Optimal Stochastic Sensor Error Modeling based on Actual Impact on Quality of GNSS-INS Integrated Navigation

Proper modeling of stochastic errors in inertial sensors plays a crucial role in the achievable quality of GNSS-INS integration especially with low-cost inertial sensors. Generalized Method of Wavelet Moments (GMWM) can model the underlying process for such errors with arbitrarily complex structure to obtain close match to the observed errors in terms of wavelet variance. In comparison to the widely used and IEEE adopted error modeling using Allan Variance, this method provides consistent estimation, ability to estimate parameters of composite stochastic models of much higher complexities, and considerably easier usage. However, the level of improvement in navigation quality does not necessarily grow proportionally to the fidelity of the error models. Therefore, opting for unnecessarily complex models may only increase computational load with no tangible gain in navigation quality. On the other hand, converging estimation of higher complexity models, generally speaking, requires longer estimation periods and higher dynamics to improve observability of error states. This implies yet another motivation to find an optimal sensor error model avoiding unnecessary complexities. In this paper, we employ two methods to investigate the effect of model complexity on integrated navigation performance. Firstly, a covariance propagation is performed on static conditions, as is the standard scenario in error analysis of inertial navigation systems. Afterwards, an emulation study is performed based on a real Unmanned Aerial Vehicle (UAV) flight and error signals of a Navchip V2 Inertial Measurement Unit (IMU). Results of both methods are in general agreement, and suggest that more complex models in general provide higher accuracy for the navigation system and a more consistent covariance prediction by the navigation filter. This difference is, however, more noticable only in GNSS outages of longer duration (tens of seconds). However, the benefits of more complex models may be only marginal in other applications, depending on the duration of inertial coasting and availability of other sensory data such as GNSS observations.