Andreas Maier, Stefan Kiesel and Gert F. Trommer Outline Objectives - - PowerPoint PPT Presentation

Andreas Maier, Stefan Kiesel and Gert F. Trommer

Institute of Systems Optimization, University of Karlsruhe, Germany Andreas Maier

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Outline

• Objectives
• SAR/INS System Overview
• Synthetic Aperture Radar
• SAR/INS Integration
• Simulation Results
• Conclusion

R crossroads trajectory

Institute of Systems Optimization, University of Karlsruhe, Germany Andreas Maier

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Sensors

• TRN

– long term – autonomous – rough terrain

• SAR (feature based)

– long term – autonomous

• IMU

– short term – autonomous

• GPS

– long term – nonautonomous

Comparison of sensor characteristics

Institute of Systems Optimization, University of Karlsruhe, Germany Andreas Maier

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Objectives

• Implementation of Sigma-point Kalman filter for SAR/

INS integration

• SAR/INS position accuracy analysis
• Investigation of required feature update rates
• SAR/INS in combination with

– Baromeric altimeter – Terrain Referenced Navigation (TRN)

Institute of Systems Optimization, University of Karlsruhe, Germany Andreas Maier

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• Features

Unambiguous and well visible e. g.

• Crossroads
• Courses of rivers
• Feature displacement

Displacement between imaged feature and map feature is used for navigation update

Feature Displacement

flight direction

Institute of Systems Optimization, University of Karlsruhe, Germany Andreas Maier

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System Overview

SAR antenna Feature matching SAR processing

Sensors

Feature data IMU Measurement: Displacement δ of the SAR image with respect to map feature SDA Navigation solution Kalman filter Baro alt. Radar alt.

Institute of Systems Optimization, University of Karlsruhe, Germany Andreas Maier

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• Definition of sensor coordinates

– x in flight direction – z upwards – y forms a right handed coordinate system – Origin is located at ground level

• Transformation matrix

– Transformation from n to s-frame by rotation around down-axis

SAR Sensor

x z y

flight direction north east down

s-frame n-frame position: velocity: aircraft pos.

Institute of Systems Optimization, University of Karlsruhe, Germany Andreas Maier

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SAR Sensor

• Information of each

reflection point form range and Doppler frequency

• SAR-Processing

forms image in xy coordinates

z x y

flight direction

s-frame

feature point

aircraft position

Institute of Systems Optimization, University of Karlsruhe, Germany Andreas Maier

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Displacement

• Map feature has to be transformed into s-frame

coordinates

• Nonlinear measurement equation depending on all

position and velocity components

Map feature: Measurement equation:

Institute of Systems Optimization, University of Karlsruhe, Germany Andreas Maier

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Sigma-Point Kalman Filter

• 15-State SPKF has been implemented
• Measurement noise includes matching errors and map errors
• Sigma-point Kalman filter takes into account higher order terms automatically
• Provides more accurate update in case of nonlinear measurement models

State vector and measurement noise Augmented state vector construction

Sigma-point Kalman filter

Institute of Systems Optimization, University of Karlsruhe, Germany Andreas Maier

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Sigma-Point Kalman Filter

• Processing steps

– Produce sigma-points – Transform by measurement equation – Calculate mean, covariance and correlation

• Example of sigma-points

weight

Institute of Systems Optimization, University of Karlsruhe, Germany Andreas Maier

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Sigma-Point Kalman Filter

• Sigma-point Kalman filtering is analogous to EKF-processing

– Calculate gain matrix – Calculate navigation error – Calculate new covariance matrix

• Correlation and covariance accurate to the second order term

SPKF EKF

Institute of Systems Optimization, University of Karlsruhe, Germany Andreas Maier

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Update step

• Update by SAR measurement
• 2 measurement equations
• Independent measurements
• Change in depression angle

x y z

covariance

change in depression angle

terrain

feature position aircraft position height meas.

r

covariance

• Different sensor characteristics
• TRN update in regions of rough terrain
• SAR update during flight over smooth terrain

Institute of Systems Optimization, University of Karlsruhe, Germany Andreas Maier

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Simulations

Navigation grade IMU Measurement noise 2% DTED level 1, 100m spacing Map error standard deviation: 3m Matching error standard deviation: 7m

Sensor accuracies Trajectory

start

Institute of Systems Optimization, University of Karlsruhe, Germany Andreas Maier

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SAR/INS

• Barometric altimeter aids

height estimation

• Navigation error depends on

feature update rate

• Feature updates in the scale of

a few minutes needed

Institute of Systems Optimization, University of Karlsruhe, Germany Andreas Maier

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SAR/TRN/INS

• TRN: No accurate estimation
• ver flat area
• SAR prevents increasing

position errors over smooth terrain

• TRN leads to reliable navigation

information even if no SAR- features are available

• TRN and SAR show different

characteristics

Institute of Systems Optimization, University of Karlsruhe, Germany Andreas Maier

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Conclusion

• SAR/INS is able to provide 3-dimensonal navigation

information

• Autonomous navigation achievable by SAR/INS
• Feature updates in the scale of a few minutes required
• SAR in combination with low cost TRN is optimal due to

complementary sensor characteristics.

Andreas Maier, Stefan Kiesel and Gert F. Trommer

Institute of Systems Optimization, University of Karlsruhe, Germany Andreas Maier

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Institute of Systems Optimization, University of Karlsruhe, Germany Andreas Maier

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Institute of Systems Optimization, University of Karlsruhe, Germany Andreas Maier

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SAR/INS

• Barometric altimeter aids

height estimation

• Navigation error depends on

feature update rate

• Feature updates in the scale of

a few minutes needed

Institute of Systems Optimization, University of Karlsruhe, Germany Andreas Maier

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Terrain Referenced Navigation

terrain

Measurement equation Update step Measurement matrix

Reasonable terrain roughness required