Wavelet-Based Moment-Matching Techniques for Inertial Sensor Calibration

Abstract

The task of inertial sensor calibration has required the development of various techniques to take into account the sources of measurement error coming from such devices. The calibration of the stochastic errors of these sensors has been the focus of increasing amount of research in which the method of reference has been the so-called "Allan variance slope method" which, in addition to not having appropriate statistical properties, requires a subjective input which makes it prone to mistakes. To overcome this, recent research has started proposing "automatic" approaches where the parameters of the probabilistic models underlying the error signals are estimated by matching functions of the Allan variance or Wavelet Variance with their modelimplied counterparts. However, given the increased use of such techniques, there has been no study or clear direction for practitioners on which approach is optimal for the purpose of sensor calibration. This paper formally defines the class of estimators based on this technique and puts forward theoretical and applied results that, comparing with estimators in this class, suggest the use of the Generalized Method of Wavelet Moments as an optimal choice.

Coning motion stability and decoupling methods analysis of spinning missiles with angle‐of‐attack feedback autopilot

“…Figure 2 shows the structure of spinning missiles applying a three‐dimensional ideal proportional navigation guidance law [32] with an AOA feedback autopilot. Here, is the forward channel gain, is the gain of the rate loop, is the gain of the attitude feedback loop, is the gain of the accelerometer, and is the distance between the location of acceleration installation and the c.g.Remark Groves and Guerrier et al [33, 34]. The distance between the location of acceleration installation and the c.g.…”

Multi-Signal Approaches for Repeated Sampling Schemes in Inertial Sensor Calibration

“…PROOF: When ν(θ) = W θ, as shown in [6], the GMWM has an explicit solution given by θ = (W ΩW ) −1 W Ω ν.…”

“…For a detailed discussion, see [5]. However, the Allan variance plot is a graphical device requiring a manual inspection and is consequently sensitive to the user's proficiency as well as being burdened with many theoretical limitations including significant bias in the estimated parameters of the postulated stochastic model [6], [7]. To overcome the limitations of the Allan variance approach as well as the important computational limitations of Maximum-Likelihood based techniques, the Generalized Method of Wavelet Moments (GMWM) was proposed in [8] providing a statistically appropriate and computationally feasible technique for stochastic calibration of inertial sensors.…”

On Performance Evaluation of Inertial Navigation Systems: The Case of Stochastic Calibration

“…Stochastic calibration of inertial sensors has been widely studied in the last decades and several methods are available, ranging from the Allan Variance (AV) Linear Regression method [6,7], which we refer to as AVLR, to the more recent Generalized Method of Wavelet Moments (GMWM) [8,9], not to mention methods based on the analysis of the power spectral density of the sensor errors [10,11], correlation of filtered sensor outputs [12], and maximum-likelihood estimation [13]. In this context, each technique allows to consider a class of possible stochastic models and selects one within this class that appears to be the most suitable according to some specific goodness-of-fit metric.…”