Numerically stable computation of heading without a reference axis

A system for tracking motion direction of a mobile device,

• the system comprising:
• an orientation sensor configured to collect data relating to orientation of the mobile device;
• a satellite positioning system (SPS) receiver configured to determine an initial direction of motion of the mobile device in terms of an Earth-based coordinate system during a calibration time period;
• an orientation analysis module communicatively coupled to the orientation sensor and configured to track changes to a three-dimensional orientation of the mobile device in terms of the Earth-based coordinate system over time based on the data collected by the orientation sensor;
• and a motion direction tracker module communicatively coupled to the SPS receiver and the orientation analysis module and configured to compute a direction of motion of the mobile device in terms of the Earth-based coordinate system relative to the initial direction of motion of the mobile device using the changes to the three-dimensional orientation of the mobile device in terms of the Earth-based coordinate system.

A method of computing motion direction of a mobile device comprising:

• determining a three-dimensional orientation of the mobile device relative to a coordinate system of Earth;
• computing a first direction, that is a three-dimensional direction of motion of the mobile device relative to a coordinate system of the mobile device;
• computing a second direction that is a three-dimensional direction of motion of the mobile device relative to the coordinate system of Earth using the first direction and the three-dimensional orientation of the mobile device relative to the coordinate system of Earth, the second direction be an angle relative to north;
• and
• projecting, to a horizontal plane at Earth's surface, the three-dimensional direction of motion of the mobile device relative to the coordinate system of Earth.

A method of tracking a motion direction of a mobile device over time comprising:

• obtaining an initial motion direction of the mobile device in a coordinate system of Earth from a satellite navigation system during an initial time period;
• determining a three-dimensional orientation of the mobile device in the coordinate system of Earth subsequent to the initial time period;
• and
• computing an updated motion direction of the mobile device in the coordinate system of Earth relative to the initial motion direction of the mobile device using the three-dimensional orientation of the mobile device in the coordinate system of Earth.

A mobile wireless communication device comprising:

• sensing means for generating orientation information for the device;
• orientation means, communicatively coupled to the sensing means, for computing a three-dimensional earth-frame orientation of the device relative to Earth based on the orientation information for the device;
• and
• direction means, communicatively coupled to the orientation means, for computing a three-dimensional sensor-frame direction of motion of the device relative to a sensor coordinate plane of the device defined by at least one sensor axis and
• computing an earth-frame direction of motion of the device relative to Earth using the three-dimensional sensor-frame direction of motion of the device and the three-dimensional earth-frame orientation of the device.

A mobile wireless communication device comprising:

• sensing means for generating orientation information for the device;
• calibration means for determining an initial earth-frame direction of 4 motion of the device relative to Earth;
• orientation means, communicatively coupled to the sensing means, for tracking changes to a three-dimensional earth-frame orientation of the device relative to Earth over time based on the orientation information for the device;
• and
• direction means, communicatively coupled to the calibration means and
• the orientation means, for computing changes to an earth-frame direction of motion of the device relative to Earth over time relative to the initial earth-frame direction of motion of the device using the changes to the three-dimensional earth-frame orientation of the device.

A non-transitory processor-readable medium comprising processor-readable instructions configured to cause a processor to:

• determine a three-dimensional orientation of a mobile device relative to a coordinate system of Earth;
• compute a first direction, that is a three-dimensional direction of motion of the mobile device relative to a coordinate system of the mobile device;
• and
• compute a second direction that is a three-dimensional direction of motion of the mobile device relative to the coordinate system of Earth using the first direction and the three-dimensional orientation of the mobile device relative to the coordinate system of Earth, the second direction being an angle relative to north;
• and
• project, to a horizontal plane at Earth's surface, the three-dimensional direction of motion of the mobile device relative to the coordinate system of Earth.

A non-transitory processor-readable medium comprising processor-readable instructions configured to cause a processor to:

• obtain an initial motion direction of a mobile device in a coordinate system of Earth from a satellite navigation system during an initial time period;
• determine a three-dimensional orientation of the mobile device in the coordinate system of Earth subsequent to the initial time period;
• and
• compute an updated motion direction of the mobile device in the coordinate system of Earth relative to the initial motion direction of the mobile device using the three-dimensional orientation of the mobile device in the coordinate system of Earth.