Measuring Integrity of Navigation in Real-Time Antti A. I. Lange Ph.D. The Inventor of the Fast Kalman Filter 21 st ITS World Congress Detroit, September 10, 2014: 10:30 AM - 12:00 PM

The Integrity of Optimal Kalman filtering Concluding remarks The Helmert-Wolf blocking (HWB) from Geodesy The Fast Kalman Filtering (FKF) is based on HWB FKF measures the Integrity with Rao’s MINQUE Overview: September 10, 2014 slide 2

Measurement Equation: y t = H t s t + F y t c t + e t for t = 1, 2,... System Equation: s t = A t s t-1 + B t u t-1 + F s t c t + a t for t = 1, 2,... where c t = the vector representing calibration drifts and adjustments to model parameters. September 10, 2014 slide 3 Optimal Kalman Filtering:

Stability of Optimal Kalman Filtering: or their possible correlations must be decorrelated by using Singular Value Decomposition (SVD) and generalized Canonical Correlation Analysis (gCCA) techniques! s t and c t must be observable u t must be controllable e t and a t must neither auto- nor cross-correlate September 10, 2014 slide 4

Decorrelating errors of the System and the Measurements: September 10, 2014 slide 5 FKF

September 10, 2014 slide 6

September 10, 2014 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 slide 9

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 September 10, 2014 slide 11 These demanding calculations are realistically done only by the FKF based on HWB, instead of ordinary Kalman filter recursions – because of mantissa length limitations

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., or , 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 21 st 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 Real- Time 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" ( during the 21st ITS World Congress Detroit, USA, 6 – 11 September ) The PCT/FI96/00192 is patented in USA, Canada, China, UK, France, Spain, Korea and Finland ( New extensions are pending (e.g. ). The owners are the inventor of FKF Dr. Antti Lange ( 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).