# A two-step strategy to fuse the height measurements of quadrotors: theoretical analysis and experimental verifications

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## Abstract

For low-cost unmanned aerial vehicles, it is practically important to estimate flight height using the measurements from low-cost accelerometer and barometer sensors. In this paper, we propose a simple two-step strategy to fuse the measurements from the two sensors. In the first step, two different filters, moving average filter and Kalman filter, are adopted to pre-process the measurements from accelerometer and barometer, respectively. In the second step, a properly designed complementary filter is employed for high-precision height estimation. Several experimental comparison results on a small-size quadrotor demonstrate the effectiveness of the strategy. The strategy is further combined with a simple height controller to yield a height feedback-control scheme. The closed-loop experimental results show that 8-cm and 20-cm control accuracies are achieved for 5-m- and 10-m-height tracking tasks, respectively.

## Keywords

Accelerometer Barometer Complementary filter Kalman filter Quadrotor## 1 Introduction

Height determination is an important task for controlling an aerial vehicle. With the increasing demands on UAV applications as well as reducing the overall UAV cost, it is reasonable to use some low-cost on-board sensors. In the past two decades, low-cost, small-size inertial measurement units (IMUs) have been widely adopted in various UAVS to measure and report a body’s specific force, angular rate, and sometimes the magnetic field surrounding the body. As far as the height measurement issue of a UAV is concerned, many kinds of sensors can be used, for instance, accelerometers, barometers, GPS, ultrasonic sensors and infrared sensors.

Ultrasonic sensors can measure the distance to an object by sound waves [1]. By recording the elapsed time between the sound wave being generated and the sound wave bouncing back, it is able to calculate the distance between the sensors and object. A laser sensor works using laser to detect object [2]. Then, it is able to receive the intensity of laser from an object, and it is easy to calculate the distance between the sensor and the object. GPS could also be utilized to determine the distance by means of triangulation method [3]. In practice, this involves determining the distances to at least four GPS satellites from the user’s GPS receiver. However, ultrasonic sensor has a limited measurement range (less than 3 m); GPS cannot provide an accurate height measurement. The price of laser sensor is higher [4]. For these reasons, the three kinds of sensors are not perfect for a low-cost UAV to obtain high-precision height measurements.

Accelerometers are used to measure body’s acceleration, and position and velocity information could be obtained by integrating acceleration measurements. Barometers measure the flight height of a quadrotor by sensing the atmospheric pressure. There are two types of industrial UAV control modules at present. One is the flight controllers (A2 and A3) of DJI Corporation. The height fusion strategies and control algorithms are not open source and hence not available for a detailed analytical evaluation. The other is Pixhawks controller or its variations. The height measurements are mainly obtained by accelerometers, and the function of barometer is to correct the acceleration offset by calculating a modified coefficient. This approach is simpler, but the height estimation performance depends heavily on the weather or atmospheric condition, and is not as stable as the performance of the approach proposed in this paper. Besides, laser–radar sensor can be used to sense the flight height. But its price is usually much higher than the low-cost MEMS IMU or barometer, and its performance depends heavily on the ground condition.

Finally, the strategy is combined with a height controller to yield a complete height feedback-control solution. This extends the results published in our recent conference paper [8]. The collected data of two closed-loop height-control experiments demonstrate that a high-accuracy control performance is achieved by implementing the solution.

## 2 Accelerometer analysis

The average values of accelerations in the time-domain figure are equal to zero approximately, and noises exist as the frequency-domain figure shows. As the duty ratio increases, high-frequency noise performs more obviously. To eliminate the effects of high-frequency noise, a 10-order FIR low-pass filter with a cut-off frequency 20 Hz is used.

By the FIR low-pass filter and moving average filter, noise is well eliminated. In engineering, in addition to the method by reducing the vibrations of the motors using filters, some physical methods could also be used, such as cushioning or laying a piece of sponge.

## 3 Barometer analysis

Mean value and variance under different situations

Situations | Static(mm) | Moving(mm) | Windy(mm) | Warming(mm) |
---|---|---|---|---|

Mean value | 52,887 | 52,948 | 52,986 | 52,902 |

Variance | 194.8 | 211.3 | 335.7 | 1319.4 |

## 4 A complementary filter for height estimation

A complementary filter for height estimation performs low-pass filtering on a low-frequency height estimate, obtained from accelerometer data, and high-pass filtering on a high-frequency height estimate, measured by barometer, and fuses these estimates together to obtain an all-pass estimate of height. The principle of complementary filter is introduced in [9].

According to the analysis of accelerometer and barometer, we know that the value measured by barometer is accurate in long term, for the results will not change over time; on the contrary, the estimated value measured by accelerometer is accurate in short term, for its value shifts away from the true value because of the integration and drift over time. We use complementary filter to process the data measured by accelerometer and barometer to make the estimated value close to the true value.

In this paper, both static and dynamic experiments are conducted to verify the performance of the complementary filter. In the static experiment, the height estimation obtained by the complementary filter is compared with the two estimations obtained in the first step, as shown in Fig. 12. The mean value is − 22.97 and the variance is 864.85 for the output of the complementary filter. In contrast, they are, respectively, − 23.88 and 3677.7 for the output of the barometer filter. We also note that the output of the accelerometer filter has a constant error (about 140 mm). Thus the complementary filter leads to a better height estimation.

## 5 Height-control and closed-loop test results

These results show that the height-control errors finally enter into the bound [− 8 cm, + 8 cm] in the 5-m tracking experiment, whereas the errors enter into the larger bounds [− 20 cm, + 20 cm] in the 10-m tracking experiment. This phenomenon is arising, because of the fact that when the small-size quadrotor flies higher, the effect of airflow disturbances on height control will be more obvious.

## 6 Conclusion

To obtain a high-accuracy height estimation for low-cost quadrotors, this paper proposed a simple two-step strategy to fuse the measurements from accelerometers and barometers. In the first step, moving average filter and Kalman filter are adopted to preprocess the measurements. In the second step, a complementary filter is designed. Comparison results from both static and dynamic experiments on a small-size quadrotor demonstrate the effectiveness of the strategy. Furthermore, we designed a cascade PID controller and combined it with the fusion strategy to yield a height feedback-control solution. The solution is finally implemented on the quadrotor and verified by flight tests at 5-m and 10-m heights, respectively.

In future study, we shall systematically evaluate the ground effect and wind disturbances acting on the quadrotor, and apply the input disturbance compensation techniques developed in [14] and [15] to improve the control accuracy.

## Notes

### Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 61773095) and the Fundamental Research Funds for the Central Universities (Grant No. ZYGX2016J161) at UESTC.

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