Table 1 Summary of estimation methods based on vehicle longitudinal dynamics

1

Torque-to-force transfer function

Analytical model

[34,35,36, 39, 40]

2

Anisotropic brush model

Least square method

[37]

3

Magic formula model

Kalman filter

[21, 22]

4

Eight DOF vehicle model

Extended Kalman–Bucy filtering

[63]

5

Magic formula model

Reduced order observer

[23, 24]

6

Magic formula model

Analytical model

[38]

7

Torque-to-force transfer function

State observer

[28]

8

LuGre dynamic model

State observer

[41, 42]

9

Magic formula model

RLS

[25, 26]

10

Magic formula model

Nonlinear curve fitting technique

[29]

11

Pseudostatic lugre model

Sliding mode observer

[43]

12

Burckhardt model

Recursive least squares

[52]

13

Tire torsion model

Sliding mode observer

[51]

14

Longitudinal vehicle model

Nonlinear curve fitting technique

[30, 32, 33]

15

Burckhardt model

Nonlinear curve fitting technique

[44, 45]

16

Longitudinal vehicle model

RLS

[54, 56,57,58]

17

Single wheel model

RLS

[59]

18

Magic formula model

Improved nonlinear observer

[48]

19

Burckhardt model

Sliding mode observer

[46]

20

Six DOF vehicle model

RLS

[60]

21

Three DOF vehicle model

Extended Kalman filter

[61]

22

Longitudinal vehicle model

Proportional integral observer

[55]

23

Quarter wheel model

Nonlinear Lipschitz observer

[50]

24

Four wheel vehicle model

Fuzzy logic and Kalman filter

[62]

25

Frequency response function

Analytical model

[64, 65]

26

Modified Burckhardt tire model

Nonlinear estimator

[47]

27

Magic formula model

Genetic algorithm

[67]

28

Novel TRFC slip curve

Nonlinear curve fitting technique

[31]

29

Longitudinal vehicle model

Fuzzy logic

[66]

30

Magic formula model

Linear extended state observer

[49]

31

Longitudinal vehicle model

Rules-based method

[27]

32

Lugre and Burckhardt models

T–S fuzzy and RLS

[53]