Autonomous Ground Systems Improved Relative Positioning for Path - - PowerPoint PPT Presentation

Autonomous Ground Systems

8/9/2018

Improved Relative Positioning for Path Following in Autonomous Convoys

Troupe Tabb, Dr. Scott Martin, Dr. David Bevly, & Jeff Ratowski

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Autonomous Ground Systems

8/9/2018 2

Motivation

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.

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8/9/2018 3

Solution

• 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.

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Multi-Antenna Dynamic Base Real-Time Kinematic Positioning (DRTK)

A differential GPS technique for centimeter level positioning

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Conventional DRTK

• 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

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8/9/2018 6

GPS Measurement Models

Single-Differenced Pseudorange

𝜠𝝇 = 𝒔𝒔,𝒄 + 𝒅𝒄𝒔,𝒄 + 𝜽𝒔,𝒄

𝒔𝒔,𝒄 - True distance between rover and base 𝒅𝒄𝒔,𝒄- Clock bias between rover and base scaled by 𝒅 the speed of light to be expressed in meters 𝜽𝒔,𝒄 - Noise on measurement increased by differencing

Single-Differenced Carrier Phase

𝜠𝝌 = 𝒔𝒔,𝒄 + 𝒅𝒄𝒔,𝒄 + 𝝁𝑶𝒔,𝒄 + 𝜽𝒔,𝒄

𝝁𝑶𝒔,𝒄- Integer ambiguity term scaled by the respective wavelength 𝝁 of

carrier to be expressed in meters

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8/9/18 7

Process

• 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)

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8/9/2018 8

Hardware Configuration

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8/9/2018 9

Fixed-Baseline RTK

• 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 𝑑𝑛2

𝑰 = 𝒚𝒔,𝒄 𝝇𝒄 𝒛𝒔,𝒄 𝝇𝒄 𝒜𝒔,𝒄 𝝇𝒄 𝟏 𝟏𝟐𝒚𝒏

𝝇𝒄 = 𝒚𝒔,𝒄

𝟑

+ 𝒛𝒔,𝒄

𝟑

+ 𝒜𝒔,𝒄

𝟑

DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited.

Autonomous Ground Systems

8/9/2018 10

DRTK with Known Baseline

𝒀 = 𝒚𝒔,𝒄 𝒚𝒔,𝒄 𝒛𝒔,𝒄 𝒛𝒔,𝒄 𝒜𝒔,𝒄 𝒜𝒔,𝒄 𝒅𝒄𝒔,𝒄 𝒅𝒄𝒔,𝒄 𝑶𝒔,𝒄

𝟐

. . . 𝑶𝒔,𝒄

𝒏

States 𝒜 = ∆𝝇𝒔,𝒄

𝑴𝟐

∆𝝇𝒔,𝒄

𝑴𝟑

𝜠𝝌𝒔,𝒄

𝑴𝟐

𝜠𝝌𝒔,𝒄

𝑴𝟐

|𝒔𝒔,𝒄| Measurements 𝑰 = 𝒃𝒚

𝒋

𝒃𝒛

𝒋

𝒃𝒜

𝒋

−𝟐 𝟏𝒏𝒚𝒏 𝒃𝒚

𝒋

𝒃𝒛

𝒋

𝒃𝒜

𝒋

−𝟐 𝞵𝑱𝒏𝒚𝒏 𝒚𝒔,𝒄 𝝇𝒄 𝒛𝒔,𝒄 𝝇𝒄 𝒜𝒔,𝒄 𝝇𝒄 𝟏 𝟏𝟐𝒚𝒏 Observation Matrix Measurement Noise Covariance 𝑺 = 𝝉𝒔𝑬𝑴𝑴

𝟑

+ 𝝉𝒄𝑬𝑴𝑴

𝟑

𝟏 𝟏 𝟏 𝝉𝒔𝑸𝑴𝑴

𝟑

+ 𝝉𝒄𝑸𝑴𝑴

𝟑

𝟏 𝟏 𝟏 𝝉𝒔𝒖𝒍

𝟑

State Covariance 𝑸𝟏 = 𝑸𝒚𝟏 ⋯ 𝟏 ⋮ ⋱ ⋮ 𝟏 ⋯ 𝑸𝑶𝟏

𝒏

DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited.

