Magnetic field sensors and method for determining position and orientation of a magnet
A magnetic field sensor for determining a position of a magnet, the position identified by one or more position variables can include: one or more magnetic field sensing element operable to generate one or more magnetic field measurements of the magnet and an associated one or more measured magnetic field variable values; a first module for identifying calculated magnetic field variable values associated with a plurality of positions of the magnet; a second module operable to perform an optimization process to determine a value of a distance function, the distance function using the one or more measured magnetic field variable values and the calculated magnetic field variable values; and a third module operable to determine the position of the magnet by associating the value of the distance function with corresponding values of the one or more position variables. A complimentary method can be used in the magnetic field sensor.
1. A method of determining a position of a magnet, the position identified by one or more position variables, the method comprises:
generating one or more magnetic field measurements of the magnet and an associated one or more measured magnetic field variable values using one or more magnetic field sensing elements, wherein the one or more magnetic field sensing elements includes first and second magnetic field sensing elements most responsive to magnetic fields along a first axis, a third magnetic field sensing element most responsive to magnetic fields along a second axis, and a fourth magnetic field sensing element most responsive to magnetic fields along a third axis;
identifying calculated magnetic field variable values associated with a plurality of positions of the magnet, wherein the identifying the calculated magnetic field values comprises using a mathematical model to calculate a respective magnetic field expected at each of the one or more magnetic field sensing elements at a plurality of positions of the magnet;
performing an optimization process to determine a minimal value of a distance function, wherein the distance function calculates at least one difference between the calculated magnetic field variable values at positions of the one or more magnetic field sensing elements and the one or more measured magnetic field variable values, wherein the optimization process searches for the minimal value of the distance function based on the calculated at least one difference; and
determining the position of the magnet by associating the minimal value of the distance function with corresponding values of the one or more position variables.
2. The method of claim 1 , wherein the one or more position variables includes an angle of rotation of the magnet around a first axis.
3. The method of claim 2 , wherein the one or more magnetic field sensing elements include at least two magnetic field sensing elements most responsive to magnetic fields along the first axis.
4. The method of claim 1 , wherein the one or more magnetic field sensing elements are arranged to generate at least one differential measurement of the magnetic fields.
5. The method of claim 1 , wherein the one or more position variables include a position of the magnet along a first axis and a position of the magnet along a second axis.
6. The method of claim 1 , further comprising:
determining initial values of the one or more position variables, wherein the optimization process is initialized with the initial values of the one or more position variables.
7. The method of claim 6 , wherein determining the initial values of the one or more position variables comprises:
discretizing ranges of values of selected ones of the one or more position variables to generate a plurality of discretized position variable values;
identifying a minimum numerical distance between the calculated magnetic field variable values at positions of the one or more magnetic field sensing elements for ones of the plurality of discretized position variable values and the one or more measured magnetic field variable values
identifying the initial values of the one or more position variables in accordance with the minimum numerical distance.
8. The method of claim 6 , wherein the determining the initial values of the one or more position variables comprises:
partitioning the one or more position variables into one or more first position variables and one or more second position variables; and
identifying a minimum numerical distance between the calculated magnetic field variable values for the one or more second position variables while holding values of the one or more first position variables fixed; and
identifying the initial values of the one or more position variables in accordance with the minimum numerical distance.
9. The method of claim 8 , wherein at least one of the one or more first position variables has a smaller range than another one of the one or more first position variables.
10. The method of claim 1 , where the one or more magnetic field measurements comprises two magnetic field measurements, and wherein the two magnetic field measurement are combined together to generate a differential magnetic field measurement.
11. The method of claim 1 , further comprising:
determining initial values of the one or more position variables;
during a first time period, using the initial values of the one or more position variables to find an associated one or more optimized position variable values during the optimizing; and
during a second time period time period after the first time period, using the one or more optimized position variable values to find another optimized one or more position variable values during the optimizing.