1. A micro-electro-mechanical system (MEMS) inertial measurement apparatus, comprising: at least one analog MEMS inertial sensor; an automatic gain control amplifier that receives measurement signals from the at least one analog MEMS inertial sensor and outputs an analog amplified measurement signal according to a gain amount controlled by an automatic gain control feedback; an analog to digital converter that receives the amplified analog measurement signals and outputs digital signals; and a digital signal processing unit that processes the digital signals and outputs the automatic gain control feedback to control the gain amount of the automatic gain control amplifier.