At LASSO we are working on the development of the Inertial Navigation System (GF‑INS) project, which is based on compact optomechanical accelerometers with lower noise floors and larger bandwidth. The motivation for a gyro‑free INS comes from the fact that any trajectory consists of translations and rotations, and rotations are always more challenging to handle. High‑grade gyroscopes are usually implemented for this purpose, but they can be bulky, expensive, and energy‑consuming. In contrast, this approach obtains all translations and rotations (including positive and negative, constant and non‑constant angular acceleration) using linear accelerometers only, which can potentially result in an accurate, compact, and cost‑effective INS. To achieve this, we need to model the performance of established configurations using the technical parameters of our optomechanical accelerometer.

We developed a universal Quaternion‑based algorithm in Matlab for a cube‑configuration INS with six accelerometers, and we tested this algorithm with several simple examples, including linear and circular trajectories such as a helix, a horizontal pendulum, a parabola, and a bouncing ball. The results showed that the algorithm is in very good agreement with reference trajectories obtained with the same initial parameters but without gyro‑free elements, and we confirmed these results with Python. In the videos below, rotations with and without misalignment are shown, where the misalignment is introduced at the right bottom corner of the configuration matrix of six accelerometers. Two trajectories, reference (red) and gyro‑free (blue), are displayed, and without misalignment, the reference and gyro‑free trajectories coincide to the numerical error (~10⁻¹⁴).

All these rotations are obtained with linear accelerometers only. Looking ahead, if the model predicts significantly improved performance on existing iterations, we will design, fabricate, and test this opto‑mechanical GF‑INS.