Underwater inertial error rectification with limited acoustic observations

Satellite Navigation

Table 4 The statistics result of APE and efficiency for different algorithms

	Methods		Results of N = 15	Results of N = 20	Results of N = 25	Results of N = 30	Average
APE (m)	DRNS	Mean ^a	238.03	239.00	239.96	240.88	239.47 m
	DRNS	Mean ^b	239.24	239.62	240.16	240.84	239.96 m
	VLBL	Mean ^a	29.71	28.77	28.34	28.46	28.82 (↓87.96%)
	VLBL	Mean ^b	7.60	9.19	10.95	12.57	10.08 (↓96.00%)
	mAB-VLBL-rot	Mean ^a	30.80	31.43	33.06	35.45	32.68 (↓86.35%)
	mAB-VLBL-rot	Mean ^b	6.95	8.47	10.29	12.04	9.44 (↓96.27%)
	mAB-VLBL	Mean ^a	10.70	6.67	6.38	6.07	7.45 (↓96.88%)
	mAB-VLBL	Mean ^b	3.78	3.54	3.46	3.22	3.50 (↓98.75%)
Time (s)	VLBL	Time ^a	0.016	0.026	0.020	0.024	0.021 s
	VLBL	Time ^b	0.022	0.024	0.021	0.023	0.023 s
	mAB-VLBL-rot	Time ^a	0.032	0.038	0.033	0.036	0.034 (↑65.85%)
	mAB-VLBL-rot	Time ^b	0.034	0.038	0.036	0.038	0.036 (↑61.08%)
	mAB-VLBL	Time ^a	0.042	0.045	0.042	0.043	0.043(↑108.51%)
	mAB-VLBL	Time ^b	0.041	0.045	0.042	0.044	0.043 (↑91.22%)

Bold values mean the performance is better than other methods under the same test condition
^aSingle acoustic beacon is available; ^bdouble acoustic beacons are available