High-performance inertial measurements using a redundant array of inexpensive inertial sensors

An apparatus comprising:

• a platform, wherein the platform comprises
• an array of inertial sensors coupled to the platform, and
• a processor coupled to the platform that receives inputs from each inertial sensors of the array of inertial sensors;
• and
• a movable member coupled to the platform, wherein
• each inertial sensor of the array of sensors outputs a rotational rate of the movable member,
• the processor defines a hidden Markov model (“HMM”), wherein hidden states of the HMM represent a discrete value measurement of the rotational rate of the movable member, and transition probability of the HHM accounts for a motion model of the movable member, and observation probability accounts for noise and bias of at least one of the inertial sensor in the array of inertial sensors;
• and
• the processor determines the rotational rate of the movable member by solving for an output of the HMM using the input received from the array of inertial sensors, and controlling motion of the movable member using the rotational rate of the movable member.

An apparatus comprising:

• a platform, wherein the platform comprises
• an array of inertial sensors coupled to the platform, and
• a processor coupled to the platform that receives inputs from each inertial sensors of the array of inertial sensors;
• and
• a movable member coupled to the platform, wherein
• each inertial sensor of the array of sensors outputs a rotational rate of the movable member,
• the processor defines a hidden Markov model (“HMM”), wherein hidden states of the HMM represent a discrete value measurement of the rotational rate of the movable member, and transition probability of the HHM accounts for a motion model of the movable member, and observation probability accounts for noise and bias of at least one of the inertial sensor in the array of inertial sensors;
• and
• the processor determines the rotational rate of the movable member by solving for an output of the HMM using the input received from the array of inertial sensors.