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. INTRODUCTION In design and implementation of integrated INS-based navigation systems, proper knowledge and modeling of inertial sensor errors is an important key to provide performant and reliable navigation systems [1]. Inertial sensors, especially those of lower grades, can have very complex error models, identification of which requires proper and modern tools. Generalized method of wavelet moments (GMWM) is a rather recent method [2]–[4] for identification of a probabilistic time series model and was especially optimized for modeling stochastic errors in inertial sensors. There is an open source R package to use GMWM [5], as well as a publicly available free web tool to facilitate its usage even further [6]. Compared to Allan variance slope method, which is the norm in industry and adopted by IEEE as a standard [7] for this purpose, GMWM is consistent estimator and is very flexible in identifying highly complex models such as the ones including several first order Gauss-Markov processes, not to forget its ease of usage due to high degree of automation. Such flexibility may be tempting toward adopting unnecessarily complex models neglecting the application requirements and potential benefits of higher fidelity models. This paper aims to present a short study on the effect of employing IMU error models of different complexities in integrated INSbased navigation. As a first and more general approach, a covariance matrix analysis is performed in static conditions, which is a standard scenario for error analysis of inertial navigation systems [1], [8]. In addition, an emulation work flow is introduced and employed to extend the study to more specific real-world applications, where a real trajectory and real sensor errors are used to study the effect of various IMU error models of different complexity on navigation solution accuracy and consistency of predicted covariances by the navigation filter. 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2019), Miami, Florida, September 16-20, 2019 2566 https://doi.org/10.33012/2019.17057 IMU AND ITS REFERENCE ERROR MODEL To demonstrate the proposed analyzes we have employed data from small MEMS IMU called Navchip V2 [9] that represent a high quality in its category. Static signals were collected during 6 hours at 200 Hz and their variation was analyzed using GMWM. We first fitted a model of high fidelity that serves hereinafter as the modeling reference representing correctly the stochastic behavior of underlying error signals. It is worth mentioning that the remaining minor imperfections of this model have no effect on the subsequent analysis, as the performance of all the models is compared to this reference model regardless the quality of this representation (remaining albeit high). Similar analysis can be applied to different IMUs, and the specific model employed here is used only as a demonstrator. Figure 1 shows the wavelet variance plot for the observed noise and the reference model fitted by GMWM. The model parameters are depicted in Table 1. The reference model comprises of a white noise and 3 correlated processes (1 order GaussMarkov) for both accelerometers and gyroscopes, plus a drift for the accelerometers. Figure 1: Wavelet Variance plots of the real IMU data (blue line w. full circles) and the reference model (orange line w. empty circles) for accelerometers (left) and gyroscopes (right) ERROR MODEL CANDIDATES In addition to the reference model for the IMU at hand we consider three other “sub-optimal” models with different levels of complexity and therefore “fitting fidelity”. The GMWM plots of these models are shown in Figure 2 to Figure 4 and their parameters are presented in Table 1. As shown in this table Model 1 comprises of white-noise only, while Model 2 and Model 3 of different combination of white-noise and correlated processes including a drift for accelerometers. Figure 2: Wavelet Variance plots for sub-optimal Model 1 (orange line w. empty circles) for accelerometers (left) and gyroscopes (right)