Unbiased estimation of target motion analyze based on non-maneuvering single station

CTLS算法步骤
输入： ${\tilde{θ}}_{0}$ ， ${\tilde{θ}}_{k + 1}$ ， ${\tilde{φ}}_{0}$ ， ${\tilde{φ}}_{k + 1}$
输出： ${\hat{p}}_{k + 1}$
Step1：生成增广矩阵 ${\tilde{A}}_{k + 1}$ 与 $u_{\tilde{θ}, k + 1}$ ， $u_{\tilde{φ}, k + 1}$
Step2：计算P（k+1）， $Ω (k + 1)$
$P (k + 1) = P (k) + {\tilde{A}}_{k + 1}^{T} {\tilde{A}}_{k + 1}$ $Ω (k + 1) = Ω (k) + u_{\tilde{θ}, k + 1}^{T} u_{\tilde{θ}, k + 1} σ_{θ, k + 1}^{2} + u_{\tilde{φ}, k + 1}^{T} u_{\tilde{φ}, k + 1} σ_{φ, k + 1}^{2}$
Step3：求解最优向量 $b^{*}$
$v^{} = m i n {e i g (P (k + 1), Ω (k + 1))}$ $b^{} = \frac{v^{} (1 ∶ 3)}{v^{} (4)}$
Step4：计算目标位置估计与距离估计 $\hat{r_{0}} = \frac{v_{c}}{\| \| b^{*} \| \|}$
$\begin{array}{l} {\hat{p}}_{k + 1} = \hat{r_{0}} (e_{0} + k T b^{*}) \\ {\hat{r}}_{k + 1} = \| \| {\hat{p}}_{k + 1} \| \| \end{array}$

Table 2. RDE and performance improvement effects under different angle measurement standard deviations

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Table 2. RDE and performance improvement effects under different angle measurement standard deviations

算法	0.1°		0.15°		0.2°		0.25°		0.3°
算法	RDE	$η$	RDE	$η$	RDE	$η$	RDE	$η$	RDE	$η$
PLE	7.3	——	15.1	——	24.6	——	34.5	——	43.3	——
EKF	6.9	5.5	9.5	37.1	16.2	34.1	16.5	52.2	27.3	37.0
IV	2.3	68.5	4.5	70.2	12.9	47.6	53.5	-55.1	50.7	-17.1
WIV	2.3	68.5	4.3	71.5	11.8	52.0	44.4	-28.7	120.6	-178.5
CTLS	2.2	70.0	2.9	80.8	4.2	82.9	5.0	85.5	6.1	85.9

Table 3. APE and performance improvement effects under different angle measurement standard deviations

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Table 3. APE and performance improvement effects under different angle measurement standard deviations

算法	0.1°		0.15°		0.2°		0.25°		0.3°
算法	APE/km	$η$ /%	APE/km	$η$ /%	APE/km	$η$ /%	APE/km	$η$ /%	APE/km	$η$ /%
PLE	8.1	——	16.3	——	26.3	——	36.8	——	46.1	——
EKF	27.3	-237.0	26.3	-61.3	35.6	-35.4	28.7	22.0	36.2	21.5
IV	3.2	60.5	6.3	61.3	19.9	24.3	80.4	-118.5	81.5	-76.8
WIV	3.2	60.5	6.0	63.2	18.0	31.6	61.9	-68.2	444.1	-863.3
CTLS	2.8	65.4	4.0	75.5	5.7	78.3	6.9	81.3	8.4	81.8

Table 4. Time-ave deviation of RDE under different angle measurement standard deviations
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Table 4. Time-ave deviation of RDE under different angle measurement standard deviations
算法 0.1° 0.2° 0.3°
RDE/% APE/km RDE/% APE/km RDE/% APE/km
PLE 21 26 50 59 70 81
EKF 16 36 54 84 73 106
IV 14 25 51 85 43 71
WIV 13 24 65 239 54 166
CTLS 6 9 12 19 21 35

Table 5. RDE and performance improvement effects under different initial distances

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Table 5. RDE and performance improvement effects under different initial distances

算法	0.5倍初始距离		1倍初始距离		1.5倍初始距离		2倍初始距离
算法	RDE	$η$	RDE	$η$	RDE	$η$	RDE	$η$
PLE	0.6	——	7.3	——	25.1	——	48.0	——
EKF	1.6	-166.7	7.7	-5.5	14.0	44.2	30.3	36.9
IV	0.4	33.3	2.1	71.2	9.6	61.8	48.1	-0.2
WIV	0.4	33.3	2.1	71.2	9.3	62.9	46.6	2.9
CTLS	0.4	33.3	2.1	71.2	4.8	80.9	9.2	80.8

Table 6. APE and performance improvement effects under different initial distances

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Table 6. APE and performance improvement effects under different initial distances

算法	0.5倍初始距离		1倍初始距离		1.5倍初始距离		2倍初始距离
算法	APE/km	$η$ /%	APE/km	$η$ /%	APE/km	$η$ /%	APE/km	$η$ /%
PLE	0.25	——	8.1	——	44.7	——	119.0	——
EKF	5.6	-2140	24.3	-200	46.9	-4.9	98.4	17.3
IV	0.2	20	2.9	64.2	26.4	40.9	167.0	-40.3
WIV	0.2	20	2.8	65.4	25.4	43.2	158.4	-33.1
CTLS	0.2	20	2.8	65.4	10.9	75.6	28.8	75.8

Table 7. Time-ave deviation of RDE under different initial distances
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Table 7. Time-ave deviation of RDE under different initial distances
算法 0.5倍初始距离 1倍初始距离 2倍初始距离
RDE/% APE/km RDE/% APE/km RDE/% APE/km
PLE 2 1 21 26 71 182
EKF 3 5 16 36 77 246
IV 1 0.7 14 25 65 214
WIV 1 0.7 13 24 71 378
CTLS 1 0.7 6 9 30 100

Table 8. Comparison of algorithm's relative running time
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Table 8. Comparison of algorithm's relative running time
算法相对时间
EKF 1.0
PLE 3.0
IV 4.5
WIV 75.9
CTLS 4.5

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Jianjun LIN, Rangyuhan WANG, Xiaojun BAN, Hongqian LU. Unbiased estimation of target motion analyze based on non-maneuvering single station[J]. Optics and Precision Engineering, 2024, 32(7): 1034

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Paper Information

Category:

Received: May. 17, 2023

Accepted: --

Published Online: May. 28, 2024

The Author Email: Xiaojun BAN (banxiaojun@hit.edu.cn)

DOI:10.37188/OPE.20243207.1034

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Steps of constrained total least squares algorithm

Table 1. Steps of constrained total least squares algorithm

Table 2. RDE and performance improvement effects under different angle measurement standard deviations

Table 2. RDE and performance improvement effects under different angle measurement standard deviations

Table 3. APE and performance improvement effects under different angle measurement standard deviations

Table 3. APE and performance improvement effects under different angle measurement standard deviations

Table 4. Time-ave deviation of RDE under different angle measurement standard deviations

Table 4. Time-ave deviation of RDE under different angle measurement standard deviations

Table 5. RDE and performance improvement effects under different initial distances

Table 5. RDE and performance improvement effects under different initial distances

Table 6. APE and performance improvement effects under different initial distances

Table 6. APE and performance improvement effects under different initial distances

Table 7. Time-ave deviation of RDE under different initial distances

Table 7. Time-ave deviation of RDE under different initial distances

Table 8. Comparison of algorithm's relative running time

Table 8. Comparison of algorithm's relative running time