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This paper presents an adaptive information fusion method to improve the accuracy and reliability of the altitude measurement information for small unmanned aerial rotorcraft during the landing process. Focusing on the low measurement performance of sensors mounted on small unmanned aerial rotorcraft, a wavelet filter is applied as a pre-filter to attenuate the high frequency noises in the sensor output. Furthermore, to improve altitude information, an adaptive extended Kalman filter based on a maximum

With the ability to land vertically, small unmanned aerial rotorcraft (SUAR) have an irreplaceable role in civil applications [

SUAR is a complex multi-input and multi-output (MIMO) system. Compared with the hovering and straight flight processes, there exists land disturbance in the landing process [

Integrated by the Euler equations, or quaternions, SUAR can get the corresponding aircraft attitude angles and position information, however, inertial sensors, especially gyroscopes, have fixed bias, drift bias, asymmetric scale factor errors and temperature-varying biases, causing the integration results to drift from true attitude [

Using filter methods, system can get high performance information based on different sensors. The most used filtering method is the extended Kalman filter (EKF) [

Inspired by the discussion above, an adaptive extended Kalman filter (AEKF) method based on the wavelet filter is proposed to get high performance altitude information for a SUAR during the autonomous landing process. The wavelet decomposition and reconstruction method is used to restrain the high frequency noise in the barometer, ultrasonic and GPS sensor information. Since the measurement noise is greatly changed after wavelet filtering, an AEKF based on a maximum

The paper is organized as follows: the dynamic model of the SUAR system is described in Section 2. The wavelet decomposition and reconstruction method is presented in Section 3. In Section 4, an AEKF based on a maximum

For SUAR, altitude information is mainly controlled by the main rotor speed and longitudinal cyclic input. Therefore, the simple altitude dynamic model for SUAR can be defined as:
_{i}^{T}_{1}, _{2})^{T}_{1} and _{2} are throttle and collective input respectively, playing an important role in longitudinal cyclic input, lateral cyclic input and blade speed. _{j}

The output accuracy of a barometer is mainly affected by the high frequency noise and constant error which is related to air pressure and temperature. The high frequency noise can be restrained largely by a wavelet filter. Thus, the barometer output _{b}_{b}_{1}. The function of the _{b}

With the location method of the ranging interchange theory, DGPS can provide position information for SUAR systems with sub-meter performance. The output of DGPS can be defined as follows:
_{g}_{2} is measurement noise

Ultrasonic sensors can provide high performance altitude information from 0.15 m to 6.05 m, and the error is less than 1 millimeter. When the altitude surpasses the upper limitation, the output of ultrasonic sensor fluctuates greatly. Therefore, the output of the ultrasonic sensor can be defined as follows:
_{u}_{u}_{lu}

When a SUAR finishes a certain task at low altitude, there exists land disturbance causing an increase of barometer error. Ultrasonic sensors can provide high precision altitude information for SUARs at low altitude, therefore the measurement matrix can be constructed with inputs from different sensors.

If the integrated navigation altitude is larger than 6 m, the SUAR is beyond the range of the ultrasonic sensor. The output of barometer and DGPS are fused. Thus, the constant error of barometer sensor can be revised by the DGPS. The measurement equation can be defined as:

If the integrated navigation altitude is less than 6 m, the barometer is easily affected by land disturbance. The output of DGPS and ultrasonic sensor are used to construct the measurement vector. The measurement equation can be defined as follows:

Therefore, the measurement equation can be expressed as:
_{k}_{k}_{k}_{k}_{b}

To get high precision altitude information, it is necessary to use a data filter to deal with high frequency noises in the output of barometer sensor, DGPS, and ultrasonic sensor. Wavelet analysis is a time and frequency domain method, having good representation for partial signal characteristics, therefore, a wavelet filter is used here as a tool to reduce high frequency noises in the sensor information. Lifting-based wavelet transform implementation has shown high potential in reducing the number of computations, so it is used to reduce computation burden in real tasks. It includes three steps:

Split: splitting the original signal ^{j}^{j},k^{j}

Predict: defining the detailed representation characteristics by choosing a predictor:

Update: averaging the signal of rough representation against original signal:

The basic principle of lifting scheme is to factorize the polyphase matrix of a wavelet filter into a sequence of alternating upper, lower triangular matrices and a diagonal matrix with constants. The factorization is obtained by using an extension of the Euclidean algorithm. The resulting formulation can be implemented by means of banded matrix multiplications.

Suppose that the z-transform of wavelet filter _{k}

The polyphase matrices are then defined as:

If the (

Therefore, the low pass samples are multiplied by the time domain equivalent of _{i}_{i}^{−1}. The polyphase-based wavelet transform in lifting scheme is shown in

In this paper, the wavelet “db4” is utilized to construct the wavelet method. The coefficients of the filter are shown in

The comparisons of original data and the wavelet filtered data of barometer and DGPS are shown in

Since the measurement noise structure has changed greatly after wavelet filtering, experiential value or the statistics of partial noise cannot be used to provide a good description of measurement noise covariance, therefore, an AEKF is proposed to estimate the measurement noise covariance in real time to improve altitude information.

