Focusing on the issue of attitude tracking for low-cost and small-size Micro-Electro-Mechanical System (MEMS) Inertial Measurement Unit (IMU) in high dynamic environment, an Adaptive Unscented Kalman Filter (AUKF) method combining sensor fusion methodology with Artificial Neural Network (ANN) is proposed. The different control strategies are adopted by fusing multi-MEMS inertial sensors under various dynamic situations. The AUKF attitude determination approach utilizing the MEMS sensor and Global Positioning System (GPS) can provide reliable estimation in these situations. In particular, the adaptive scale factor is used to adaptively weaken or enhance the effects on new measurement data according to the predicted residual vector in the estimation process. In order to solve the problem that the new measurement data is not available in case of GPS fault, an attitude algorithm based on Radial Basis Function (RBF)-ANN feedback correction is proposed for AUKF. The estimated deviation of predicted system state can be provided based on RBF-ANN in GPS-denied environment. The corrected predicted system state is used for the estimation process in AUKF. An experimental platform was setup to simulate the rotation of the spinning projectile. The experimental results show that the proposed method has better performance in terms of attitude estimation than other representative methods under various dynamic situations.

MEMS Inertial Measurement Unit (MIMU) and magnetic sensor have wide application for attitude determination in civilian and military fields, such as Unmanned Aerial Vehicle (UAV) systems [

On one side, different MEMS inertial sensors are affordable for attitude calculation. The gyroscope is the principal sensor available for attitude measurement using quaternion algorithm, which quickly degrades over time [

In addition, considerable work has been carried out on attitude estimation using adaptive filters and fusion algorithms. The Extended Kalman Filter (EKF) [

In order to overcome the drawbacks of the abovementioned methods and take full advantage of fusion and adaptive filtering scheme, some fusion methodologies combining complementary filtering or Kalman filtering are proposed. Koksal et al. [

The above works on attitude determination algorithm lie in the following problems. The traditional EKF and other improved EKF have the drawbacks such as low estimation accuracy and poor stability, which will cause the biased estimation or even divergence due to which the statistical properties of system and measurement noise cannot be predicted accurately, especially for low-cost MEMS-based sensors [

This paper concentrates on developing the customized attitude determination algorithm of low-cost MEMS sensor in high dynamic environment. The corresponding technique can be widely applied in measuring the attitude of the projectile and spinning shell of low dynamic rotating. Combined with the proposed adaptive Kalman filtering method and intelligent control scheme, it is suitable for dealing with time-varying noise of low-cost, small-size micro-IMU, and dynamic interference. The novel aspects of this paper can be summarized as follows:

According to dynamic rotating environment, a new attitude estimation scheme of AUKF is designed. Meanwhile, different control strategies are also adopted to fuse MEMS multi-inertial sensors under different dynamic conditions. AUKF attitude determination method based on MEMS sensor and GPS can provide reliable estimation under high dynamic environment change. Using the adaptive scale factor, the influence on the new measurement data is weakened or enhanced during the process of the estimation according to the predicted residual vector.

The proposed method can accommodate sensor failure, particularly GPS failure in adverse environment. When GPS signals are temporarily blocked, the attitude algorithm based on RBF-ANN feedback correction can continue to provide reliable estimated deviation information. The corrected predicted system state will be used in the estimation process in AUKF.

Considering the space limitations in spinning projectile, the small size MEMS IMU is designed. The customized prototype of the DSP controller is developed for it. The corresponding programs of the proposed algorithm can be compiled and run on in real time.

The remainder of this paper is organized as follows. Section

According to application background of the spinning projectile, a small size, low power consuming, and low-cost MEMS IMU is developed. Microinertial navigation system consists of a DSP microcontroller, A/D converter, flash, power module, micro-IMU, and magnetometer. The micro-IMU is composed of three single-axis gyroscopes and accelerometers. It is shown in Figure

The prototype of MEME IMU and micronavigation system.

In Figure

Low-cost, small size MEMS inertial sensors are widely used in these applications due to the dimension constraint, cost consideration in projectile, and spinning shell [

The main diagonal elements

An accelerometer sensor is a dynamic MEMS sensor used to measure acceleration forces up to three orthogonal axes. The accelerometer in the body frame is defined as

The main diagonal elements

The magnetic field components on local geography coordinate (west magnetic field, south magnetic field, and vertical magnetic field) can be measured by the geomagnetic vector measurement system, which mainly contains a three-axis magnetometer. The performance of the magnetometer sensor is distorted by hard iron and soft iron effects. Intrinsic and cross sensor calibration of the three-axis magnetometer is indispensable to eliminate scale factor, cross coupling, and bias errors. The output of the magnetometer is represented as

Define

Correspondingly, yaw angle

Before MEMS IMU was used for attitude estimation in the actual application, there were measurement errors and installation errors, which will affect the measurement output. Therefore, the calibration method is one effective way to compensate for the deterministic and other errors of the MEMS inertial sensor. Considering the application in high dynamic environment, the coupling effect between sensitive axes will significantly affect the measurement accuracy of micro-IMU. According to the spinning characteristics in the projectile application that the rotation of one sensitive axis is highly dynamic and the rotation of the other sensitive axis is low dynamic, the coupling coefficient of the model is estimated by the compounded calibration method [

Compounded calibration experiments of micro-IMU.

