Field system-level calibration method for accelerometer considering nonlinear coefficients

doi:10.23919/JSEE.2025.000066

Abstract

Abstract:

In order to get rid of the dependence on high-precision centrifuges in accelerometer nonlinear coefficients calibration, this paper proposes a system-level calibration method for field condition. Firstly, a 42-dimension Kalman filter is constructed to reduce impact brought by turntable. Then, a biaxial rotation path is designed based on the accelerometer output model, including orthogonal 22 positions and tilt 12 positions, which enhances gravity excitation on nonlinear coefficients of accelerometer. Finally, sampling is carried out for calibration and further experiments. The results of static inertial navigation experiments lasting 4000 s show that compared with the traditional method, the proposed method reduces the position error by about 390 m.

Key words: accelerometer, nonlinear coefficient, system-level calibration, rotation path

Haotian WU, Ruihang YU, Juliang CAO, Caixia MA, Bainan YANG. Field system-level calibration method for accelerometer considering nonlinear coefficients[J]. Journal of Systems Engineering and Electronics, 2025, 36(3): 814-824.

Figures/Tables 16

Table 1

Table 2

Table 3

Table 4

Singular value and corresponding state combination"

Singular value	Result	State combination
${\sigma _1}$	314.84	0.99$\delta {k_{2\text{a}y}}$
${\sigma _2}$	288.63	0.99$\delta {k_{2\text{a}z}}$
${\sigma _3}$	284.14	0.99$\delta {k_{2\text{a}x}}$
${\sigma _4}$	95.95	0.99$\delta {k_{2\text{a}yy}}$
${\sigma _5}$	95.94	0.77$ \delta {k_{2\text{a}yx}} $
${\sigma _6}$	95.93	−0.63$\delta {k_{2\text{a}yx}}$−0.77$\delta {k_{2\text{a}yz}}$
${\sigma _7}$	95.83	−0.99$\delta {k_{2\text{a}xx}}$
${\sigma _8}$	95.83	−0.99$\delta {k_{2\text{a}xy}}$
${\sigma _9}$	95.83	−0.99$\delta {k_{2\text{a}xz}}$
${\sigma _{10}}$	83.67	−0.97$\delta {k_{2\text{a}zz}}$
${\sigma _{11}}$	83.40	−0.44$\delta {k_{2\text{a}zx}}$+0.86$\delta {k_{2\text{a}zy}}$
${\sigma _{12}}$	82.83	0.88$\delta {k_{2\text{a}zx}}$+0.46$\delta {k_{2\text{a}zy}}$
${\sigma _{13}}$	60.25	−0.89${\phi _N}$
${\sigma _{14}}$	59.46	0.9${\phi _E}$
${\sigma _{15}}$	47.59	0.97${\varepsilon _x}$+0.22${\varepsilon _y}$
${\sigma _{16}}$	46.96	−${\varepsilon _z}$
${\sigma _{17}}$	45.28	0.22${\varepsilon _x}$−0.97${\varepsilon _y}$
${\sigma _{18}}$	34.19	0.74$ \delta {k_{\text{a}yx}} $+0.58$\delta {k_{\text{a}yz}}$−0.28$\delta {k_{\text{a}zx}}$
${\sigma _{19}}$	33.80	−0.23$ \delta {k_{\text{a}xy}} $−0.53$ \delta {k_{\text{a}yx}} $+0.58$ \delta {k_{\text{a}yz}} $+0.48$ \delta {k_{\text{a}zy}} $
${\sigma _{20}}$	32.36	−0.71$ \delta {k_{\text{a}xy}} $+0.47$ \delta {k_{\text{a}yy}} $−0.5$ \delta {k_{\text{a}zy}} $
${\sigma _{21}}$	31.69	0.67$ \delta {k_{\text{a}xz}} $+0.27$ \delta {k_{\text{a}yz}} $+0.64$ \delta {k_{\text{a}zx}} $
${\sigma _{22}}$	29.27	0.41$ \delta {k_{\text{a}xy}} $+0.86$ \delta {k_{\text{a}yy}} $+0.21$ \delta {k_{\text{a}zy}} $
${\sigma _{23}}$	27.53	0.98$ \delta {k_{\text{a}xx}} $
${\sigma _{24}}$	26.52	−0.64$ \delta {k_{\text{a}xz}} $+0.63$ \delta {k_{\text{a}zx}} $
${\sigma _{25}}$	25.46	0.19${\phi _E}$+0.31${\phi _N}$+0.45$ \delta {k_{\text{a}xy}} $− 0.3$ \delta {k_{\text{a}yx}} $+0.39$ \delta {k_{\text{a}yz}} $−0.6$ \delta {k_{\text{a}zy}} $
${\sigma _{26}}$	23.02	0.99$ \delta {k_{\text{a}zz}} $
${\sigma _{27}}$	5.83	0.88$\delta {V_N}$+0.47$\delta {V_U}$
${\sigma _{28}}$	5.83	0.47$\delta {V_N}$−0.88$\delta {V_U}$
${\sigma _{29}}$	5.83	$\delta {V_E}$
${\sigma _{30}}$	3.87	−0.45${\nabla _x}$+0.88${\nabla _z}$
${\sigma _{31}}$	3.32	−0.88${\nabla _x}$−0.46${\nabla _z}$
${\sigma _{32}}$	3.23	−0.99${\nabla _y}$

Table 4

Table 5

Table 6

Table 7

Table 8

Table 9

Fig 1

Table 10

Fig 2

Table 11

Fig 3

Table 12

Fig 4

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Serial number	Stance/(°)			Serial number	Stance/(°)
Serial number	X	Y	Z	Serial number	X	Y	Z
1	45	0	0	7	0	225	0
2	135	0	0	8	0	315	0
3	225	0	0	9	90	45	0
4	315	0	0	10	90	135	0
5	0	45	0	11	90	225	0
6	0	135	0	12	90	315	0

Coefficient	Truth	Result	Error
$\delta {k_{\text{a}xx}}$	10	9.98	0.02
$\delta {k_{\text{a}yy}}$	10	9.97	0.03
$\delta {k_{\text{a}zz}}$	10	9.61	0.39

Coefficient	Truth	Result	Error
$\delta {k_{\text{a}yx}}$	20	20.02	0.02
$\delta {k_{\text{a}zx}}$	20	19.99	0.01
$\delta {k_{\text{a}zy}}$	20	20.02	0.02

Coefficient	Truth	Result	Error
$ \nabla _x^\text{b} $	50	50.07	0.07
$ \nabla _y^\text{b} $	50	49.91	0.09
$ \nabla _z^\text{b} $	50	50.00	0

Coefficient	Truth	Result	Error
$\delta {k_{2x}}$	20	19.92	0.08
$\delta {k_{2y}}$	20	20.08	0.08
$\delta {k_{2z}}$	20	19.61	0.39