An integrated artificial neural network–unscented Kalman filter vehicle sideslip angle estimation based on inertial measurement unit measurements

Actual (sampling) Linearized (EKF) UT sigma points

true mean

UT mean

and covariance weighted sample mean mean UT covariance covariance true covariance transformed sigma points

ANN module UKF module Integrator Correction Observer Velocity observer IMU Sensor ⋆ ANN module correction

Hidden layer

Σ

Σ

Σ

Σ

Σ

Σ

Output layer

Σ

0 0.2 0.4 0.6 1. Number of manoeuvres 0 0.2 0.4 0.6 R o o t M e a n S q u a re E rr o r [° ] 3. Number of Neurons

Training Validation Test Overall

0 0.2 0.4 0.6 4. Number of delays 0 0.2 0.4

0.6 2. Ratio of Sine to Step

0 2 4 6 8 10 -1 -0.5 0 0.5 1 Real Predicted 0 2 4 6 8 10 -1 -0.5 0 0.5 1 0 2 4 6 8 10 -1 -0.75-0.5 -0.250 0.25 N o rm a lis e d S id e s lip A n g le 0 20 40 60 80 100 Time [s] -1 -0.5 0 0.5 1 b) c) d) a)

11

-50 0

50 Yaw rate [°/s]

Noisy data Filter data

-5 0 5 Longitudinal acceleration [m/s 2_] 0 50 100 150 200 250 300 350 400 450 Time [s] -10 0 10 Lateral acceleration [m/s 2 ] a) b) c) 0 10 20 Vertical acceleration [m/s 2_]

Noisy data Filter data

-10 0 10 Roll rate [°/s] 0 50 100 150 200 250 300 350 400 450 Time [s] -10 0 10 Pitch rate [°/s] a) b) c) 0 100 200 300 400 Time [s] 0 10 20 30 L o n g it u d in a l v e lo c it y [ m /s

] Correvit S-Motion DI-IDIRV Integral value reset

0 1 2 0 0.2 0.4 0.6 0.8 1 P D F

Error - Longitudinal velocity [m/s]

0 10 20 30 0 10 20 30 R e a l v s E s ti m a te d R = 0.98 a) b)

-5

0

5

Correvit S-Motion Corrected ANN ANN

0

100

200

300

400

Time [s]

-5

0

5

N

o

rm

a

liz

e

d

s

id

e

s

lip

a

n

g

le

Correvit S-Motion ANN + UKF

a)

b)

-5 0 5 A N N R = 0.94 -5 0 5 C o rr e c te d A N N R = 0.95 -5 0 5 Real vs Estimated -5 0 5 A N N + U K F R = 0.98 0 0.5 1 1.5 P D F ANN 0 0.5 1 1.5 2 P D F Corrected ANN * -8 -6 -4 -2 0 2 4 6 8

Error - Sideslip angle error [°]

0 0.5 1 1.5 2 2.5 P D F ANN + UKF * * b2) b3) b1) a1) a2) a3)