Heading-sensitive azimuth error analysis and scheme modification for the multi-position alignment of a fiber-optic gyro strapdown inertial navigation system

Yifu Jiang; Sihai Li; Qiangwen Fu; Gongmin Yan; Bo Xie

doi:10.1364/AO.451199

Applied Optics
Vol. 61,
Issue 15,
pp. 4259-4269
(2022)
•https://doi.org/10.1364/AO.451199

Heading-sensitive azimuth error analysis and scheme modification for the multi-position alignment of a fiber-optic gyro strapdown inertial navigation system

Yifu Jiang, Sihai Li, Qiangwen Fu, Gongmin Yan, and Bo Xie

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Yifu Jiang, Sihai Li, Qiangwen Fu, Gongmin Yan, and Bo Xie, "Heading-sensitive azimuth error analysis and scheme modification for the multi-position alignment of a fiber-optic gyro strapdown inertial navigation system," Appl. Opt. 61, 4259-4269 (2022)

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Abstract

As two-position is the most widely used scheme of multi-position alignment, azimuth error analysis regarding the whole alignment procedure as an entity is explicitly discussed. A formula to calculate an equivalent north accelerometer bias drift rate is developed. The effecting extent of each inertial measurement error is also theoretically deduced and validated through simulation. It is pointed out that the main error sources causing heading-sensitive azimuth error are accelerometer triad non-orthogonality and lever arm error. In a Kalman filter alignment algorithm, affected by the equivalent accelerometer bias change rate, extra azimuth error emerges from the mistake estimation of fiber-optic gyroscope drift. A three-sequence scheme and a reciprocating slow-rotation scheme are proposed to achieve the most inertial measurement error self-compensation. Theoretical error comparison and a turntable four-orientation alignment test show the superiority of the reciprocating slow-rotation scheme over the other two schemes. The heading-sensitive azimuth alignment error is reduced from 0.2268° to better than 0.0015° through scheme modification.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Error Source	Two-Position Scheme	Three-Sequence Scheme	Reciprocating Rotation Scheme
$\nabla_{x}^{p}$ , $\nabla_{y}^{p}$	$δ f_{1 N}^{n} \approx - \frac{3}{t_{w}} (\nabla_{x}^{p} \sin ψ + \nabla_{y}^{p} \cos ψ)$	$δ f_{1 N}^{n} = 0$	$δ f_{1 N}^{n} = 0$
$\nabla_{z}^{p}$	$δ f_{E}^{n} = \nabla_{z}^{p} θ \sin ψ$	$δ f_{E}^{n} = \nabla_{z}^{p} θ \sin ψ$	$δ f_{E}^{n} = \nabla_{z}^{p} θ \sin ψ$
$\nabla_{1 y}^{p}$	$δ f_{1 N}^{n} \approx - \frac{3}{2} \nabla_{1 y}^{p} \cos ψ$	$δ f_{1 N}^{n} \approx \frac{3}{4} \nabla_{1 y}^{p} \cos ψ$	$δ f_{1 N}^{n} = \frac{3}{2 π} \nabla_{1 y}^{p} (- \sin ψ + \frac{1}{π} \cos ψ)$
$\nabla_{1 y}^{p_{1}}$ , $\nabla_{1 y}^{p_{2}}$	$δ f_{1 N}^{n} \approx - (\nabla_{1 y}^{p_{1}} + \frac{1}{2} \nabla_{1 y}^{p_{2}}) \cos ψ$	$δ f_{1 N}^{n} \approx \frac{3}{8} (\nabla_{1 y}^{p_{1}} + \frac{1}{2} \nabla_{1 y}^{p_{2}}) \cos ψ$	$δ f_{1 N}^{n} \approx \frac{3 (\nabla_{1 y}^{p_{1}} + \nabla_{1 y}^{p_{2}}) (\cos ψ - π \sin ψ)}{4 π^{2}}$
$δ_{zy}$	$δ f_{1 N}^{n} = 3 δ_{zy} θ^{2} g \cos ψ / 2 t_{s}$	$δ f_{1 N}^{n} = 0$	$δ f_{1 N}^{n} = 0$
$l_{axx}$ , $l_{ayy}$	$δ f_{1 N}^{n} = \frac{24 (l_{axx} \sin ψ + l_{ayy} \sin ψ)}{t_{w}^{3}}$	$δ f_{1 N}^{n} = 0$	$δ f_{1 N}^{n} = 0$
$δ k_{ay}$ , $δ k_{ay}$ , $δ k_{az}$	$δ f_{E}^{n} = (δ k_{ay} - δ k_{az}) g θ \sin ψ$	$δ f_{E}^{n} = (δ k_{ay} - δ k_{az}) g θ \sin ψ$	$δ f_{E}^{n} = g θ \sin ψ δ k_{az} - g θ \sin ψ (δ k_{ax} + δ k_{ay}) / 2$
$δ k_{gz}$	$δ ω_{E}^{n} = \sin (π δ k_{gz}) ω_{ie} \cos L / 2$	$δ ω_{E}^{n} = 0$	$δ ω_{E}^{n} = 0$
$ε_{z}^{p}$	$δ ω_{E}^{n} = ε_{z}^{p} (θ \sin ψ + t_{s} ω_{ie} \cos L / 2)$	$δ ω_{E}^{n} = ε_{z}^{p} (θ \sin ψ + t_{s} ω_{ie} \cos L / 2)$	$δ ω_{E}^{n} = ε_{z} θ \sin ψ + ε_{z}^{p} t_{s} ω_{ie} \cos L / 2$
$σ_{yx}$	$δ ω_{E}^{n} = - \sin^{2} ψ σ_{zy} ω_{ie} \cos L$	$δ ω_{E}^{n} = - \sin^{2} ψ σ_{zy} ω_{ie} \cos L$	$δ ω_{E}^{n} = - σ_{zy} ω_{ie} \cos L / 2$

