Estimation of angular velocity and acceleration with Kalman filter, based on position measurement only Johnny Rodriguez-Maldonado State University of Nuevo Leon, (UANL), Pedro de Alba s/n, San Nicolas de Los Garza, Nuevo Leon 66455, Mexico article info Article history: Received 30 October 2018 Received in revised form 2 May 2019 Accepted 11 May 2019 Available online 18 May 2019 Keywords: Tracking filter Velocity estimation Taylor Kalman filter Digital differentiator Acceleration estimation abstract This paper presents a method to obtain good synchronous and instantaneous estimates in position, veloc- ity and acceleration; using a position measurement only. The proposed method shows better estimates in position, velocity and acceleration than other methods such as nonlinear tracking differentiator (TD), extended state estimation (ESO) and digital differentiator based on Taylor series (DDBTS). The proposed method allows for an increased accuracy of estimates by generating a feedback frequency obtained to the position measurement signals. The model and method proposed in this paper reduce the error when the measurement signal presents a change in frequency. The model update and adjusts simultaneously to changes in sample rates using a feedback frequency estimate. The proposed method was validated with the QNET DC Motor Control Trained (DCMCT). Since the method requires the measurement position only from an encoder, it eliminates the need for more sensors for velocity and acceleration, thus begin less costly. Ó 2019 Elsevier Ltd. All rights reserved. 1. Introduction Nowadays in many applications as robotics, monitoring by GPS, control motors, controlled motion systems, and others, the infor- mation as position, velocity, and acceleration are very important. This information provided by the monitoring of the systems is cru- cial to make a decision or control of the systems. For example, the measurement of position in the displacement is crucial, as is demonstrated in [1] where is measurement the displacement for understanding and characterizing the behavior of civil infrastruc- ture using an RTK-GPS. But in the application are used three sen- sors to obtain the estimates of displacement, velocity an acceleration. Another application that considered the velocity change to designing the control strategy for the connected cruise control is presented in [2]. The track condition monitoring based on the bogie and car body acceleration measurement is presented in [3] using a mathematical model. The disadvantage to used a model, is that in some systems is very difficult or imprecise the estimation of the model. One of the most used sensor to obtain the signal position in electrical motors is the encoder. Some estimations of angular velocity based in the measured position are presented in [4–8]; unfortunately, most of these are unsatisfactory in control applica- tions due to the delay that is inherited in the derivative estimates provided by this filters, that produce adverse effects in stability [9]. As an alternative, some methods employ a Kalman filter to esti- mate the velocity. However, the Kalman filter model presented in [10–12] requires a target velocity trajectory. In [13] is proposed an adaptive model-free observer for robot manipulators in the task-space without the use of task-space velocity measurement. Also in [14] are used a combination of an accelerometer and an encoder to estimate velocity, using an obser- ver, the application is considering a robot performing in rigid con- tact modeling and control. In the sense of the fault detection, was proposed in [15] an algorithm extract the features of helical gear fault, using an optimal encoder and tracking analysis based on the angular domain asynchronous averaging. In [16] was proposed a finite-response filter with adaptive window length to estimate position and velocity, the estimates are concentrated in velocity jump, the precision in its estimates have a threshold that depends to the sampling position data and predicted position, one advan- tage of the method is that not need a system model. On the other hand, the comparison study between different velocity and accel- eration estimators are presented in [17] using an encoder to mea- sure position. The model used in [11,17–19] estimate the angular velocity and angular acceleration with the Kalman filter, but this model requires a constant sampling interval obtained through the enco- der system with an interpulse angle. Another method that needs a constant sampling interval is presented in [4]. A disadvantage https://doi.org/10.1016/j.measurement.2019.05.043 0263-2241/Ó 2019 Elsevier Ltd. All rights reserved. E-mail address: johnny.rodriguezml@uanl.edu.mx Measurement 145 (2019) 130–136 Contents lists available at ScienceDirect Measurement journal homepage: www.elsevier.com/locate/measurement