The effective use of guided munitions requires electronic hardware and software components to survive and function normally at over 15,000 g's. Such stringent demands are required for precision guided munitions (PGMs) that use an inertial measurement unit (IMU) for inertial guidance in case of global positioning signal jamming. Functional, gun-hardened IMUs can be produced using micro-electro-mechanical systems (MEMS) technology. The MEMS technology typically refers to small mechanical elements micro-machined into a silicon substrate, which also contains microcircuitry in the form of embedded microprocessors.
Such microprocessors typically use fixed point arithmetic, which is a manner of doing arithmetic on a computer where a fixed number of decimal (or binary) digits is kept after the decimal point, and any remaining digits are rounded. It is necessary to determine valid ranges for algorithmic variables using fixed point arithmetic. Determining valid ranges is essential in avoiding arithmetic overflow errors, and determining ranges of sufficient width is essential in preserving arithmetic expressiveness and precision.