The calibration process is composed of the initial calibration and compounded calibration. The optimal bias of gyro is estimated and provided to AUKF as the initial calibration process. The bias

Deterministic errors for MEMS gyro.

Axis | Gyro deterministic error in indoor temperature | |
---|---|---|

Biases (°/s, g, Gauss) | Scale factor | |

Gyro x | −2.0511 | 0.9976 |

Gyro y | −2.5848 | 1.0033 |

Gyro z | −0.0043 | 1.0021 |

The estimated adjustment value

According to the output characteristic of MEMS sensor, the filter algorithm can effectively improve the accuracy of sensor measurement output. Considering the nonlinear characteristic of the system, the adaptive UKF fusion algorithm is preferred to solve the attitude estimation in the case of dynamic environment changes.

Establishing the perfect state equation and measurement equation is the key to improving the solution. Considering the effect of the model error, the quaternion vector

Here,

The single spline algorithm based on the quaternion vector in equation (

In a high dynamic environment, the cubic spline algorithm based on the quaternion vector is used for the estimation of attitude angle:

The differential equation for the rotating vector can be obtained by neglecting the high order items:

The polynomial fitting equation of the angular rate is expressed as follows:

The attitude algorithm with incremental angle could be constructed as follows:

The equivalent rotating vector is expressed according to Taylor series expansion equation:

As can be seen from the Section

In the high dynamic environment, the aforementioned attitude estimation approaches utilizing only the single sensor are difficult to provide reliable estimation due to sensor errors. The dynamic accuracy of the attitude angle that are calculated in virtue of the accelerometer and magnetometer is affected largely due to the motion of body in the high dynamic environment. In such a case, the measurement vectors

The measurement vector

Here, the vector

Due to the fact that the statistical characteristics of the noise are real-time changed, it is essential to adjust noise estimation in the filter algorithm. Based on the nature of UKF algorithm, unscented transformation (UT) is an approximate method to change the mean and covariance of random variables when they undergo nonlinear transformation [

Step 1: generation of sigma points and weights.

The estimated state and corresponding covariance of the system can be expressed as follows:

Sigmal points

Correspondingly, the weights of mean and covariance are presented:

where

Step 2: time update:

where

Step 3: measurement update:

where

where

Step 4: the tuning of the adaptive scale factor.

Define the predicted residual vector is

By placing the condition that output residual vectors at different sampling time maintain orthogonal to each other, the residual vector is satisfied:

The adaptive scale factor

where the adaptive factor

According to equations (

where

Considering the condition that the measurement model

Define

The adaptive scale factor model can be calculated as

Based on (

Depending on the predicted residual statistics, the adaptive scale factor is used to adaptively inflate the covariance matrix of the

Define

Here, the adaptive scale factor is introduced:

where

It is noted that model disturbance usually exists in the first stage of AUKF. In order to reduce model disturbances on current estimates in filer algorithm, the weight of model prediction in the estimation process should be low. The scale

Considering the case of GPS failure, the reliable new measurement data will not be updated. In order to continue to provide reliable information in GPS-denied environment, an attitude algorithm based on RBF-ANN feedback correction is adopted for AUKF. RBF-ANN shows good performance in classification modeling. It consists of three layers: one input layer, one hidden layer, and one output layer. The output of the network is a linear combination of input radial basis function and neuron parameters. Its diagram is shown in Figure

Radial feedforward neuron structure diagram.

When GPS works normally, the estimated deviation of predicted nonaugmented system state

When GPS signals are temporarily blocked, the estimated deviation of system state

Considering the error effect resulted from low-cost micro-IMU, the processed data of accelerometer, gyro, and magnetometer after calibration process are selected as the input of RBF-ANN. The estimated deviation of the system state

Input sample dataset is introduced as

Considering that the matrix

According to the low dynamic and high dynamic environment, the different control strategies of low and high dynamic environments are adopted to solve dynamic accuracy of attitude calculation. The proposed method can estimate the attitude angles utilizing affordable sensors under different dynamic situations. The switching criterion is determined according to roll angle rates of body. The attitude algorithm of single sample quaternion vector and attitude algorithm based on accelerometer, gyro, and magnetometer are adopted in low dynamic environment. Alternatively, cubic spline algorithm based on quaternion vector based on Micro-IMU and GPS is designed in the high dynamic environment. Considering the situation of GPS failure, an attitude algorithm based on RBF-ANN feedback correction is adopted to guarantee the reliable measurement. The estimated deviation of system state

The scheme of combining AUKF fusion algorithm with RBF-ANN for low-cost micro-IMU and GPS.

