Measuring Integrity of Navigation
in Real-Time
Antti A. I. Lange Ph.D.
The Inventor of the Fast Kalman Filter
21st ITS World Congress Detroit, September 10, 2014: 10:30 AM - 12:00 PM
Overview:
• The Integrity of Optimal Kalman filtering
• The Helmert-Wolf blocking (HWB) from Geodesy
• The Fast Kalman Filtering (FKF) is based on HWB
• FKF measures the Integrity with Rao’s MINQUE
• Concluding remarks
September 10, 2014
slide 2
Optimal Kalman Filtering:
Measurement Equation:
yt = Ht st + Fyt ct + et for t = 1, 2,...
System Equation:
st = At st-1 + Bt ut-1 + Fst ct + at
for t = 1, 2,...
where ct = the vector representing calibration drifts
and adjustments to model parameters.
September 10, 2014
slide 3
Stability of Optimal Kalman Filtering:
st and ct must be observable
ut must be controllable
et and at must neither auto- nor cross-correlate
or their possible correlations must be decorrelated
by using Singular Value Decomposition (SVD) and
generalized Canonical Correlation Analysis (gCCA)
techniques!
September 10, 2014
slide 4
Decorrelating errors of the System and
the Measurements:
FKF
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slide 5
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slide 6
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slide 7
Error covariances of the HWB method in 1982:
September 10, 2014
slide 8
Minimum-Norm-Quadratic-Unbiased-Estimation
(MINQUE) theory:
How to measure the true accuracies
of the correlated observations was
solved in 1970 by C.R.Rao’s MINQUE,
which is the only mathematically rigorous
method to exploit the observed internal
consistencies among the many GNSS
and other available real-time signals.
September 10, 2014
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The Fastest Possible computation of MINQUEs:
September 10, 2014
slide 10
Concluding remarks:
• The Fast Kalman Filtering (FKF) using the HWB method extends the Geodetic
precision of Real-Time-Kinematic (RTK) and Virtual-Refence-Station (VRS)
surveys to all precision navigation and piloting applications
• The Real-Time precision of navigation depends crucially on the local
information density, which is a function of both the speed of the vehicle and the
amount of available GNSS signals and frequencies, including all other supporting
data, as well as Inertial Navigation Systems (INS)
• Ultra-reliable accuracy estimates of the GNSS and other signals including INS
are now operationally computable using Minimum Norm Quadratic Unbiased
Estimation (MINQUE), but only by using the patented FKF (PCT/FI2007/00052)
methods
• These demanding calculations are realistically done only by the FKF based on
HWB, instead of ordinary Kalman filter recursions – because of mantissa length
limitations
September 10, 2014
slide 11
Concluding remarks cont'd:
• Early warnings of tsunamis, earth quakes, shaking buildings and
collapsing bridges, etc. are now made possible with GPS, Glonass, Galileo,
Beidou, IRNSS, DORIS, QZSS, SBAS, GBAS, etc. receivers in all available
combinations in order to achieve absolutely reliable results
• Project proposals for expedient implementations of the FKF methods are
now welcome for ultra-reliable precision positioning, piloting and
navigation of safety-critical ITS applications
• Please contact directly the inventor of FKF:
Mr. Antti A. I. Lange Ph.D., +358400373182 or +35891355450,
lange@fkf.net, www.fkf.net, skype: kalmanfilter.
• .....
September 10, 2014
slide 12
Measuring Integrity of Navigation in Real-Time
Antti A. I. Lange Ph.D.
The Inventor of the Fast Kalman Filter
21st ITS World Congress Detroit, September 10, 2014: 10:30 AM - 12:00 PM
Executive Summary
The Fast Kalman Filtering (FKF) project serves the necessity of ultra-reliable navigation of security-critical transports such as modern cars
with increasing automation and, ultimately, their driverless control. The reliability can now be achieved uncompromisingly by FKF that
applies Best Linear Unbiased Estimation (BLUE for MINQUE) of the navigational errors. Thr true precision is computed in real-time from
the observed instantaneous consistency among all signals from Global Navigation Satellite Systems (GNSS) and other sources.
Please let me refer to the following:
1) The required extremely demanding calculations can be competitively materialized only by applying the fastest possible computing
method of the Helmert-Wolf blocking (HWB) instead of ordinary Kalman filters. GPS-based land-surveys already exploit HWB for RealTime Kinematic (RTK) and Virtual Reference System (VRS) positioning with a centimeter level of accuracy. The patented FKF method
generalizes the HWB computing to navigation and piloting where the best possible reliability is demanded in real-time. These
mathematics are presented in my paper "Measuring Integrity of Navigation in Real-Time" (http://www.fkf.net/World-ITS-2014-Lange.pdf)
during the 21st ITS World Congress Detroit, USA, 6 – 11 September 2014.
2) The PCT/FI96/00192 is patented in USA, Canada, China, UK, France, Spain, Korea and Finland (http://www.fkf.net/97018442.pdf). New
extensions are pending (e.g. http://www.fkf.net/07096466.pdf ). The owners are the inventor of FKF Dr. Antti Lange
(http://www.fkf.net/lange.html) together with some professionals as well as a number of ethical smaller investors.
3) The emergence of new software-based GNSS development tools, such as the commercial LABSAT3 and the open source RTKLIB from
Japan etc., facilitates testing and development of different navigation receivers using GNSS, IMU and Inertial Navigation Systems (INS).
Increasing speed of a car affects decreases accuracy of its navigation receiver. It needs to be demonstrated how to reach varying accuracy
demands by using different signals and receiver solutions under different circumstances.
4) COST (European Cooperation in Science and Technology) is currently developing standards for Intelligent Transport Systems and
Services (ITS) to be based on augmented Global Navigation Satellite Systems (GNSS) under Action TU1302 Satellite Positioning
Performance Assessment for Road Transport (SaPPART).