Mathematical Problems in Engineering

Volume 2017, Article ID 4517673, 14 pages

https://doi.org/10.1155/2017/4517673

## Attitude Determination Method by Fusing Single Antenna GPS and Low Cost MEMS Sensors Using Intelligent Kalman Filter Algorithm

Research Centre of Weaponry Science and Technology, Shenyang Ligong University, Shenyang, Liaoning, China

Correspondence should be addressed to Lei Wang; moc.361@adnauu

Received 2 March 2017; Revised 10 May 2017; Accepted 12 June 2017; Published 17 July 2017

Academic Editor: Kalyana C. Veluvolu

Copyright © 2017 Lei Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

For meeting the demands of cost and size for micronavigation system, a combined attitude determination approach with sensor fusion algorithm and intelligent Kalman filter (IKF) on low cost Micro-Electro-Mechanical System (MEMS) gyroscope, accelerometer, and magnetometer and single antenna Global Positioning System (GPS) is proposed. The effective calibration method is performed to compensate the effect of errors in low cost MEMS Inertial Measurement Unit (IMU). The different control strategies fusing the MEMS multisensors are designed. The yaw angle fusing gyroscope, accelerometer, and magnetometer algorithm is estimated accurately under GPS failure and unavailable sideslip situations. For resolving robust control and characters of the uncertain noise statistics influence, the high gain scale of IKF is adjusted by fuzzy controller in the transition process and steady state to achieve faster convergence and accurate estimation. The experiments comparing different MEMS sensors and fusion algorithms are implemented to verify the validity of the proposed approach.

#### 1. Introduction

Attitude estimation is essential information for control of micronavigation system, such as Micro Autonomous Vehicle, Micro Aerial Vehicle (MAV), and Guided Munition Shell [1–4]. In these specific applications, the size and cost are limited. Low cost and small size MEMS IMU, which consists of MEMS gyroscope and accelerometer, could be used in micronavigation system. Lower price, smaller sized MEMS IMU is less accurate, has large biases, and is more noisy. The errors of MEMS sensors will lead to a great impact on the calculation performance and reduce the estimation accuracy significantly [5, 6]. Thus, the effective calibration and error compensation method is essential to evaluate and improve the performance of MEMS IMU before attitude estimation [7–9].

Nowadays, the different attitude estimation algorithms have been developed, which are employed to Micro IMUs and integrated with magnetic sensors, Global navigation satellite system (GNSS) receiver, and other sensors [1–4, 10–17]. Among them, representative researches like multi-information fusion technique utilize the different MEMS sensor [10–12], different Kalman filtering methods for attitude estimation [3, 13–15], and methodology combining data fusion with filtering strategies [16, 17]. Utilizing barometer and low cost IMU, the data fusion method via the complementary filter is proposed to fuse altitude data for unmanned aerial vehicle (UAV) system [10]. A quaternion-based complementary filter for estimating the attitude of a smartphone using IMU and magnetic sensor is developed. The optimal tuning correction factors of the algorithm across all the body movements were also identified [11]. An attitude estimation method is proposed using low cost gyroscope, magnetometer, and GPS receiver. The pseudoattitude, magnetic attitude, and gyroscope measurement are fused based on Euler angle. The simulation and flight test verified the proposed method [12]. For small UAVs, an attitude estimation method fusion of gyroscopes and single antenna GPS with quaternion-based EKF is proposed. The results of the simulations and the flight experiment demonstrate the ability of the proposed algorithm [3]. The sideslip angle is estimated in Kalman filter using the velocity signals from GPS and angular signals from magnetometer in case that no longitudinal tire force and no pitch angle exist. Road tests are implemented [13]. According to practical application of quadcopter UAV, the adaptive gain parameter in EKF filter was tuned [14]. The attitude estimation algorithm is developed by incorporating a nonlinear observer in order to fuse measurements from both the gyroscope and accelerometer. The attitude rotation matrix is evaluated with estimated the gyro bias and tilt error [15]. A wireless IMU with the smallest volume and weight is designed. The data fusion is implemented before a Kalman filter combined with the zero velocity update. The methodology for wireless IMU is adopted to track a person in an indoor area [16]. Integrating double-antenna Global Positioning System (DA-GPS) with other low cost in-vehicle sensors, two parallel extended Kalman filters (EKFs) are adopted to estimate the roll angle firstly; then vehicle sideslip and yaw angles are estimated through fusion methodology [17].

