Use of Tikhonov Regularization to Improve the Accuracy of Position Estimates in Inertial Navigation

Table 2

Computing times as 𝑁 and 𝑀 increase. All times are average computing times over 100 cycles and include only the solution phase. Tests were performed with Matlab 7.9.0 running on a 32-bit operating system. The used computer has a 2 GHz processor and 2 GB of memory. CSNE stands for the method described in Section 3.2, “∖” for the “backslash” operator, and LSQR for the iterative least-squares problems solution routine implemented in Matlab. “It” indicates the number of iterations made by CSNE and 𝛿/𝑁^1/2 indicates the “size” of the last correction step.

		CSNE			“∖”	LSQR
𝑁	𝑀	It	𝑇 (ms)	𝛿/𝑁^1/2	𝑇 (ms)	𝑇 (ms)
500	20	1	1	6.4𝑒−9	2	5
1000	40	1	2	3.4𝑒−8	4	7
2000	80	1	4	3.1𝑒−7	8	12
4000	160	1	8	5.5𝑒−6	16	20
8000	320	1	16	8.7𝑒−5	34	36
16000	640	1	34	4.1𝑒−4	76	63
32000	1280	2	103	1.7𝑒−5	148	117
64000	2560	2	212	4.0𝑒−4	302	271
128000	5120	7	1106	3.1𝑒−4	635	618