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A dual extended kalman filter for tilt estimation

Abstract:

Accelerometers and Gyroscopes are typically used to measure rotation angles. However, the nature of both sensors makes difficult to estimate an angle using only one of these sensors. This is because gyroscopes return high bias data, and, since accelerometers detects every small acceleration in each axis, the output of this sensor is very noisy. A common solution is to combine both signals in so-called sensor fusion. Two popular techniques are Complementary Filters and Constant Gyro Bias Kalman Filters. These algorithms are attractive because they are simple to implement and do not depend on specific parameters of the system. Because these filters use the arctangent function, they cannot resolve a discontinuity on the estimated signal. This discontinuity is caused by a flip among the two endpoints in the range of arctangent function. This range is usually [-π/2, π/2] or [-π,π]. This problem occurs because of the discontinuous nature of the tangent function, and because tangent is strictly not invertible. To solve this, an additional routine must be implemented to patch these flips. This paper presents a practical Dual Extended Kalman Filter algorithm for angle estimation. This work focus on the restricted problem of measuring the angle of rotation of a body respect to one axis parallel to the earth surface. The main characteristic of the developed algorithm is that it does not depend on physical parameters and does not use the inverse tangent function on its implementation. For the implementation, the accelerometer and gyro signals were acquired from the IMU MPU-6050 with a 50 ms sampling time. The complete algorithm was implemented in a MATLAB script and then it was compared with two other methods usually used in tilt estimation: Complementary Filters and Constant Gyro Bias Kalman Filter.