Maximum Likelihood Identification of Stochastic Models of Inertial Sensor Noises

Abstract

This article applies maximum likelihood estimation (MLE) to the identification of a state-space model for inertial sensor drift. The discrete-time scalar state considered is either a first-order Gauss-Markov process or a Wiener process (WP), both of which are common noise terms in inertial sensor noise models. The measurement model includes an additive white measurement noise. In setting up the MLE, the likelihood function (LF) is derived within the steady-state Kalman filter (KF) framework. The resulting log-likelihood function (LLF) can be expressed as a quadratic function of the measurements. This allows for an explicit expression of the LLF, facilitating the evaluation of the Cramér-Rao lower bound (CRLB) and thence testing and ultimately confirming the statistical efficiency, i.e., the optimality, of the ML estimators. Simulations demonstrate the optimal performance of the estimators, and applications to real sensor data indicate advantages over the Allan variance (AV) method for noise modeling.