Experimental analysis of a low-cost dead reckoning navigation system for a land vehicle using a robust AHRS

Highlights

• The paper present an attitude and heading estimation algorithm.

• It is presented an odometer aided dead reckoning navigation system for a land vehicle.

• Attitude and heading is robust in the presence of external disturbances and dynamic condition.

• A two steps off-line method and an online method are used for magnetic sensor calibration.

• The capability of the proposed navigation system (AHRS–INS–Odometer) is verified by several experimental trials.

Abstract

In navigation and motion control of an autonomous vehicle, estimation of attitude and heading is an important issue especially when the localization sensors such as GPS are not available and the vehicle is navigated by the dead reckoning (DR) strategies. In this paper, based on a new modeling framework an Extended Kalman Filter (EKF) is utilized for estimation of attitude, heading and gyroscope sensor bias using a low-cost MEMS inertial sensor. The algorithm is developed for accurate estimation of attitude and heading in the presence of external disturbances including external body accelerations and magnetic disturbances. In this study using the proposed attitude and heading reference system (AHRS) and an odometer sensor, a low-cost aided DR navigation system has been designed. The proposed algorithm application is evaluated by experimental tests in different acceleration bound and existence of external magnetic disturbances for a land vehicle. The results indicate that the roll, pitch and heading are estimated by mean value errors about 0.83%, 0.68% and 1.13%, respectively. Moreover, they indicate that a relative navigation error about 3% of the traveling distance can be achieved using the developed approach in during GPS outages.

Introduction

Attitude and heading estimation is one of main issues of navigating and motion controlling of autonomous vehicles, particularly, when the navigation system is based on DR strategies and no localization system such as GPS is available [1], [2], [3], [4]. Today, due to advances in manufacturing technology of the low-cost and miniature inertial and magnetic sensors, the orientation estimation with inertial and magnetic sensors has attracted many researchers [1], [5], [6]. In orientation estimation system which is called AHRS, accelerometer is used for attitude estimation, since, the accelerometer cannot sense the orientation of the vertical axis other sensors such as magnetometer are needed for accurate measuring of the heading. But, magnetometer signals are corrupted by some magnetic disturbances (due to ferromagnetic and permanent magnetic materials and hysteresis). Therefore, the sensors should be calibrated before application. Different calibration methodologies have been developed for improving the accuracy of the magnetometer sensors. Compass swinging is a heading based calibration method for calibration of magnetometer sensor [7]. This method can be used only for heading determination and is not used for other applications, such as attitude estimation presented in Egziabher et al. [8] works. Caruso [9], presented a calibration method with calculating of correction parameters of Earth’s magnetic field measurement instead of correcting the heading parameters. For improving the calibration method, Egziabher [10] developed an Earth’s magnetic field calibration method based on ellipsoid fitting. Similar methodologies were presented in Fang et al. [11] work. All of the calibration methodologies are off-line. Using the off-line magnetometer calibration methods, the sensor can be used in an AHRS but the external magnetic disturbances in the vicinity of sensors must be decreased in online applications as well.

Different methods have been developed for land vehicle’s attitude and heading estimation in DR navigation methodology. Aghili and Salerno [12], calculated a mobile robot geographical location and orientation using a low-cost inertial sensor and a GPS. Doostdar and Keighobadi [13] designed a sliding mode observer for a nonlinear MIMO AHRS in land vehicle applications. Although the AHRS have been used in many applications such as human body orientation estimation [5], [14], AUV applications [15] and UAV orientation estimation [3], [16], [17], [18], the external disturbances including external body acceleration and magnetic disturbances as the main sources of the estimation errors have not been investigated in these works.

