Observability Analysis of Fixed Position Initial Alignment of Strapdown Inertial Navigation System

Table 1. Observability degree of each state in fixed position alignment
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Table 1. Observability degree of each state in fixed position alignment
State variable ϕ_E ϕ_N ϕ_U δv_E δv_N ε_x ε_y ε_z $\begin{matrix} \nabla_{x} \end{matrix}$ $\begin{matrix} \nabla_{y} \end{matrix}$
Observabilitydegree 0.81357 0.81357 9.6793×10^-21 3.479 3.479 0.01124 0.01124 5.7287×10^-9 2.7266×10^-17 1.5591×10^-17

Table 2. Observable states dimension of seven-order model
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Table 2. Observable states dimension of seven-order model
State removed ε_z $\begin{matrix} \nabla_{x} \end{matrix} \begin{matrix} \nabla_{y} \end{matrix}$ ε_y $\begin{matrix} \nabla_{x} \end{matrix} \begin{matrix} \nabla_{y} \end{matrix}$ ε_yε_z $\begin{matrix} \nabla_{y} \end{matrix}$ ε_yε_z $\begin{matrix} \nabla_{x} \end{matrix}$ ε_x $\begin{matrix} \nabla_{x} \end{matrix} \begin{matrix} \nabla_{y} \end{matrix}$
Dimension of observable states 6 6 5 6 7
State removed ε_xε_z $\begin{matrix} \nabla_{y} \end{matrix}$ ε_xε_z $\begin{matrix} \nabla_{x} \end{matrix}$ ε_xε_y $\begin{matrix} \nabla_{y} \end{matrix}$ ε_xε_y $\begin{matrix} \nabla_{x} \end{matrix}$ ε_xε_yε_z
Dimension of observable states 6 6 6 7 6

Table 3. Observability degree of each state of the two combinations

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Table 3. Observability degree of each state of the two combinations

State variable	ϕ_E	ϕ_N	ϕ_U	δv_E	δv_N	ε_y	ε_z
Observability degree	0.49648	0.49669	2.8354×10^-7	2.7616	2.7616	0.0044858	1.5142×10^-9
State variable	ϕ_E	ϕ_N	ϕ_U	δv_E	δv_N	ε_z	$\begin{matrix} \nabla_{y} \end{matrix}$
Observability degree	0.49884	0.49648	2.8354×10^-7	2.7616	2.7628	1.5142×10^-9	1.6622×10^-8

Table 4. Position errors of two models of SINS A with P3
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Table 4. Position errors of two models of SINS A with P3
P₃ 0.1p₃ 0.2p₃ 0.5p₃ p₃ 10p₃
Maximum position error of ten-order model /m 1291 770 491 417 468
Maximum position error of seven-order model /m 413 410 408 407 407

Table 5. Position errors of two models of SINS A with Q and R

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Table 5. Position errors of two models of SINS A with Q and R

Q	0.1q	1.0q	10.0q
Maximum position error of ten-order model /m	417	417	417
Maximum position error of seven-order model /m	407	407	407
R	1.0r	10.0r	100.0r
Maximum position error of ten-order model /m	417	420	451
Maximum position error of seven-order model /m	407	407	427

Table 6. Position errors of two models of SINS B with P3
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Table 6. Position errors of two models of SINS B with P3
P₃ 0.1p₃ 0.2p₃ 0.5p₃ 1.0p₃ 10.0p₃
Maximum position error of ten-order model /m 795 740 715 709 705
Maximum position error of seven-order model /m 704 704 704 704 704

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Wang Qi, Gao Chunfeng, Ying Zhihui, Wei Guo, Long Xingwu. Observability Analysis of Fixed Position Initial Alignment of Strapdown Inertial Navigation System[J]. Chinese Journal of Lasers, 2018, 45(1): 101004

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