Determining gravity toolface and inclination in a rotating downhole tool

A method for controlling a drilling operation by determining gravity toolface and inclination, comprising:

• positioning a downhole tool comprising an internal bore through which a drilling fluid passes during a drilling operation within a borehole, wherein:
• the downhole tool comprises a sensor assembly disposed, wherein the sensor assembly is in a radially offset location within the downhole tool, wherein the radially offset location is relative to a longitudinal axis of the downhole tool;
• the downhole tool comprises a steering assembly;
• and
• the sensor assembly consisting of a three-axis accelerometer package and an angular rate sensing device, wherein the three-axis accelerometer package comprises three accelerometers, wherein the angular rate sensing device senses an angular velocity of the downhole tool;
• determining a centripetal acceleration of the downhole tool based, at least in part, on an output of the sensor assembly;
• determining a tangential acceleration of the downhole tool based, at least in part, on a first output at a first time from the angular rate sensing device and a second output at a second time from the angular rate sensing device, wherein a digital filter is implemented to determine at least one of the centripetal acceleration and the tangential acceleration;
• determining at least one of the gravity toolface and the inclination of the downhole tool using at least one of the centripetal acceleration and a tangential acceleration;
• transmitting the at least one of the gravity toolface and the inclination to a steering control, wherein the steering control alters at least one of a direction and a rotation of the steering assembly based, at least in part, on the at least one of the gravity toolface and the inclination.

A system for controlling a drilling operation by determining gravity toolface and inclination, comprising:

• a downhole tool comprising an internal bore through which a drilling fluid passes during a drilling operation in a borehole;
• a steering assembly;
• a first sensor assembly disposed in a first radially offset location within the downhole tool, wherein the first radially offset location is relative to a longitudinal axis of the downhole tool, wherein the first sensor assembly is implemented on a first printed circuit board (PCB), wherein the first sensor assembly consists of a first accelerometer and a second accelerometer;
• a second sensor assembly disposed in a second radially offset location within the downhole tool, wherein the second radially offset location is relative to a longitudinal axis of the downhole tool, wherein the second sensor assembly is implemented on a second PCB, wherein the second sensor assembly consists of a third accelerometer and a fourth accelerometer;
• and
• a processor in communication with the steering assembly, the first sensor assembly, and the second sensor assembly, wherein the processor is coupled to at least one memory device containing a set of instruction that, when executed by the processor, cause the processor to:
• receive a first output from the first sensor assembly;
• receive a second output from the second sensor assembly;
• determine a centripetal acceleration of the downhole tool based, at least in part, on the first output and the second output;
• determine a first tangential acceleration of the downhole tool based, at least in part, on the first output, wherein a digital filter is implemented to determine at least one of the centripetal acceleration and the first tangential acceleration;
• determine at least one of the gravity toolface and the inclination of the downhole tool using at least one of the centripetal acceleration and a tangential acceleration;
• and
• alter at least one of a direction and a rotation of the steering assembly based, at least in part, on the least one of the gravity toolface and inclination.