A Field Calibration Method for Low-Cost MEMS Accelerometer Based on the Generalized Nonlinear Least Square Method
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ORIGINAL RESEARCH
A Field Calibration Method for Low‑Cost MEMS Accelerometer Based on the Generalized Nonlinear Least Square Method Mahmood ul Hassan1 · Qilian Bao1 Received: 13 March 2020 / Revised: 31 July 2020 / Accepted: 1 September 2020 © Korean Multi-Scale Mechanics (KMSM) 2020
Abstract This paper proposes a field calibration method for an accelerometer without the need of having any external devices for calibration. In the proposed calibration method, generalized nonlinear least-square (GNLS) is used to estimate deterministic errors. A novel sensor’s data collection procedure is developed to collect data of an accelerometer along all three axes and all possible orientations where the expectation of influence of all possible errors is very high. The proposed calibration method is verified by applying it to two different accelerometers. The proposed calibration method achieved an accurate estimation of calibration parameters. The results of the proposed GNLS based calibration method are compared with two other commonly used algorithms, such as Levenberg–Marquardt (LM) and Gauss–Newton (GN). Simulation and experimental results show that the proposed GNLS-based calibration method is slightly more accurate than the LM and GN. The GNLS convergence rate for estimating the calibration parameters is also faster than the LM and GN. Keywords Calibration · Low-cost MEMS accelerometers · Sensor error model · Generalized nonlinear least square method · Gauss–newton and levenberg–marquardt
Introduction The accelerometer is one of the essential components of an inertial navigation system (INS). During navigation, its measurement errors directly cause navigation errors of the same order of magnitude. Moreover, its measurement errors also affect the calibration of the gyroscope and initial alignment, which indirectly cause navigation errors [1]. The accelerometer errors are divided into two categories: Deterministic errors and stochastic errors [2]. Random errors mainly contain random noise, which can be modelled stochastically. Systematic errors consist of scale-factor, bias offset, misalignment errors, and non-orthogonality errors, which can be eliminated by specific calibration procedure [3]. Calibration is the procedure of finding unknown deterministic errors such as scale-factor, bias, and misalignment of a sensor [4]. The desired deterministic errors in a vector form are represented as 𝜃 in Eq. (1)
* Mahmood ul Hassan mahmood‑ul‑[email protected] 1
School of Electronic Information and Electrical Engineering (SEIEE), Shanghai Jiao Tong University, Shanghai, China
] [ 𝜃 = sx , sy , sz , sxy , sxz , syz , bx , by , bz
(1)
where bx , by , and bz are bias along x-axis, y-axis, and z-axis. sx , sy , and sz are scale-factors along x-axis, y-axis, and z-axis. sxy, sxz, and syz are misalignment angles. There are various techniques used for the calibration of an accelerometer. These calibration techniques can be divided into two major categories based on the requirement of any external devices for calibration. In the
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