	Azimuth1 (°)	Azimuth2 (°)	Azimuth3 (°)	Azimuth4 (°)
1	269.3418	179.2981	89.4809	359.5226
2	269.3310	179.3022	89.4788	359.5278
3	269.3440	179.2900	89.4722	359.5152
4	269.3433	179.2855	89.4750	359.5221
5	269.3499	179.2957	89.4643	359.5180
6	269.3352	179.2971	89.4837	359.5246
7	269.3360	179.2984	89.4781	359.5312
8	269.3457	179.3001	89.4779	359.5206
$\bar{ψ}$ (°)	269.3409	179.2959	89.4764	359.5227
$δ$ (°)	0.2268

	Azimuth1 (°)	Azimuth2 (°)	Azimuth3 (°)	Azimuth4 (°)
1	269.4047	179.4073	89.4174	359.4132
2	269.3938	179.4114	89.4152	359.4185
3	269.4085	179.3991	89.4082	359.4058
4	269.4080	179.3947	89.4104	359.4127
5	269.4151	179.4050	89.3995	359.4085
6	269.4005	179.4064	89.4179	359.4150
7	269.4024	179.4077	89.4122	359.4217
8	269.4122	179.4095	89.4119	359.4111
$\bar{ψ}$ (°)	269.4057	179.4051	89.4116	359.4133
$δ$ (°)	0.0082

	Azimuth1 (°)	Azimuth2 (°)	Azimuth3 (°)	Azimuth4 (°)
1	2.2415	272.0891	182.0318	92.1932
2	2.2418	272.0917	182.0402	92.2123
3	2.2422	272.0791	182.0327	92.2156
4	2.2311	272.0794	182.0438	92.2074
5	2.2251	272.0989	182.0297	92.1904
6	2.2413	272.0850	182.0378	92.1887
7	2.2377	272.0898	182.0333	92.2082
8	2.2434	272.0793	182.0410	92.2028
$\bar{ψ}$ (°)	2.2380	272.0865	182.0363	92.2023
$δ$ (°)	0.2017

