Pos (Orbit Traj) Parameters: F C=6.0 N, V=1.0 m/s, h
Pos (Orbit Traj) Parameters: F C=6.0 N, V=1.0 m/s, h d=2.five, r=5.(d)EKF Estimated Pos (Orbit Traj) Parameters: F C=10.0 N, V=1.0 m/s, h d=2.5, r=5.North(m)North(m)5 0 -5 0 five 10 15 20 25 305 0 -5 0 five ten 15 20 25 30East(m)East(m)4 2 0 -2 -4 0 5 10 15 20 25 304 2 0 -2 -4 0 five 10 15 20 25 30 35 four 2 0 five 10 15 20 Time(s)EKF3SDown(m)four 3 two 0 5 10 15 20 Time(s)EKF3SDown(m)TruthEKF4STruthEKF4S(e)(f)Figure 9. Position estimates utilizing the 3-state and 4-state EKFs below various cable-tension force magnitudes ( f c ): (a) f c = 0.five N, (b) f c = 1 N, (c) f c = two N, (d) f c = 4 N, (e) f c = 6 N, and (f) f c = 10 N.Drones 2021, 5,15 ofEstimated position error (Orbit Traj) bounded with three covariance Parameters: F C=0.five N, V=1.0 m/s, h d=2.5, r=5.2 0 -2 0 2 0 -2 0 0.5 0 -0.five 0 five ten 15 20 25 30 35 5 10 15 20 25 30 35 5 10 15 20 25 30Estimated position error (Orbit Traj) bounded with 3 covariance Parameters: F C=1.0 N, V=1.0 m/s, h d=2.five, r=5.two 0 -2 0 2 0 -2 0 0.5 0 -0.five 0 five 10 15 20 25 30 35 5 10 15 20 25 30 35 five 10 15 20 25 303s4s3s4s(a)Estimated position error (Orbit Traj) bounded with three covariance Parameters: F C=2.0 N, V=1.0 m/s, h d=2.five, r=5.2 0 -2 0 2 0 -2 0 0.five 0 -0.5 0 5 ten 15 20 25 30 35 5 10 15 20 25 30 35 5 10 15 20 25 30(b)Estimated position error (Orbit Traj) bounded with three covariance Parameters: F C=4.0 N, V=1.0 m/s, h d=2.five, r=5.2 0 -2 0 two 0 -2 0 0.five 0 -0.5 0 five 10 15 20 25 30 35 five 10 15 20 25 30 35 5 10 15 20 25 303s4s3s4s(c)Estimated position error (Orbit Traj) bounded with 3 covariance Parameters: F C=6.0 N, V=1.0 m/s, h d=2.five, r=5.2 1 0 -1 0 2 1 0 -1 0 0.five 0 -0.5 0 five ten 15 20 25 30 35 five ten 15 20 25 30 35 5 10 15 20 25 30(d)Estimated position error (Orbit Traj) bounded with three covariance Parameters: F C=10.0 N, V=1.0 m/s, h d=2.five, r=5.two 1 0 -1 0 2 1 0 -1 0 0.four 0.2 0 -0.two -0.4 0 five ten 15 20 25 30 35 5 ten 15 20 25 30 35 5 10 15 20 25 303s4s3s4s(e)(f)Figure 10. Position estimation errors generated by the 3-state EKF (3s), and 4-state EKF (4s) with various cable force magnitudes ( f c ): (a) f c = 0.5 N, (b) f c = 1 N, (c) f c = 2 N, (d) f c = four N, (e) f c = 6 N, and (f) f c = ten N. The 3 boundaries refer for the 4-state EKF.Drones 2021, 5,16 ofEstimated Cable Force with Fc C2 Ceramide Autophagy Sensor = 0.5 N0.6 1.Estimated Cable Force with Fc Sensor = 1.0 N0.1.1.1 0.2 1 0 0.9 -0.two 0.8 -0.Ground Truth EKF4s0.Ground Truth Tenidap Cancer EKF4s-0.six 0 five 10 15 20 25 300.6 0 five 10 15 20 25 30(a)Estimated Cable Force with Fc Sensor = 2.0 N2.(b)Estimated Cable Force with Fc Sensor = four.0 N4.two.4.2.4.four.1.1.3.1.Ground Truth EKF4s3.Ground Truth EKF4s1.six 0 5 10 15 20 25 303.7 0 5 10 15 20 25 30(c)Estimated Cable Force with Fc Sensor = 6.0 N6.(d)Estimated Cable Force with Fc Sensor = 10.0 N10.three 10.2 6.two ten.1 six.1 10 six 9.9 9.eight five.9 9.7 5.Ground Truth EKF4s9.6 9.Ground Truth EKF4s5.7 0 5 ten 15 20 25 30(e)(f)Figure 11. Cable-tension force estimates vs. the ground truth for distinctive cable-tension force magnitudes ( f c ): (a) f c = 0.5 N, (b) f c = 1 N, (c) f c = 2 N, (d) f c = 4 N, (e) f c = six N, and (f) f c = 10 N.Table 2 summarizes the estimation benefits under different cable-force magnitudes applying the root mean square error (RMSE) metric. We are able to see that for smaller cable-tension force values (i.e., 1 N), the 3-states model produces far more precise position estimates within the north and east directions.Drones 2021, 5,17 ofTable 2. Root-Mean-Square-Error (RMSE) comparison of the 3-state (3S) and also the 4-state (4S) EKFs. f c = 0.5 N Position North (m) East (m) Down (m) f c (N) 3S two.022 two.146 0.010 4S five.075 three.