The above works on attitude estimation algorithm lie in following problems. Some attitude estimation methods could provide reliable estimation, but it has to rely on the use of multiple antennas, which incurs a complex structure, large volume, and high cost of the system [1, 17]. It is restricted in such micro navigation system. For traditional extended Kalman filter and other improved Kalman filter methods for attitude estimation, it would cause the inaccurate estimation or even divergence because the statistical properties of process and measurement noise cannot be predicted accurately, especially for low cost MEMS-based sensors [3, 13, 14]. Some complicated nonlinear filter and optimal control methods could obtain optimal estimate. On the other hand, the main drawback lies in introducing a heavy computational burden that leads to difficulty of application in real time navigation system [15, 18].

For meeting the demands of cost and size for micro navigation system, such as spinning shell, Missiles, and aircrafts, the scheme of attitude estimation combining single antenna GPS with low cost MEMS IMU and magnetometer is designed. This paper concentrates on developing a combined fusion methodology with intelligent Kalman filter, which realizes the fusion of Micro IMU, GPS, and magnetometer. It could continue to provide reliable information, particularly in larger sideslip angle, GPS failure situation. Testing experiments using the proposed approach are presented by comparison with different fusion algorithms and filter methods. The novel aspects of this paper can be summarized as follows.

To utilize the strengths of the fusion estimation algorithm and adaptive filter approaches, the combined approach has been proposed. The different control strategies fusing the MEMS multi-inertial sensors are adopted under different driving situations.

The high gain scale in IKF is tuned by fuzzy controller to resolve the problem of robust control and characters of the uncertain noise statistics influence for low micro IMU. GPS-measured yaw angle for Micro IMU/GPS system is afforded as measurement to enhance the observability of IKF. Besides, the fusion information of yaw angle using gyroscope, accelerometer, and magnetometer fusion algorithm is added into IKF observer, which could provide reliable information, particularly under unavailable larger sideslip angle, GPS failure situation. Integrating data fusion algorithm with IFK method, the proposed methodology could significantly improve the estimation performance.

#### 2. Methodology

##### 2.1. Gyroscope Model and Attitude Algorithm

MEMS inertial sensors of low cost, small size, and low power consumption are now widely used in micronavigation system and guidance system of tactical weapons. The application of these sensors is restricted for low precision and bias instability. It is essential to test, calibrate, and compensate for these sensors. The systematic error sources for MEMS inertial sensors mainly embody in biases, scale factors, nonorthogonality, or misalignment errors. The output model of a triad of MEMS gyro sensor in matrix form can be represented as

In (1), the definition of angular rates is based on the following conventions. The upper index defines the referenced coordinate system, whereas the lower index refers to the described value. The rotation refers to the relative movement of coordinate system. Used indices are -Earth frame, -Navigation frame, -inertial frame, and -body frame, where is the raw measurement angular rate of the gyroscope; is the true angular rate; is the output bias. The scale factor and misalignment matrix is given by

The main diagonal elements are scale factors that account for the sensitivities of the individual sensors by scaling the outputs. The variable represents the nonorthogonality and misalignment of the triaxial gyroscope sensors. The biases, scale factors, nonorthogonality, or misalignment errors are main systematic error or deterministic sources for MEMS inertial sensors. The body angler rates with respect to the navigation frame are given by the difference between the body angler rates, , and the navigation frame rotation, .

The coordinate transformation from navigation frame to body fixed frame is based on the three angles, namely, pitch, roll, and yaw, denoted by the symbols, , and . The attitude matrix from navigation frame and body frame by three Euler angles is given by

The propagation of the Euler angles with time yields is derived in

By (3), neglecting of the earth rate and the angular velocity of the local-level frame for the spherical earth model, the gyroscope rates are approximately equal as

##### 2.2. Accelerometer Model and Attitude Algorithm

Define the as the raw measurements of accelerometer in body frame. The vector is the true output of accelerometer. Considering the scale factor error and fixed error, the relation is given by

The matrix representing scale factor error for accelerometer and the skew symmetric matrix representing the fixing error of accelerometer are given by

The parameters of matrix and are computed by calibration method. is the error vectors of accelerometer. Define as the value in the navigation frame. The relation between the output of accelerometer and is inwhere is the gravity. is the vehicle acceleration. The following two cases are considered in (8). One is that the vehicle is in stationary or low dynamic condition, accelerometer measures gravity mainly. The accelerometer output in navigation frame is given by

Thus, the roll and pitch angles are determined by the following equations, respectively,

On the other side, when the vehicle is accelerated, the accelerometer measurement reflects not only gravity but also the acceleration of the vehicle. The vehicle acceleration, , is determined by Costa theorem. The vector is the vehicle velocity in body frame

##### 2.3. Magnetometer Model and Attitude Algorithm

Magnetometer sensor is designed and manufactured by making use of alloy resistance having sensitive response to direction magnetic field. The performance of magnetometer sensor is distorted by hard iron and soft iron effects. Intrinsic and cross sensor calibration of three-axis magnetometer is indispensable to eliminate scale factor, cross coupling, and bias errors. Thus, the magnetometer’s output can be modeled by

