The most important theory of K- Filtering (KF) was established in the early 1960's. Since then all digital navigation and piloting systems have relied on the KF computations due to their most stringent safety and reliability requirements. However, automatic Guidance, Navigation and Control (GN&C) systems of the near future are becoming increasingly sophisticated. These new developments are posing computational difficulties to the conventional method of KF computing. Meteorologists were the first to face this problem of "1000 desktop CRAYs working in tandem" (Gal-Ghen, T., 1988, Bull. Am. Met. Soc., Vol. 71, No. 5, May 1990, see page 684). Fortunately, an extremely fast KF computing method for very large systems was discovered in 1989 by Dr. Antti Lange, a Senior Scientist of the Finnish Meteorological Institute, Helsinki, Finland. The invented algorithm is based on F.R.Helmert's (1841-1917) andHelmut Wolf's (1910-1994)Blocking Method that is extensively used in modern GPS Geodesy.It is becoming known as the Fast K- Filter (FKF).  

Potential FKF applications 

FKF is the most reliable KF computing method for many large sophisticated GN&C systems. Thus, it is to be expected that automation will be increasingly based on FKF processing in the following applications:

- Local tsunami warning systems based on geodetic GPS-receivers on buoys,
- Realtime or Near-Real-Time (NRT) prediction of satellite orbits for geophysics,
- Lightweight navigation receivers for property tracing, social services and logistics,
- Hybrid navigation receivers for personal mobile phones,
- Virtual Real-Time-Kinematic (RTK) and Virtual Reference Station (VRS) land surveying,
- Surveillance tracking systems,
- Picture enhancement in wireless communications,
- Electronic stabilization of cameras and radars,
- Process control systems,
- Computational optimization of server processors,
- Driverless cars and autonomous vehicles,
- Environmental and Numerical Weather Prediction (NWP) systems,
- Asynchronous Transmission Mode (ATM) data-communications,
- Videogame applications simulating STARWARS, etc.
- Tomographic measurement systems in Weather Prediction and Medicine, etc.
- Statistical calibration of hydrid remote sensing and in-situ observing systems, etc.

The FKF patents

The FKF method has been patented successfully in about 50 countries including USA (5506794, 5654907 and 6202033),Europe, Japan, etc. The coverage of these patents will be extended probably up to 100 countries through a third international patent application (PCT/FI96/00621, 1996). A new Finnish company called FKF-Finland Oy was founded in 1997 by eight hi-tec professionals for promoting scientific and commercial FKF applications worldwide. This company holds of the FKF patent rights for Finland, representing other FKF patents worldwide.

Mathematicians consider it improbable that a simpler and faster alternative to optimal KF computing can still be found because the FKF algorithm is a semi-analytical solution i.e. the inherent very demanding computations have been nearly done beforehand through using the FKF formulas.

Developments in Electronics

This technology is experiencing its fastest developments in areas of those products that are manufactured in large volumes. The rapid development of mobile phones is the best example. New features are continuously being added on. A navigation capability is expected to become a compulsory feature of mobile phones by year 2002. This will also push the technological development of personal computing (PC) into new realms.

Existing navigation technology is not easily applied to small pocket, wrist or head devices as battery-savings call for special processors and algorithms. These considerations propose that a most simple navigation receiver is to be used and signals from only one network are listened to. A simple navigational solution would indeed minimize many complexities of the KF computations.

However, such simple systems cannot detect and correct local anomalies of navigation signals. The computed positional information can be inaccurate or unavailable. The reliability of a navigation system is improved only by calibrating the receiver using signals from many sources and analyzing their simultaneous time series. These expensive hybrid navigation receivers are primarily used only by commercial and tactical aircraft as their conventional KF algorithms need much computing and battery power. 

Fortunately, the FKF method will remove this computational obstacle from the way of cheap personal navigation receivers of high reliability and accuracy. Such receivers will, in the long run, exploit all available sources of positional information and not only signals from one of the navigation satellite systems (GPS, GLONASS and GALILEO). The FKF computations make it also possible to obtain reliable real-time estimates of the actual positioning accuracies that vary significantly depending on circumstances.

Future mix of systems for positioning, navigation and timing

The radionavigation signals from all satellites employ frequencies that do not penetrate into houses or under shelters where people normally spend most of their time. Navigation receivers using only GPS (or other satellite) signals are not a safe solution. However, the past US radionavigation policy was to terminate all terrestial radionavigation networks by 2000. Fortunately, the US authorities are currently making it sure that the Loran-C radionavigation service will continue. This long-prevailed uncertain situation has, however, prevented the navigation industry from making decisive plans for combining all different navigational aids (NAVAIDS) optimally.  

Logistics and mobile phones equipped with navigation receivers 

New mobile phones will be equipped with navigation receivers by year 2003. Battery saving is crucial for personal mobile phones. Combined products of mobile phones and palmtop computers will take a role in these developments. Now, the FKF method offers an economic way of performing the most sophisticated KF computations for the best possible reliability of position finding and location.

Commercial opportunities

One can only guess the growing importance of the FKF patents as new opportunities can be offered to small/big countries/industries for manufacturing hi-tec products under worldwide market protection. Entirely new products and community services can be developed without risks that investments are torn into pieces by the market forces resulting from a savage price competition.


Manufacturers of mobile phones and computing devices should join their efforts for the development of most reliable personal navigation receivers. The FKF computations have by far the most economic battery consumption. Many human lives will respectively be saved in rescue operations. Thus, the navigation receiver, mobile phone, personal computer, etc. manufacturing industries are welcome to participate in:


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* Last revised January 8, 2014.