Autonomous Ground Systems

8/9/2018 11

State Transition & Process Noise

𝝔 = 𝜸 𝟏𝟑𝒚𝟑 𝟏𝟑𝒚𝟑 𝟏𝟑𝒚𝟑 𝟏𝟑𝒚𝒏 𝟏𝟑𝒚𝟑 𝜸 𝟏𝟑𝒚𝟑 𝟏𝟑𝒚𝟑 𝟏𝟑𝒚𝒏 𝟏𝟑𝒚𝟑 𝟏𝟑𝒚𝟑 𝜸 𝟏𝟑𝒚𝟑 𝟏𝟑𝒚𝒏 𝟏𝟑𝒚𝟑 𝟏𝟑𝒚𝟑 𝟏𝟑𝒚𝟑 𝜸 𝟏𝟑𝒚𝒏 𝟏𝒏𝒚𝟑 𝟏𝒏𝒚𝟑 𝟏𝒏𝒚𝟑 𝟏𝒏𝒚𝟑 𝑱𝒏𝒚𝒏

𝜸 = 𝟐 ∆𝒖 𝟏 𝟐

𝑹 = 𝑹𝒚 𝟏𝟑𝒚𝟑 𝟏𝟑𝒚𝟑 𝟏𝟑𝒚𝟑 𝟏𝟑𝒚𝒏 𝟏𝟑𝒚𝟑 𝑹𝒛 𝟏𝟑𝒚𝟑 𝟏𝟑𝒚𝟑 𝟏𝟑𝒚𝒏 𝟏𝟑𝒚𝟑 𝟏𝟑𝒚𝟑 𝑹𝒜 𝟏𝟑𝒚𝟑 𝟏𝟑𝒚𝒏 𝟏𝟑𝒚𝟑 𝟏𝟑𝒚𝟑 𝟏𝟑𝒚𝟑 𝑹𝒅𝒄 𝟏𝟑𝒚𝒏 𝟏𝒏𝒚𝟑 𝟏𝒏𝒚𝟑 𝟏𝒏𝒚𝟑 𝟏𝒏𝒚𝟑 𝑹𝑶

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Autonomous Ground Systems

8/9/2018 12

Multi-Antenna DRTK

Vector addition provides additional measurements

𝝌𝟑𝟒 = 𝝌𝟐𝟒 − 𝝌𝟐𝟑 Carrier Measurement Model 𝝌𝟐𝟒 = 𝝌𝟑𝟒 +𝒔𝟐𝟑 + 𝝁𝑶𝟐𝟑 + 𝒅𝒄𝟐𝟑 = 𝒔𝟐𝟒 + 𝝁𝑶𝟐𝟒 + 𝒅𝒄𝟐𝟒 Similarly, for Pseudorange, 𝝇𝟐𝟒 = 𝝇𝟑𝟒 + 𝒔𝟐𝟑 + 𝒅𝒄𝟐𝟑 = 𝒔𝟐𝟒 + 𝒅𝒄𝟐𝟒 𝒜 = 𝝇𝟐𝟒

𝑴𝟐

𝝇𝟐𝟒

𝑴𝟑

𝝇𝟐𝟒

𝑴𝟐

𝝇𝟐𝟒

𝑴𝟑

𝝌𝟐𝟒

𝑴𝟐

𝝌𝟐𝟒

𝑴𝟑

𝝌𝟐𝟒

𝑴𝟐

𝝌𝟐𝟒

𝑴𝟑

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8/9/2018 13

Simulations

• Simulated data was used for algorithm

development.

• 10 Minutes of experimental data

including cycle slips, signal loss, and multipath error was used for validation.

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Simulated Data

Float estimates converging to the correct single-differenced integer ambiguities

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8/9/2018 15

Simulated Data (ERROR)

Multi-Antenna Conventional

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8/9/2018 16

Experimental Data

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8/9/2018 17

Statistics

Time-to-Fix Multi-Antenna Conventional 𝜈 = 1.75 𝑡 𝜈 = 2.40 𝑡 𝜏 = 1.40 𝑡 𝜏 = 2.60 𝑡 Time-to-fix statistics are derived from 1000 runs of simulated data. This error data includes signal loss and cycle slips; the estimator is reset after these are detected. Total Error after 10 Minutes Multi-Antenna Conventional 𝜈 = 1.83 𝑑𝑛 𝜈 = 4.72 𝑑𝑛 𝜏 = 7.97 𝑑𝑛 𝜏 = 9.16 𝑑𝑛

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Multi-Antenna Error

• Time-to-fix is improved.
• Centimeter-level error after

fixing, regardless of method.

Initial fixing of correct integer ambiguities

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Conclusion

• 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.

DISTRIBUTION STATEMENT A. Approved for public release; distribution unlimited.