Application of Improved Sparrow Algorithm in Sky-Wave Radar Location

Fig. 6. Latitude and longitude error of target predict. (a) Latitude and longitude error of ELM model target predict; (b) latitude and longitude error of KELM model target predict

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Table 1. Benchmark function
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Table 1. Benchmark function
Function Function name Dimension Search scope Optimal value
$f_{1}$ Sphere 30 $[- 100,100]$ 0
$f_{2}$ Schwefel2.22 30 $[- 10,10]$ 0
$f_{3}$ Rastrigin 30 $[- 5.12,5.12]$ 0
$f_{4}$ Ackley 30 $[- 32,32]$ 0

Table 2. Simulation results of improved SSA

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Table 2. Simulation results of improved SSA

Function	Algorithm	Optimal value	Worst value	Average value	Standard deviation
$f_{1}$	DA	0.0032	873.2685	169.777	226.3133
	GWO	$1.1338 \times 10^{- 9}$	$2.2480 \times 10^{- 16}$	$2.5185 \times 10^{- 17}$	$5.5118 \times 10^{- 17}$
	SSA	$5.3392 \times 10^{- 113}$	$4.2810 \times 10^{- 10}$	$4.8375 \times 10^{- 11}$	$1.1872 \times 10^{- 10}$
	ISSA	$1.6590 \times 10^{- 19}$	$5.0929 \times 10^{- 12}$	$3.5981 \times 10^{- 13}$	$1.2056 \times 10^{- 12}$
	CACMSSA	$4.2356 \times 10^{- 112}$	$1.9696 \times 10^{- 42}$	$9.8482 \times 10^{- 44}$	$4.4042 \times 10^{- 43}$
$f_{2}$	DA	1.2641	34.8134	8.3417	8.2309
	GWO	$6.6862 \times 10^{- 12}$	$5.6068 \times 10^{- 10}$	$8.7514 \times 10^{- 11}$	$1.2369 \times 10^{- 10}$
	SSA	$3.8350 \times 10^{- 281}$	$5.5796 \times 10^{- 5}$	$3.2048 \times 10^{- 6}$	$1.2482 \times 10^{- 5}$
	ISSA	$3.4242 \times 10^{- 15}$	$1.2965 \times 10^{- 6}$	$1.0399 \times 10^{- 7}$	$2.8982 \times 10^{- 7}$
	CACMSSA	$5.3089 \times 10^{- 46}$	$2.4327 \times 10^{- 20}$	$1.4225 \times 10^{- 21}$	$5.4119 \times 10^{- 21}$
$f_{3}$	DA	69.3874	283.9612	181.3864	58.2389
	GWO	6.194	40.1776	16.2064	7.2727
	SSA	0	$2.2072 \times 10^{- 6}$	$1.2850 \times 10^{- 7}$	$4.9306 \times 10^{- 7}$
	ISSA	0	$1.0406 \times 10^{- 9}$	$1.1010 \times 10^{- 10}$	$2.9733 \times 10^{- 10}$
	CACMSSA	0	0	0	0
$f_{4}$	DA	8.9344	20.2145	15.834	3.6235
	GWO	$1.4055 \times 10^{- 5}$	$1.0287 \times 10^{- 3}$	$5.1042 \times 10^{- 5}$	$3.0064 \times 10^{- 5}$
	SSA	$8.8818 \times 10^{- 16}$	$8.5112 \times 10^{- 5}$	$4.3437 \times 10^{- 6}$	$1.9013 \times 10^{- 5}$
	ISSA	$1.1102 \times 10^{- 13}$	$3.3480 \times 10^{- 7}$	$5.2499 \times 10^{- 8}$	$1.0168 \times 10^{- 7}$
	CACMSSA	$8.8818 \times 10^{- 16}$	$8.8818 \times 10^{- 16}$	$8.8818 \times 10^{- 16}$	0

Table 3. Error of seven ELM prediction methods

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Table 3. Error of seven ELM prediction methods

No.	Method	$M_{A E} / (°)$	$M_{A P E} / (°)$
1	ELM location model	0.1064	0.0429
2	SSA-ELM location model	0.0224	0.0094
3	LACMODA-ELM location model	0.0200	0.0083
4	CACMSSA-ELM location model	0.0183	0.0073
5	CACMSSA-KELM location model	0.0180	0.0072
6	SSA-HKELM location model	0.0189	0.0075
7	CACMSSA-HKELM location model	0.0145	0.0060

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Shen Chen, Yian Liu, Hailing Song. Application of Improved Sparrow Algorithm in Sky-Wave Radar Location[J]. Laser & Optoelectronics Progress, 2023, 60(10): 1020001

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