Magnetic Attitude Update (MAU) for Frame Misalignment Correction in Pedestrian Dead Reckoning (PDR)
Maan Khedr, University of Calgary, Canada & Arab Academy for Science and Technology, Egypt; Ahmed Radi, Naser El-Sheimy, University of Calgary, Canada
Location: Big Sur
Alternate Number 2
Pedestrian navigation is one of the most challenging navigation problems. This is due to the high dynamics of pedestrian motion and its variability from one user to another, in addition to the low integrity of GNSS in environments where day-to-day activities occur; such as indoors. Advancements in Micro-Electro-Mechanical Systems (MEMS) technology has led to the integration of low-cost MEMS Inertial Measurements Units (IMU) in nearly all smart devices, including smartphones. The MEMS-based inertial sensors typically used in smartphones suffer from high noise and errors, that tend to make them unreliable for long-time navigation using the conventional methods such as Dead Reckoning (DR). other techniques; such as Pedestrian Dead Reckoning (PDR), try to overcome the errors in the DR by breaking down the user’s travelled distance into sequence of steps and an estimated stride length in a certain direction.
For reliable PDR navigation, accurate estimation of the misalignment between the navigation frame and sensor body frame is needed. Misalignment errors reflect on the accuracy of the navigation drastically as it leads to: wrong elimination of gravity component from accelerations, and wrong estimation of heading. The wrong elimination of gravity components leads to wrong estimation of travelled distance based on estimated stride length, while the wrong estimation of heading adds up to the position error, as it accumulates distance moved in the wrong direction. Both errors lead to the short-term accuracy of the inertial navigation systems.
This paper presents a new algorithm for correcting the misalignment between the sensor/body frame and the Local Level Frame (LLF) also referred to as navigation frame. This is done through the use of magnetic measurements, and the available information about earth magnetic map from the World Magnetic Map (WMM), without the use of the gyroscope-based attitude mechanization; thus, decreasing the accumulated error over time from the measurements integration. This in turn will lead to a better position estimation for the navigation process.
This work assumes three different coordinate frames, namely: body frame, magnetic frame, and navigation frame. The conventional navigation process relates the body frame directly to the navigation frame in a three rotational sequence depicted by the Direction Cosine Matrix (DCM). In this work, we assume an intermediate frame which is the magnetic frame. This frame is characterized by having the vertical axis aligned with the magnetic vector obtained from the WMM depending on the user’s location. This is similar to how the navigation frame is aligned with the gravity vector.
The underlying assumption is that the misalignment between the navigation frame and the magnetic frame can be achieved in the same manner as the initial alignment of mechanization-based Inertial Navigation System (INS). That is, a roll and pitch angles relating the two frames can be computed using simple trigonometric functions. It is important to note that the magnetic frame is nearly static and only changes slightly over time. Hence the alignment is not carried out regularly. Using a constructed DCM between the navigation and magnetic frames, the gravity components are known in the magnetic frame.
During navigation, as the magnetic measurements tend to the magnitude of the reference magnetic vector magnitude from the WMM, and as the accelerations measured in the body frame tend to gravity with some variation, a DCM based on quaternion construction between the magnetic vector in body frame and the magnetic frame is constructed. The alignment resulting from the magnetic vectors is a vector alignment and not frame alignment. Frame alignment requires at least two vectors in each frame, while in this case only one vector is used. The resulting rotation suffers from an angle ambiguity around the z-axis.
By using the DCM for alignment between the body and magnetic frames, the accelerations are leveled into the magnetic frame, but they lack the write heading in the frame. As the accelerations are tending to the gravity value, the expected horizontal components are known from the first alignment between the navigation and magnetic frame. Hence, a rotation around the z-axis of the magnetic frame can be achieved so that the leveled horizontal components have the same ratio of x-axis to y-axis as those of the reference from the initial alignment between the navigation and magnetic frames.
From the two levels of alignment, acceleration components in the navigation frame are computed. Those components are then used for a direct mapping between the body and navigation frame to calculate the roll, pitch, and azimuth between the two frames.
The proposed methodology works on an epoch-by-epoch manner and resets the attitude angles obtained from the angular mechanization of the gyroscope measurements, hence providing correction whenever the conditions apply. Direct frame alignment using the acceleration when it tends to gravity and magnetic vector as it tends to the reference would also result in attitude angles estimation, but the acceleration components will have greater effect on the resulting alignment. By using the intermediate frame alignment proposed, the magnetic vector is the main alignment component, and the ambiguity is resolved through the aiding of the acceleration vector. The resulting alignment relies more on the relation between measured magnetic field in the body frame to the reference magnetic vector obtained from the WMM.
The proposed methodology has been tested using static data from smartphones, where the orientation of the device is changed based on a reference trajectory without displacement, hence yielding a nearly static acceleration. It was also tested using simulated data with introduced noise. Preliminary results show the feasibility of obtaining attitude angles on epoch basis using the developed method, where the attitudes provided by the method are considered as corrections, and attitude mechanization is then employed until correction conditions are met.
More tests are to be carried out in different phone orientation placement during walking. The expected results are that they would be the same as the ones obtained so far. The major factor that would affect the performance of this method is high magnetic fluctuations for long periods, resulting in not satisfying the conditions for applying the correction and relying on the attitude mechanization alone for attitude angle computation.
In conclusion, the proposed method can keep track of the misalignment between the body and navigation frames by providing attitude corrections on regular basis to aid the attitude mechanization. This is achieved through the use of magnetic measurements and knowledge of the reference magnetic field at any given point on earth at any given time provided by the WMM.
The significance of this work is that it attempts to eliminate the accumulated errors in pedestrian navigation over time from the integration of measurements over time which in turn will give a better estimation of the pedestrian position. The proposed algorithm is to be integrated with a full PDR system with the capability of step detection and stride length estimation for obtaining a full navigation state.