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Generalized method of wavelet moments for inertial navigation filter design

机译：惯性导航滤波器设计的小波矩广义方法

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摘要

The integration of observations issued from a satellite-based system (GNSS) with an inertial navigation system (INS) is usually performed through a Bayesian filter such as the extended Kalman filter (EKF). The task of designing the navigation EKF is strongly related to the inertial sensor error modeling problem. Accelerometers and gyroscopes may be corrupted by random errors of complex spectral structure. Consequently, identifying correct error-state parameters in the INS/GNSS EKF becomes difficult when several stochastic processes are superposed. In such situations, classical approaches like the Allan variance (AV) or power spectral density (PSD) analysis fail due to the difficulty of separating the error processes in the spectral domain. For this purpose, we propose applying a recently developed estimator based on the generalized method of wavelet moments (GMWM), which was proven to be consistent and asymptotically normally distributed. The GMWM estimator matches theoretical and sample-based wavelet variances (WVs), and can be computed using the method of indirect inference. This article mainly focuses on the implementation aspects related to the GMWM, and its integration within a general navigation filter calibration procedure. Regarding this, we apply the GMWM on error signals issued from MEMS-based inertial sensors by building and estimating composite stochastic processes for which classical methods cannot be used. In a first stage, we validate the resulting models using AV and PSD analyses and then, in a second stage, we study the impact of the resulting stochastic models design in terms of positioning accuracy using an emulated scenario with statically observed error signatures. We demonstrate that the GMWM-based calibration framework enables to estimate complex stochastic models in terms of the resulting navigation accuracy that are relevant for the observed structure of errors.
机译：通常，通过贝叶斯滤波器（例如扩展卡尔曼滤波器（EKF））将基于卫星的系统（GNSS）发出的观测结果与惯性导航系统（INS）进行集成。设计导航EKF的任务与惯性传感器误差建模问题密切相关。加速度计和陀螺仪可能会因复杂的光谱结构的随机误差而损坏。因此，当多个随机过程重叠时，在INS / GNSS EKF中识别正确的错误状态参数变得很困难。在这种情况下，由于难以在频谱域中分离误差过程，像Allan方差（AV）或功率谱密度（PSD）分析之类的经典方法会失败。为此，我们建议基于小波矩的广义方法（GMWM）应用最近开发的估计器，该估计器被证明是一致的且渐近正态分布。 GMWM估计器匹配理论和基于样本的小波方差（WV），并且可以使用间接推断的方法进行计算。本文主要关注与GMWM相关的实现方面，以及其在常规导航过滤器校准过程中的集成。关于这一点，我们通过构建和估计无法使用经典方法的复合随机过程，将GMWM应用于基于MEMS的惯性传感器发出的误差信号。在第一阶段，我们使用AV和PSD分析验证生成的模型，然后在第二阶段，使用具有静态观察到的错误签名的模拟方案，研究生成的随机模型设计对定位精度的影响。我们证明，基于GMWM的校准框架能够根据与观察到的错误结构相关的结果导航精度来估计复杂的随机模型。

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