Since the nonlinear dynamic equation of SUAR is continuous and the measurements are a discrete series, a continuous-discrete EKF is proposed to fuse altitude sensor information. In EKF, the state equation and measurement equation can be expressed as:
_{k}_{k}_{k}

In EKF, measurement noise covariance matrix _{k}

The prediction stage:

The update stage:
_{k}_{/}_{k}_{−1} is the predicted measurement vector for the next epoch, _{k}_{/}_{k}_{−1} and _{k}_{/}_{k}_{−1} are the predicted measurement vector and the predicted state covariance matrix respectively. Ø_{k,k}_{−1} is the transition matrix after discretization. The innovation _{k}_{k}_{k}_{k}_{k}_{k}_{0}, the measurement noise covariance matrix can be estimated in real time to improve filtering performance.

Experiments were conducted on a radio-controlled Raptor 90 helicopter, shown in

For SUAR, there exist weight and size constraints for onboard control components. Thus, a micro guidance navigation control (MGNC) system with little weight was self-developed to realize stable control. The MGNC is only 207 g in weight, with a size of 120 mm × 61 mm × 48 mm. It consists of a horizontal main board, housing three angular rate sensors, two 2-axis accelerometers and a barometer. The barometer, DGPS, and ultrasonic sensor are used to provide altitude information for the SUAR system. The MPXA6115 barometer, produced by Freescale Semiconductor Company, has a range of 15 kPa∼115 kPa. The DGPS module employs the Novatel RTK, whose position accuracy is about 0.02 m, and the range of the Mini-S electrostatic ultrasonic transducer is from 0.15 m to 6.05 m.

To test the effectiveness of the proposed information fusion method, a static distance test has been done on the stairs. A six-floor building is chosen as the basis for its high precision measurement. Three marking points are selected on the stairs. The distances between points and ground have been tested by flexible rulers and the distances are 5.12 m (first point), 9.32 m (second point) and 13.52 m (third point). The SUAR is stretched to measure the distance between the current point and the ground. Besides, the sampling time is 60 s per point.

The comparison result of the proposed method and the real altitude, the output of the barometer and the real altitude, the output of the DGPS and the real altitude, the output of the ultrasonic sensor and the real altitude are shown in

To test the dynamic performance of the proposed method, a hovering flight test has been done on the SUAR system. Under a 3.4 m/s wind disturbance, the SUAR hovers in the air at 10 m altitude. The LQR control method has been used to adjust altitude and position in real time [

To test the effectiveness of the proposed method, a series of autonomous landing tests have been done on the SUAR system with the adaptive radial basis function neural network and pilot model. When the SUAR received an autonomous landing command, it changed work station, and flew to the planned hovering point (0,0,10). To satisfy the criteria for position error, speed error and heading error, the SUAR hovered at the planned hovering point. With the constant adjustment for the planned hovering altitude, SAUR descends with hovering stations. Finally, the SUAR landed on the ground. Ten landing tests were conducted from different altitudes, while the wind velocity was less than 3 m/s. The landing results are shown in

The comparison of landing performance with AEKF and KF [

In this paper, an adaptive information fusion method based on wavelet decomposition and reconstruction is proposed to improve the accuracy and reliability of altitude measurement information in the landing process for a SUAR. With the proposed method, the high frequency noises in sensors can be eliminated greatly, and then high performance altitude information can be fused to provide support for SUAR in the autonomous landing process. The effectiveness of the proposed method has been demonstrated by static tests, hovering tests and a series of autonomous landing tests.

The research is supported by the National Natural Science Foundation of China (Grant No. 60905056, 60904093, 61121003, 61273033).

The scheme of altitude fusion.

The polyphase-based wavelet transform in lifting scheme. (

(

The Raptor-90 helicopter.

(

The altitude generated by the AEKF method, barometer and DGPS in a hovering process.

The result of autonomous landing tests from different altitudes.

(

The coefficients of the “db4” filter.

_{0} |
_{0} |
||
---|---|---|---|

_{1} |
0.83651630373780 | _{1} |
0.22414386804201 |

_{2} |
0.22414386804201 | _{2} |
−0.83651630373780 |

_{3} |
−0.12940952255126 | _{3} |
0.48296291314453 |

Altitude accuracies for AEKF and each sensor (in meters).

0.31 | 0.32 | 4.94 | 1.49 | |

0.08 | 0.14 | 0.44 | 0.49 | |

0.098 | 0.16 | 0.94 | 0.41 |