Wireless measurement of linear and angular velocity and acceleration, and position, range, and orientation, via weakly-coupled quasistatic magnetic fields

A method to provide drift-free kinematic measurements of a device comprising:

• providing a transmitter configured to transmit quasistatic magnetic fields in one or more transmitter axes;
• providing a receiver configured to receive quasistatic magnetic fields in one or more receiver axes;
• wherein either the transmitter or the receiver is situated in the device;
• transmitting, by the transmitter, the quasistatic magnetic fields in one or more frequency bands;
• detecting, by the receiver, one or more quasistatic magnetic field couplings between each axis of the one or more transmitter axes and each axis of the one or more receiver axes;
• calculating a drift-free orientation-invariant range between the transmitter and the receiver, the drift-free orientation-invariant range describing, in a frame of reference, a magnitude of a vector between the receiver and the transmitter;
• calculating one or more drift-free range-invariant orientation angles of the device, the one or more drift-free range-invariant orientation angles describing an orientation of the device in the frame of reference;
• calculating one or more drift-free range-invariant direction angles of the vector between the receiver and the transmitter in the frame of reference;
• calculating a drift-free position of the device in the frame of reference;
• applying a filter to the drift-free orientation-invariant range, to the one or more drift-free range-invariant orientation angles, to the one or more drift-free range-invariant direction angle, and to the drift-free position, to reduce white noise, thereby obtaining a filtered drift-free range, a filtered drift-free orientation, and a filtered drift-free position of the device;
• and
• based on the filtered drift-free range, filtered drift-free orientation, and filtered drift-free position, calculating vector velocity and vector acceleration of the device,
• wherein:
• a center frequency of each of the one or more frequency bands corresponds to a wavelength A, and a range between the transmitter and the receiver r is:
• r<λ/2π.