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To overcome the limitations of existing methods in acquiring the vertical kinematic states of implements subject to vulnerable signal or operating surroundings, the Kalman filter was used to fuse a laser receiver's rough height indicated by photocell set and its acceleration to obtain the vertical displacement and velocity of the implement. This is called the Kalman filter based method for fusing laser receiver and accelerometer (KFLA). By using the linear motion transducer as a comparative metric, laboratory experiments of accuracy evaluation were conducted within the motion range of −77 to +77 and −11 to +11 mm, respectively. The maximum absolute errors of the displacement estimated by the KFLA were 14.6 mm and 5.7 mm, respectively; and the root mean square errors were 5.6 mm and 1.9 mm, respectively. Meanwhile, the velocity estimated by the KFLA showed similar but smoother variations than the displacement difference. Vertical height estimation result of the implement of a field-travelling levelling machine showed that the KFLA curve passed through the bars represented by the rough height and corresponding deviation with a higher frequency of 50 Hz. Above all, the KFLA could calculate the height of the implement when the motion was beyond the sensing range of the receiver, which showed the stable acquisition of sensing signal enables KFLA to be competent for measurement tasks operating in complex terrain. Overall, the KFLA is a promising method to estimate the kinematic states of the implements in indoor/outdoor environments, dryland, and paddy fields. • A KFLA based method is proposed to obtain vertical kinematic states of implements. • The vertical displacement and velocity of the implement are estimated. • In the process, the Kalman filter fuses the receiver's height and acceleration. • Laboratory experiments are performed to validate the method. • KFLA shows similar but smoother variations of the displacement difference. [ABSTRACT FROM AUTHOR]

Highlights • This paper proposed an external acceleration roll angle Kalman filter. • The external acceleration was estimated using a simplified acceleration model. • The error was less than 1° in paddy field dynamic situation. Abstract The agricultural machinery implements in paddy field are required to measure the roll angle dynamically. In order to reduce the effects of external acceleration on roll estimation thus improving dynamic measurement precision with low cost, this paper proposed an algorithm, the external acceleration roll angle Kalman filter (EARAKF), which estimated the external acceleration model with a one-order low pass filter and Gaussian white noise. After subtracting the estimated real roll angle from the value of accelerometers, the external acceleration superimposing on the single-axis accelerometer was estimated. Eventually, the roll angle estimation without external acceleration effect was obtained after the estimated external acceleration being subtracted from the Kalman filter (KF) in the measurement equation. Furthermore, a parallel track platform was used to impose external acceleration on the accelerometer. The test results shown that the acceleration on Y-axis increased significantly. The root mean square error (RMSE) of the EARAKF was 0.49°, while that of the KF algorithm was 1.91°, which demonstrated that the EARAKF was less influenced by the external acceleration. In the paddy field tests, the RMSE of the KF algorithm were figured out as 1.74°, while that of the EARAKF algorithm was 0.77°, which concluded that the EARAKF can estimate the external acceleration of the accelerometer and obtain a more accurate roll angle. The proposed algorithm presented a roll angle measurement method for the agricultural implements which working in paddy field dynamic scenario and could get less affected by the external acceleration with low cost and high accuracy. [ABSTRACT FROM AUTHOR]