Discrete-time complementary filter for attitude estimation based on MARG sensor

The MARG sensor, which stands for the combination of a magnetometer, an accelerometer, and a gyroscope, is widely used for 3D attitude measurement. Among the mainstream solutions for MARG-based attitude estimation, the complementary filter (CF) is normally regarded as a simplified alternative to the Kalman filter (KF), mainly because CF can reduce the amount of calculations. A dual-vector discrete-time CF (DV-DTCF) and its tuning methods are introduced in this paper. Different from the quaternion-based attitude estimation algorithms, DV-DTCF has a linear measurement model, since it utilizes the gravity and geomagnetic vectors as its state variables instead of quaternions. This feature of DV-DTCF can avoid linearization error or the use of nonlinear algorithms, and can also greatly reduce its computational complexity. More interestingly, it is analytically revealed, and experimentally proven, that the proposed DV-DTCF is fully equivalent to a fixed-gain KF. This fascinating fact leads straightforwardly to the tuning methods of DV-DTCF via the corresponding fixed-gain KF and Riccati equation. These tuning methods of DV-DTCF are based on the statistic characteristics of MARG sensor noise, and that makes them solid and feasible. According to experimental results, DV-DTCF can achieve the same accuracy as that of commonly-used KF algorithms in MARG-based attitude estimation, but with much lower time consumption. Hence, the proposed DV-DTCF is especially suitable for applications that have strict limitations on computational costs.