Time-Reversal-Based Correction Algorithms for $\omega$-Free Trajectory Reconstruction Method.

The low-energy $\omega$ -free accelerometer pair (OFAP) system can achieve great performance in trajectory reconstruction. However, similar to conventional inertial systems, measurement errors in OFAP systems can get accumulated in the reconstruction process, which needs a trajectory correction algorithm to improve its long-term performance. Unfortunately, the linear correction algorithm used in conventional inertial systems is inapplicable, because the nonlinear $\omega$ -free calculations will conflict with the linear correction process. To overcome this obstacle, this letter proposes three algorithms, namely Linear-correction OFAP (LO), Time-Reversal OFAP (TRO), and Time-Reversal Linear-correction OFAP (TRLO), which integrate linear correction and TR symmetry into an OFAP optimization problem to achieve trajectory correction. The three proposed algorithms are solved analytically and compared with conventional approaches in physical experiments. The results show that the proposed correction algorithms significantly enhance the performance of the OFAP system on trajectory reconstruction.