Error analysis of strapdown inertial navigation using dual quaternion algebra

The general displacement of a rigid body in a strapdown inertial navigation system (SDINS) is traditionally separately modeled and analyzed using matrix algebra, i.e., direction cosine matrix or quaternion for rotation analysis and vector for translation analysis. This paper adopts dual quaternion algebra, a most concise and unified mathematical tool, to represent the general displacement of a rigid body and analyze the error characteristics of SDINS. The content of this paper is organized as follows. First of all, the continuous strapdown inertial navigation equations are developed in terms of dual quaternions. Then two error models of SDINS are derived based on quaternion algebra, namely, the additive dual quaternion error (ADQE) model and multiplicative dual quaternion error (MDQE) model. It is shown that the equivalent tilt (ET) error model, which is the attitude error propagation model in conventional SDINS, can be classified into the MDQE model. The error analysis in this paper will help to construct the future filtering algorithms based on dual quaternions, such as for the integrated navigation aided by dynamic vision.