# Patenting mathematical methods: Decision “Airplane attitude” by the German Federal Court of Justice (FCJ)

a) Mathematical methods are patentable according to § 13 (3) No. 1 Patent Act only if they serve the solution of a concrete technical problem with technical means.

b) A mathematical method can be regarded as being non-technical only if it has in connection with the claimed teaching no relation to the purposeful utilization of forces of nature.

c) A sufficient relation to the purposeful utilization of forces of nature is present if a mathematical method is used for the purpose to obtain – based on the available measurement data – a more reliable knowledge about the attitude of an airplane and thereby to influence the functioning of the system for detection of this attitude.

d) Subject matter which is new and based on an inventive step cannot be regarded as not patentable solely on the ground that it does not provide a recognizable advantage compared to the prior art.

The invention: The patent application in question (DE 10 2007 002 672) relates to a method for the detection of the attitude of an airplane, namely its position, speed and orientation. For this purpose it was known to use a so-called Kalman filter which calculates based on a plurality of measurement data obtained by e.g. an inertial navigation system an estimation value of the physical quantities, e.g. the location and orientation of the plane. The processing speed of the Kalman filter depends on the amount of data to be processed such that real-time position determination was not possible with Kalman filtering based on the raw measurement data. From the closest prior art reference it was known to therefore feed the Kalman filter with averaged data instead of the raw data such as to reduce the processing burden and processing time of the filtering procedure.

It was therefore the technical problem of the invention to provide an alternative attitude determination method which allows a reliable and fast attitude detection of the plane.

According to the invention this problem is solved by a particular averaging preprocessing: The raw data, which are represented as points in a k-dimensional space of the measurement parameters, are replaced by the center point vector and the radius of a k-dimensional sphere having a minimal radius and including all measurement points. The difference between the method according to the invention and that of the closest pior art is therfore only the mathematical method of avaraging the raw data before feeding them to the Kalman filter, or expressed differently, the averaging algorithm.

Upon refusal of the application by the patent office, the applicant appealed to the Federal Patent Court. The 17th Senate – known for its rather critical stance toward software-implemented inventions – rejected the application on the ground that the distinguishing features would be based on non-technical considerations in the filed of data representation and statistics.

The decision: In its decision X ZB 1/15 of 30 June 2015 the FCJ reversed the lower instance decision and allowed the patent application. According to the ruling, an invention which distinguishes over the prior art only by its mathematical method is patentable if the mathematical method is new and non-obvious over the prior art and serves the solution of a concrete technical problem (determination of the state of an airplane based on measurement data) with technical means (sensors, data processing means). In this respect it is not necessary that the found mathematical solution of the technical problem has a technical advantage over the prior art. It is sufficient to provide an alternative mathematical solution as long as this is not rendered obvious by the prior art.

In short, an invention distinguished over the prior art by a new and non-obvious algorithm is patentable if the the algorithm is used for a concrete technical purpose, thereby relating to the use of forces of nature.

It is thus quite clear that the FCJ would not have accepted the patent application in its original wording, related to a mathematical method for the determination of the state of a (not further defined) object. Only the restriction of the method to the attitude determination of an airplane provides the required concrete technical application. Would the application also be allowed if the claims were directed not to the attitude determination of a real airplane but one simulated on a computer ? My guess is yes, it would, as in accordance with the rationale expressed by headnote c) of the decision a more reliable knowledge about the attitude of an airplane and thereby influence on the functioning of the attitude detection system (thus the relation to the purposeful use of forces of nature) is obtained also by performing the method of the invention on a flight simulator.