The present invention relates to a method for calibrating the offset of angle sensors, which determine an angle to be determined on the basis of a sine signal that can be assigned to the angle and a cosine signal that can be assigned to the angle. 
For measuring mechanical angles, measuring methods that are based on the evaluation of sine signals and cosine signals of a sensor are often employed.  As examples that can be named in this respect are resolvers in the form of inductive transducers, anisotropic magnetoresistive sensors (AMR sensors), sensors which exploit the giant magnetoresistive effect (GMR sensors), Hall sensors in the form of magnetic angle encoders, and optical or micromechanical transducers. 
AMR sensors are used for measuring steering wheel angles, for instance.  In such sensors, the angle to be determined is determined via electronic processing of the sine signals and cosine signals of the sensors that can be assigned to the angle to be determined. 
The angular precision of such sine-cosine sensors is limited by offset effects.  Offset effects can occur especially when the sensors are used at high temperatures.  For example, an angle measurement in the motor vehicle engine compartment, where high temperatures typically prevail, leads in the case of conventional angle sensors to offset effects that are not negligible.  As a result, the ranges of production variation and operating tolerances for the mechanical, magnetic, optical or micromechanical components of such sensors must be set as low as possible, which increases their production costs. 
The object of the present invention is a method with which the angular precision in angle sensors, especially in angle measurements at high temperatures, can be improved in a simple way without having to make overly stringent demands in terms of operating tolerance ranges. 
According to the invention the method for calibrating an offset of an angle sensor, which measures an angle based on a sine signal assigned to the angle and a cosine signal assigned to the angle, comprises the following steps:
a) determining the sine signal and the cosine signal for at least three different angles to obtain at least three sine and cosine value pairs, each pair containing one sine signal value and one cosine signal value;
b) displaying the at least three value pairs in an at least two-dimensional coordinate system that represents a sine signal-cosine signal plane; and
c) determining a point, representing the offset to be calibrated, in the coordinate system, in relation to which point the at least three value pairs are located on an arc. 
This object is attained by the above-described method according to the invention.  By means of the method of the invention, the offset of an angle sensor can be calculated and compensated for in a simple way during operation.  Compared with conventional versions, this makes it possible to enhance the angular precision, and in particular satisfactory angle measurements can be made at high temperatures, such as in the engine compartment of motor vehicles, The invention makes it possible to increase the ranges of production variation or operating tolerances for the mechanical, magnetic, optical or micromechanical components of the sensors used. 
In an especially preferred feature of the method of the invention, the determination of the offset O sin of the sine signal is done in accordance with an equation
xe2x80x83O sin=xc2xdxc2x7{[U 
cos(1)xe2x88x92U cos(3)]+[(U 
sin(2)xe2x88x92U sin(1))xc2x7(U 
sin(2)+U sin(1))/(U 
cos(2)xe2x88x92U cos(1))]xe2x88x92
[(U sin(3)xe2x88x92U sin(2))xc2x7(U 
sin(3)+U sin(2))/(U 
cos(3)xe2x88x92U cos(2))]}/{
[(U sin(2)xe2x88x92U 
sin(1))/(U cos(2)xe2x88x92U 
cos(1))]xe2x88x92[(U sin(3)xe2x88x92U 
sin(2))/(U cos(3)xe2x88x92U 
cos(2))]},
O cos=xc2xdxc2x7{[U 
sin(1)xe2x88x92U sin(3)]+[(U 
cos(2)xe2x88x92U cos(1))xc2x7(U 
cos(2)+U cos(1))/(U 
sin(2)xe2x88x92U sin(1))]xe2x88x92
[(U cos(3)xe2x88x92U 
cos(2))xc2x7(U cos(3)+U 
cos(2))/(U sin(3)xe2x88x92U 
sin(2))]}/{[(U 
cos(2)xe2x88x92U cos(1))/(U 
sin (2)xe2x88x92U sin(1))]xe2x88x92
[(U cos(3)xe2x88x92U 
cos(2))/(U sin(3)xe2x88x92U 
sin(2))]},
and the determination of the offset O cos of the cosine signal is done in accordance with an equation
O cos=xc2xd*{U 
sin(1)xe2x88x92U 
sin(3)+[((U cos(2)xe2x88x92U 
cos(1))*(U cos(2)+U 
cos(1))/(U sin(2)xe2x88x92U 
sin(1)]xe2x88x92[(U cos(3) xe2x88x92U 
cos(2))*(U cos(3)+U 
cos(2)/(U sin(3)xe2x88x92U 
sin(2)]}/[(U 
cos(2)xe2x88x92U cos(1))/(U 
sin(2)xe2x88x92U sin(1))xe2x88x92(U 
cos(3)xe2x88x92U cos(2))/(U 
sin(3)xe2x88x92U sin(2))],
in which U sin(i), U cos(i) represent the determined sensor signals for the positions i=1, 2, 3. 
The equations given contain merely elementary operations with regard to three pairs of measurement values, each for different angles.  Other types of calculation and in particular trigonometric types of calculation are also possible.