Analytical Modeling of Sensor Quantization in Strapdown Inertial Navigation Error Equations

Abstract

Although generally not considered a major contributor to system inaccuracy, inertial sensor quantization error, if not properly modeled, can lead to erroneously large estimates of its impact on inertial navigation system performance. Analytical methods are described for modeling inertial sensor quantization in strapdown inertial system error parameter propagation and measurement equations. Error propagation equations are derived in classical differential error state dynamic and discrete difference format. It is shown how the attitude, velocity, and sensor error parameters in these equations must be modified to enable proper sensor quantization error modeling as white noise and to account for differences in attitude, velocity, and position update frequencies. The discrete difference error equation form is used to develop values for attitude/velocity measurement noise covariances and for spectral densities of white quantization noise terms in the differential error propagation equations. A general discussion is included of how quantization white noise spectral densities should be computed for the differential error propagation equations for compatibility with two-speed attitude, velocity, and position updating algorithms. Validity limits for white noise modeling approximations and methods for reducing quantization noise are discussed. Numerical examples are provided.