In the previous studies, there are two methods to reduce the effects of the external body acceleration and the magnetic disturbance on the attitude and heading estimation errors. The first method that is called threshold-based switching method, is based on using the acceleration and the total intensity (Earth’s magnetic field strength) bound criteria and switching of the measurement and dynamic process covariance matrices. Rehbinder and Hu [19] investigated the attitude estimation problem of an accelerated body using an inertial sensor. The linearity of the measurement and dynamic process model are the main advantage of the algorithm, but it cannot be used in high acceleration mode in a long time. Suh et al. [20] designed an adaptive attitude estimation system for compensating the error caused by the external body acceleration. Lee and Park [21] presented a quaternion-based KF for estimation of the body orientation angles. They developed an adaptive filter for Euler angle estimation using the inertial and magnetic sensors. In this method, due to using the quaternion-based dynamic process model, the measurement process model becomes complex and nonlinear which in turn influences the observability and the estimation accuracy. A similar method has been used by Sabatini [6]. Based on optimal condition of the orientation estimation, Chou et al. [22] developed a new method with two fusion algorithm and using MEMS based low-cost sensors. The method that was called two-step optimal filter, was composed of an optimal filter and a fast estimation algorithm.

The second method of eliminating the estimation errors caused by the external body acceleration and the magnetic disturbance is called external body acceleration or magnetic disturbance model-based method. Roetenberg et al. [23], designed a complementary and robust KF for orientation estimation. In this filter, the gyroscope drift error, orientation error and magnetic disturbance error were estimated and the error dynamic models were used for the error estimations. Luinge and Veltink [24], designed an orientation estimation algorithm for measuring of the body segment orientation. In this algorithm, gyroscope drift, accelerometer and magnetic sensor bias were estimated. Yun et al. [25], presented a simplified quaternion-based algorithm. The proposed algorithm can be used just for quasi static and slow rigid body motions. Since, the accelerometer measures the resultant of the gravity and external body accelerations, for differentiation of these two accelerations a low-pass filter was used.

For navigation and positioning of a land vehicle, an integrated INS/GPS system can be used when GPS signals are available [26], [27]. In this system, GPS can overcome the INS position and velocity drift error. But, GPS signal due to satellite number, external environment and path conditions (tunnels or indoor environments) is not available every time. In other to overcome the INS error during GPS outages is used of aided sensors such as odometer [28], [29], magnetometer [30], [31] and etc. Nedgen et al. [28] used of a low cost IMU–Odometer–GPS ego localization for unusual maneuvers. Stancic and Graovac [29] presented an integration of strap-down INS and GPS based on adaptive error damping. They used an odometer sensor for decreasing of positioning errors and investigated the algorithm positioning ability during GPS outages. But in these literatures, the accuracy of the attitude and heading estimation had not been investigated in dynamic conditions.

Although, the estimation of the external body acceleration and the magnetic disturbance are very important in attitude and heading estimation accuracy, in the literatures, their error efficacy on the accuracy of the attitude and heading estimation have not been investigated in dynamic conditions of a land vehicle. In this paper, using a new dynamic process model and a linear measurement model, an EKF is proposed for estimation of attitude, heading and gyroscope sensor bias. Moreover, using a first-order low-pass filtered white noise process for modeling of the external body acceleration and by tuning of its parameters, the external body acceleration is estimated for dynamic conditions of a land vehicle. The magnetic sensor is calibrated by a two-step off-line calibration method, as well as in online applications the error effect of the external magnetic disturbances is decreased by a total intensity bound criteria and a switching method in the proposed AHRS algorithm. The accuracy of the proposed algorithm is evaluated by experimental tests of a land vehicle not only for attitude and heading estimation, but also for the external body acceleration estimation in dynamic conditions. The accuracy of the estimated attitude, heading and external body acceleration with the proposed algorithm is evaluated by a reference INS/GPS system.

For the position and the velocity prediction in during GPS outages a DR navigation system has been used. In this navigation system, the aided velocity is measured by an odometer sensor. In other to verify the prediction capability of the proposed integrated system (AHRS–INS–Odometer) GPS measurement gaps (during GPS outage) are simulated in the data set. Since, the GPS information is still available, it is used as a reference to estimate the position and velocity prediction accuracy.