This scheme is actually a combined adaptive filtering approach and RBF algorithm architecture. It comprises two parts: AUKF based on multisensor fusion module and RBF estimation method. The multisensor fusion module consists of micro-IMU, magnetometer, and single antenna GPS. The dominant errors are compensated by the calibration process before fusion algorithm. Different fusion strategies provide efficient solutions to enhance the accuracy of the attitude estimation.

To verify the effect of the proposed algorithm in the low dynamic environment, the attitude testing experiments are implemented in tracking human body motions, as shown in Figure

Attitude testing experiment in low dynamic environment.

The different algorithms are implemented in DSP development prototype. The attitudes estimated separately by different sensors and filter algorithms are demonstrated in Figure

Attitude results in low dynamic environment.

The result shows that the single spline quaternion algorithm based on gyro has short-term accuracy, but the error will be accumulated over time due to gyro bias drift. The attitude algorithm of the accelerometer is used to provide the long-term accuracy estimation of the roll and pitch. The yaw angle is later calculated by the magnetometer. It is also affected by sensor error and vibration noise.

The complementary filter (CF) method can provide accurate Euler estimate in low dynamic condition. It utilizes characters of accelerometers that has long-term accuracy, the gyroscope has only short-term accuracy and magnetometer that has low noise and high bandwidth. According to the characteristics of the MEMS sensor, the cut-off bandwidths of low-pass filter and high-pass filter are chosen as the weight coefficient.

The attitude algorithms based on EKF and UKF have similar estimation performances. The UKF has better accuracy than EKF due to undergoing the nonlinear measurement equation in filter. The STD of the pitch, roll, and yaw angle is 1.72°, 3.11°, and 5.75°, respectively, at all times in EKF. The STD of attitude angles is 0.55°, 0.87°, and 0.93°, respectively, in UKF. The estimation of the yaw angle is affected by the error of pitch and roll angle calculated by the accelerometer and gyro.

Considering the characteristics of spinning projectile, the testing experiments are performed to simulate the situation that the rotation of the symmetry axis is in high dynamic and rest the rotations of other orthogonal axes are in low dynamic. A portable, single rotating table is designed, which can be mounted in a mobile vehicle. The single axis rotating table driving by the servo motor is used to simulate the motion of the roll attitude for the spinning projectile. Meanwhile, the attitude changes for the pitch and yaw angle are achieved when the testing vehicle equipped with portable table moves quickly in different routes. The experimental platform consists the prototype of low-cost IMU, a single-antenna GPS receiver, prototype of DSP microcontroller, the MTi-G, servo motor, slip ring, DC to AC inverter, DC regulated power, laptop, and testing vehicle. The experimental system is shown in Figure

Experimental platform of microembedded navigation system.

In experiment system, the Mti-G device from the Xsens Motion Technologies is used to provide reference attitude, which consists MEMS gyro, accelerometer, and magnetometer. The sampling frequency is 100 Hz to collect raw data. The measurements of the GPS receiver are provided at 10 Hz sampling frequency. The single antenna is mounted in the long pole, which is held up outside the testing vehicle. The micro-IMU, GPS receiver, and MTi-G are mounted in the single axis rotating table, which is connected to the servo motor directly. The reference frames of micro-IMU and MTi-G are consistent during the rotating motion. At the beginning of the experiment, the single axis rotating table is fitted into the floor of the testing vehicle. The rated speed of the servo motor is 3000 rpm. The experimental collecting real-time data are transmitted to the laptop PC with the USB port from converting the RS232 serial port by slip ring between rotating and nonrotating mechanism. Experimental tests were performed in the urban section.

In order to verify the effect of the different filter algorithms and the proposed method, several testing experiments are implemented in different rotating motions and traveling paths. A set of comparative experiments are carried out to verify the accuracy of different algorithms. The results are shown in Figure

(a) Roll angle and (b) pitch angle in high dynamic condition.

Figure

To produce as many as possible driving maneuvers to validate the performance in complex driving conditions, the experiment was conducted on an overpass over the road. The testing trajectory is shown in Figure

Testing trajectory of the attitude determination system.