The matrix represents the raw measurement in body frame. represents the calibrated magnetometer output. Here, can be decomposed as , where , , and matrix represent effect of sensor imperfection and magnetic disturbance. The subscript “” means the scale factor error, “” means nonorthogonality and misalignment error, and “” means the soft iron effect. The vector represents the noise of magnetic disturbance. Define as the local magnetic vector in -frame. The relationship of magnetic vectors in -frame and -frame is given by

Considering the horizontal plane projection of magnetic field , corresponding representation is given by

Eventually, yaw angle is calculated in

##### 2.4. Different Sensor Attitude Fusion Estimation Algorithm

For the scheme of attitude estimation combining low cost MEMS IMU, magnetometer with single antenna GPS, Strapedown Inertial Navigation system (SINS) of MEMS gyroscope, and accelerometer could provide angles utilizing the differential equation for quaternion vector but suffer from accumulating errors induced by gyroscopes bias drift. The differential equations of the quaternion vector are expressed as

Here, is the error quaternion vector, . The operator “” denotes the quaternion multiplication. The vector .

Accelerometers can provide the pitch and roll angles by measuring the gravity vectors if the vehicle is stationary or in low dynamic environment in (10). Triaxis magnetometers are used for calculating the yaw angle in (14) and (15). Its accuracy is heavily affected by local magnetic environments.

Derived from the single antenna GPS, the pseudoattitude method [19, 20] is adopted. The velocity vector is the single antenna GPS-measured velocity vector in the east, north, and down directions of the navigation frame, respectively. The lift acceleration vector is equivalent to the difference between the normal acceleration component and gravitational acceleration component . Then is given by . A horizontal reference vector is derived from and , in the form . The Euler angle denoting pseudoattitude algorithm is determined in

It has been verified that GPS could reliably provide the estimation. However, some common limitations are that GPS failure is not considered or larger sideslip angle could not be estimated for single antenna GPS.

For attitude estimation algorithm by fusing data from MEMS inertial sensors, complementary filter (CF) is usually utilized to estimate attitudes due to the complementary characteristic of gyroscopes and accelerometer [10, 11]. The classical form of the complementary filters can be reformulated. is the estimation of the complementary filter. and are the estimation by gyro and accelerometer, respectively. The transfer function is first-order high pass filter and is first-order low pass filter. The transfer functions of the filters are as follows

For attitude algorithm, gyroscopes can provide angles but suffer from accumulating errors induced by gyroscopes bias drift. High pass filter could eliminate the low-frequency random noise of the Euler angle integrated by gyroscope, while the low pass filter could eliminate the high frequency random noise of calculation by accelerometer.

##### 2.5. IKF Fusion Algorithm for Attitude Estimation

According to the micro navigation system of low cost Micro IMU, magnetometer, and a single antenna GPS receiver, the aforementioned attitude estimation approaches utilizing different sensors separately are difficult to provide reliable estimation due to sensor errors and dynamic environmental variations. The single fusion algorithm employing complementary filter is also difficult to achieve good robustness for different driving situations and complementary filter parameters. In practice cases, small adjustment in fusion and control strategy may finally affect the estimation performance. In addition, for trying to solve the attitude estimation utilizing conventional EKF or modified EKF methods, the uncertain noise for low micro IMU would not be estimated accurately.

To overcome the drawbacks of above-mentioned methods, it is preferable to develop a reliable approach to estimate attitude angles using affordable sensors in micro navigation system. Utilizing the advantage of the fusion estimation algorithm and adaptive filter approach, the combined approach has been also developed. The proposed method could estimate the yaw angle utilizing affordable sensors under different driving situations. It could accommodate GPS failure or the situation of unavailable sideslip, which could continue to provide reliable information. In IKF module, the adaptive gain scale is adjusted by the fuzzy controller to compensate the uncertainty of measurement and process noise. Furthermore, the control strategies of different measurements considering sensor failure are adopted to solve the lack of observability of yaw angle. The switching criterion is determined according to GPS satellite number, yaw error estimate result, and the vehicle acceleration measurements to make a distinction between normal driving condition, vehicle turning, and GPS outage. One side, besides measurements from accelerometer, GPS-measured heading angle for micronavigation system is afforded as the measurement to enhance the observability in normal driving condition. Additionally, in case of GPS failure or the situation of unavailable sideslip, the fusion information of yaw angle using gyroscope, accelerometer, and magnetometer fusion algorithm is added into IKF observer. The scheme of the proposed methodology is shown in Figure 1.