Parametric and State Estimation of Stationary MEMS-IMUs: A Tutorial
Daniel Engelsman, Yair Stolero, Itzik Klein
TL;DR
MEMS-IMU INS drift due to sensor biases and noise is addressed with a linear Gaussian framework for a 15‑state error model. The paper analyzes both single-sensor and multi-sensor arrays, deriving propagation and noise covariances, and demonstrates that averaging across $K$ sensors reduces mean bias roughly by $1/K$ and decreases process-noise effects roughly by $1/K$, while accumulating more measurements over time yields a $1/\sqrt{N}$ improvement per time window. Continuous-time propagation is captured by $\Phi(\tau) = e^{F\tau}$ and a derived $Q(\tau)$, with state covariances following $P(\tau) = \Phi(\tau) P_0 \Phi(\tau)^T + Q(\tau)$. Experimental validation uses two 5-sensor arrays (10 sensors) and confirms that increasing $K$ tightens error ellipsoids and brings estimates closer to ground truth, in line with the CRLB-inspired scaling.
Abstract
Inertial navigation systems (INS) are widely used in almost any operational environment, including aviation, marine, and land vehicles. Inertial measurements from accelerometers and gyroscopes allow the INS to estimate position, velocity, and orientation of its host vehicle. However, as inherent sensor measurement errors propagate into the state estimates, accuracy degrades over time. To mitigate the resulting drift in state estimates, different approaches of parametric and state estimation are proposed to compensate for undesirable errors, using frequency-domain filtering or external information fusion. Another approach uses multiple inertial sensors, a field with rapid growth potential and applications. The increased sampling of the observed phenomenon results in the improvement of several key factors such as signal accuracy, frequency resolution, noise rejection, and higher redundancy. This study offers an analysis tutorial of basic multiple inertial operation, with a new perspective on the error relationship to time, and number of sensors. To that end, a stationary and levelled sensors array is taken, and its robustness against the instrumental errors is analyzed. Subsequently, the hypothesized analytical model is compared with the experimental results, and the level of agreement between them is thoroughly discussed. Ultimately, our results showcase the vast potential of employing multiple sensors, as we observe improvements spanning from the signal level to the navigation states. This tutorial is suitable for both newcomers and people experienced with multiple inertial sensors.