The results of the on-vehicle test are presented from 0 s to 100 s. During the testing period, all attitude data were collected and recorded in the embedded navigation system. The GPS satellite signal is obstructed artificially to simulate external environmental disturbance in part path. To evaluate the effect of the proposed algorithm, the real experimental tests in the high dynamic environment are carried out. During the testing experiments, the servo motor of single rotating table is performed actions automatically to predesigned motion program. The maximum roll angle rate can reach 1080°/s to simulate the rotating of the spinning shell. In the meantime, the changes of the pitch and yaw angle is simulated by the testing vehicle riding in different routes. The results are presented in Figure

Attitude determination results in high dynamic environment.

As shown in Figure

It can also be found that the performance degrades during the GPS outage(i.e., from 40 to 50 s). As the GPS-failure interval, the performance of the proposed method becomes worse in comparison with that at the same interval without GPS failure. Owing to lack of enough measurement data, the estimation of the roll angle has no convergence and a trend of divergence in high rotating environment in Figure

In Figures

The convergence of RBF in UKF and AUKF is shown in Figure

The convergence process of RBF-ANN.

As can be seen from above, the training time in AUKF algorithm takes about 8.25 s. Compared with UKF algorithm, the costing time of training process takes about 13.25 s. Obviously, in the process of training RBF network, it spends less time than UKF algorithm.

The attitude angles are estimated in both UKF and AUKF-RBF algorithms. The AUKF-RBF algorithm has better estimation precision than UKF during the GPS outage section. RBF correction algorithm is regarded to be reliable and can be utilized by AUKF. The estimated precision of RBF depends on the accuracy of training data. The estimated attitude angles in AUKF-RBF algorithm provided more reliable results as training samples than UKF algorithm during the GPS nonoutage stage. Compared with the performance of GPS normal working sections (i.e., 10–20 s) and GPS outage section (i.e., 40–50 s), the RMS of the proposed AUKF-RBF is shown in Table

Contrast of mean square error of GPS failure and GPS normal.

Roll | Pitch | Yaw | |
---|---|---|---|

UKF-GPS outage | 2.0048 | 0.9882 | 0.8042 |

UKF-GPS normal | 1.9740 | 0.6633 | 0.5834 |

AUKF-RBF- GPS outage | 0.4185 | 0.3816 | 0.3658 |

It can also be found that the performance degrades during the GPS outage. The estimation error in GPS outage section is larger than the error in GPS normal working section. The reason is that the reliable measurements are provided by GPS and accelerometer in the GPS normal working section. On the contrary, the measurements were estimated by RBF in GPS outage. The corresponding programs of the proposed algorithm is compiled and run on CCS 3.3 environment for the DSP controller in real time. The calculating time takes 8.96 ms in a sampling period. For brevity, we will concentrate on comparing the performances of proposed in the whole stage. The AUKF-RBF algorithm can not only provide accurate estimation GPS normal working section but also guarantee reliable estimation in the GPS-denied section. The attitude angle estimation error statistics of various methods in testing experiment are summarized in Table

Mean square error of the attitude angle in the whole stage.

Roll | Pitch | Yaw | |
---|---|---|---|

UKF | 1.9857 | 0.7913 | 0.8049 |

AUKF-RBF | 0.4212 | 0.3879 | 0.4254 |

Compared with performance of the abovementioned methods, the proposed AUKF-RBF method provides more accurate and reliable estimation whether in normal working condition or GPS failure. It has good estimation performance in the whole section, which suffers from vibration noises due to inevitable disturbances and high rotating motion. The MSE of roll, pitch, and yaw based on the proposed method is 0.4212°, 0.3879°, and 0.4254°, respectively.

The attitude determination method combining AUKF with RBF-ANN is proposed. Considering the situations in low dynamic and high dynamic environment, the different control strategies fusing the MEMS multisensors are adopted. Using the adaptive scale factor, the influence on the new measurement data is weakened or enhanced during the process of the estimation in AUKF. The attitude algorithm based on RBF-ANN feedback correction can continue to provide reliable estimated deviation information in GPS outage. A portable experiment system to simulate high rotating motion of spinning projectile simulate is setup. The performance of the proposed method has been evaluated and verified through testing experiments for comparing with other representative methods for attitude estimation. Experimental results indicate that the proposed method exhibits reliable and satisfactory performance under various dynamic conditions, as well as GPS-friendly or temporarily GPS-denied conditions. The calculating time of the proposed method in DSP controller takes 8.96 ms in a sampling period. The proposed method has good estimation performance in the whole section The MSE of roll, pitch, and yaw based on the proposed method is 0.4212°, 0.3879°, and 0.4254°, respectively.

The datasets used to support the findings of this study are available from the corresponding author on reasonable request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

The work was supported by Natural Science Foundation of Liaoning Province (Grant no. 20180550714). Corresponding experimental tests are carried out at Research Centre of Weaponry Science and Technology in Shenyang Ligong University. The authors would like to thank their colleagues for their support in implementing the experiments.