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

Table 1

Simulation results for various values of parameters 𝑠 and 𝜇. Terms 𝜎_I, 𝜎_II and 𝜎_III refer to the standard deviation of the position error (in meters) in case of solution methods I, II, and III. The value of the regularization parameter obtained via the L-curve method is represented as 𝜆_𝐿 and 𝜆 represents the value of the regularization parameter minimizing the position error.

𝑠	𝜇	𝜎^2	argmin𝜆𝜎I(𝜆)	𝜆	𝜎I(𝜆𝐿)	𝜆𝐿	𝜎II	𝜎III
−0.05	−0.5	1	1.137	4.200	1.137	4.501	5.310	1.236
−0.05	0.0	1	0.453	0.000	1.024	1.438	0.453	0.568
−0.05	0.5	1	0.109	0.149	0.995	5.663	4.040	1.413
0.00	−0.5	1	0.813	4.073	0.813	4.255	4.781	0.723
0.00	0.0	1	0.282	0.000	0.737	1.330	0.282	0.693
0.00	0.5	1	0.101	0.221	0.729	5.185	4.353	1.015
0.05	−0.5	1	0.286	3.407	0.286	3.611	3.823	0.757
0.05	0.0	1	0.139	1.230	0.260	1.581	0.666	1.634
0.05	0.5	1	0.132	0.678	0.336	5.243	4.881	0.758

𝑎(𝑡)=(1+𝑠)𝑎(𝑡)+𝒩(𝜇,𝜎²).