An $\omega$-Free Accelerometer Array Method for 2-D Trajectory Reconstruction

Abstract

A trajectory can be reconstructed by integrating acceleration and angular velocity (i.e. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\omega$</tex-math></inline-formula> ) sampled by a single inertial measurement unit (IMU) which consists of an accelerometer (ACC) and gyroscope (GYRO). To reduce the system power consumption, a GYRO-free-IMU (GF-IMU) method was proposed which disabled the more power-consuming GYRO and utilized only an ACC array (AA) to obtain acceleration and calculate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\omega$</tex-math></inline-formula> . To alleviate the error accumulation problem in the GF-IMU method, we previously proposed an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\omega$</tex-math></inline-formula> -free ACC pair (OFAP) method which doesn't require the calculation of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\omega$</tex-math></inline-formula> and can estimate the trajectory by solving a constrained optimization problem. However, the constrained problem makes it computationally expensive to generalize the proposed approach for different AA setups with more ACCs. To enhance the scalability and robustness of the system, this paper proposes a new <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\omega$</tex-math></inline-formula> -free inertia-based method, namely <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\omega$</tex-math></inline-formula> -free AA (OFAA), which transforms the constrained problem into an unconstrained one, and derives its scalable and computational-efficient closed-form solution. In both physical experiments and simulations, compared with conventional inertial methods, the proposed OFAA method has a lower trajectory-reconstruction error per distance traveled and is more robust to errors in raw inertial data, while still having a low energy consumption.