Unlike wheeled vehicles, tracked vehicles are widely popular due to their non-linear contact characteristics between the tracks and the ground, which allows them to be operated under adverse field conditions for agricultural production, and allows turning at high speed with a small turning radius or higher steering command. Under autonomous conditions, the tracked vehicle has a global positioning system and inertial sensor for providing the vehicle state and direction, but when this tracked vehicle is turning, the inertial sensor reading has measurement uncertainties. Since the vehicle direction is more important for autonomous guidance and other navigation purposes, it is necessary to compensate this uncertainty of the inertial sensor measurements.
The main controlling feature of auto guidance is to steer the vehicle to follow a desired path automatically, which requires a proper guidance system able to detect the vehicle’s position and direction, create proper steering signals, and steer the vehicle according to the signals [
1].There are different guidance sensing systems, including global positioning system, inertial sensors, geomagnetic direction sensors, machine vison and laser scanners which are used to find the control parameters of the autonomous vehicles such as heading and offset [
2,
3,
4,
5]. The functional characteristics of each sensor provides the desired information, which contains erroneous measurement readings due to noise, measurement errors, and time delays. In general, a single sensor is not able to provide enough information, whereas multi-sensor integration can provide more useful information, which is more helpful and informative than what can be observed using a single sensor. This information needs to be fused in a way that reduces sensor uncertainties and the additional task of interpretation must be performed [
6]. There are different approaches used for sensor fusion to obtain the position and direction of vehicles, such as complementary filters [
7] or Kalman filters with various architectures [
8,
9,
10,
11,
12,
13], particle filters or sequential Monte Carlo methods [
14,
15,
16,
17,
18]. Since the dynamic motion of a vehicle is non-linear, a non-linear dynamic model and extended Kalman filter are commonly used for navigation purposes. For instances, Rohac [
19] addressed a cost-effective solution by using a non-linear observer and extended Kalman filter with commercial grade inertial sensors, and studied the performances of different approaches to obtain navigation solutions with robustness to GNSS outages. Noguchi [
20] developed a guidance system based on the real time global positioning system (RTK-GPS), geomagnetic sensor (GDS) and machine vision by using an extended Kalman filter method which provided the most appropriate vehicle heading in real time. Alatise and Hancke [
21] used an extended Kalman filter with inertial sensors and camera to estimate the position and direction of a mobile robot. With a non-linear extended Kalman filter, a tracked vehicle model and sensor measurements are used to estimate the trajectory, orientation and other soil parameters for small-scale tracked vehicles [
22].
An autonomous tracked combine harvester developed by Zhang [
23] was used to cut wheat and paddy rice in real time by using an appropriate harvesting map which is created based on a real time global positioning system (RTK-GPS) and inertial measurement units (IMUs); before harvesting, the outside crop near to headland is cut twice or thrice by the tracked combine harvester, and during this time the sensor measurements are logged for making a navigation map. Generally, the tracked combine harvester makes turns at moderate to high speed with a small turning radius, which is very popular with farmers, and this turning position is represented by a circle marked in
Figure 1. During this turn, the measured heading of a tracked combine harvester contains drift errors, which result from the IMU gyro measurement bias. To get an absolute heading, this bias needs to be compensated by using a tracked combine harvester model and sensor fusion method. In this research, the main contributions are the estimated absolute heading of tracked combine harvester during non-linear conditions (especially high speed turns with small turning radii) by using a tracked combine harvester dynamic model which was developed by us based on a real time global positioning system (RTK-GPS) and inertial measurement units (IMU). For more details readers should see [
24]. In practice, this estimated heading can further be used to obtain the exact crop periphery for calculating the harvesting map of a robot combine harvester (for more details see [
25]).