	Azimuth1 (°)	Azimuth2 (°)	Azimuth3 (°)	Azimuth4 (°)
1	2.1313	272.1571	182.1381	92.1380
2	2.1507	272.1591	182.1486	92.1457
3	2.1347	272.1283	182.1319	92.1527
4	2.1496	272.1398	182.1449	92.1416
5	2.1353	272.1457	182.1416	92.1413
6	2.1494	272.1507	182.1395	92.1377
7	2.1444	272.1441	182.1391	92.1454
8	2.1436	272.1490	182.1399	92.1414
$\bar{ψ}$ (°)	2.1424	272.1467	182.1404	92.1430
$δ$ (°)	0.0063

	Azimuth1 (°)	Azimuth2 (°)	Azimuth3 (°)	Azimuth4 (°)
1	269.3470	179.3833	89.4186	359.4198
2	269.3645	179.3856	89.4096	359.4124
3	269.3469	179.3812	89.4089	359.4060
4	269.3690	179.3824	89.4005	359.4138
5	269.3763	179.3822	89.4053	359.4147
6	269.3668	179.3964	89.4045	359.4128
7	269.3683	179.3901	89.4142	359.4159
8	269.3738	179.3853	89.4055	359.4076
$\bar{ψ}$ (°)	269.3641	179.3858	89.4084	359.4129
$δ$ (°)	0.0488

	Azimuth1 (°)	Azimuth2 (°)	Azimuth3 (°)	Azimuth4 (°)
1	269.3772	179.3891	89.4295	359.4277
2	269.3947	179.3914	89.4208	359.4203
3	269.3745	179.3870	89.4203	359.4139
4	269.3957	179.3878	89.4136	359.4218
5	269.4022	179.3870	89.4190	359.4229
6	269.3923	179.4013	89.4201	359.4214
7	269.3911	179.3949	89.4301	359.4244
8	269.3908	179.3900	89.4216	359.4161
$\bar{ψ}$ (°)	269.3898	179.3911	89.4219	359.4211
$δ$ (°)	0.0321

	Azimuth1 (°)	Azimuth2 (°)	Azimuth3 (°)	Azimuth4 (°)
1	2.1492	272.1509	182.1385	92.1430
2	2.1325	272.1533	182.1486	92.1485
3	2.1491	272.1234	182.1313	92.1551
4	2.1330	272.1352	182.1446	92.1452
5	2.1477	272.1405	182.1426	92.1479
6	2.1413	272.1458	182.1399	92.1379
7	2.1427	272.1381	182.1373	92.1489
8	2.1448	272.1442	182.1422	92.1444
$\bar{ψ}$ (°)	2.1425	272.1414	182.1406	92.1464
$δ$ (°)	0.0058

	Azimuth1 (°)	Azimuth2 (°)	Azimuth3 (°)	Azimuth4 (°)
1	2.1484	272.1528	182.1392	92.1404
2	2.1490	272.1553	182.1494	92.1459
3	2.1318	272.1254	182.1321	92.1525
4	2.1541	272.1372	182.1454	92.1425
5	2.1445	272.1426	182.1434	92.1452
6	2.1468	272.1478	182.1407	92.1352
7	2.1453	272.1402	182.1382	92.1462
8	2.1437	272.1462	182.1422	92.1417
$\bar{ψ}$ (°)	2.1458	272.1434	182.1413	92.1437
$δ$ (°)	0.0045

	Azimuth1 (°)	Azimuth2 (°)	Azimuth3 (°)	Azimuth4 (°)
1	2.1330	272.1394	182.1325	92.1504
2	2.1401	272.1475	182.1410	92.1380
3	2.1399	272.1414	182.1432	92.1329
4	2.1372	272.1285	182.1354	92.1356
5	2.1326	272.1316	182.1262	92.1361
6	2.1418	272.1425	182.1511	92.1353
7	2.1392	272.1363	182.1457	92.1336
8	2.1403	272.1339	182.1386	92.1408
$\bar{ψ}$ (°)	2.1380	272.1377	182.1392	92.1378
$δ$ (°)	0.0015

Abstract

Data availability

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Equations (56)

Applied Optics