 + 𝒅𝒄 𝟐𝟑 𝝇 𝟐𝟒 𝒜 = = 𝒔 𝟐𝟒 + 𝝁𝑶 𝟐𝟒 + 𝒅𝒄 𝟐𝟒 𝑴𝟐 𝝌 𝟐𝟒 𝑴𝟑 𝝌 𝟐𝟒 Similarly, for Pseudorange, 𝑴𝟐 𝝌 𝟐𝟒 𝝇 𝟐𝟒 = 𝝇 𝟑𝟒 + 𝒔 𝟐𝟑 + 𝒅𝒄 𝟐𝟑 = 𝒔 𝟐𝟒 + 𝒅𝒄 𝟐𝟒 𝑴𝟑 𝝌 𝟐𝟒 DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited. 8/9/2018 12
Autonomous Ground Simulations Systems • Simulated data was used for algorithm development. • 10 Minutes of experimental data including cycle slips, signal loss, and multipath error was used for validation. 8/9/2018 DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited. 13
Autonomous Ground Simulated Data Systems Float estimates converging to the correct single-differenced integer ambiguities 8/9/2018 DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited. 14
Autonomous Ground Simulated Data (ERROR) Systems Multi-Antenna Conventional 8/9/2018 DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited. 15
Autonomous Ground Experimental Data Systems 8/9/2018 DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited. 16
Autonomous Ground Statistics Systems Time-to-Fix Multi-Antenna Conventional Time-to-fix statistics are derived 𝜈 = 2.40 𝑡 𝜈 = 1.75 𝑡 from 1000 runs of simulated data. 𝜏 = 2.60 𝑡 𝜏 = 1.40 𝑡 Total Error after 10 Minutes Multi-Antenna Conventional 𝜈 = 1.83 𝑑𝑛 𝜈 = 4.72 𝑑𝑛 This error data includes signal loss and cycle slips; the estimator is 𝜏 = 9.16 𝑑𝑛 𝜏 = 7.97 𝑑𝑛 reset after these are detected. 8/9/2018 DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited. 17
Autonomous Ground Multi-Antenna Error Systems • Time-to-fix is improved. • Centimeter-level error after fixing, regardless of method. Initial fixing of correct integer ambiguities 8/9/2018 DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited. 18
Autonomous Ground Conclusion Systems • Time-to-fix is improved over conventional method by incorporating known baseline information between antennas. • Float solutions are improved upon with this proposed multi-antenna technique. • The multi-antenna algorithm is more robust to disturbances caused by signal loss and cycle slips. 8/9/2018 DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited. 19
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