Pedestrian Inertial Navigation with Self-Contained Aiding. Andrei M. Shkel
1.3.1 Approaches
There are two general approaches in the pedestrian inertial navigation. One is the strapdown inertial navigation as introduced in Section 1.2, where IMU readouts are integrated into position and orientation. This approach is universally applicable, but the integral step makes the algorithm computationally expensive and the navigation error accumulates as time cubed due to the gyroscope bias. In order to limit the error propagation, the most commonly used method is to apply the Zero‐Velocity Updates (ZUPTs) when the velocity of the foot is close to zero (the foot is stationary on the ground) [12]. The stationary state can be used to limit the long‐term velocity and angular rate drift, thus greatly reduce the navigation error. In this implementation, IMU is fixed on the foot to perform the navigation and to detect the stance phase at the same time. Whenever the stance phase is detected, the zero‐velocity information of the foot is fed into the Extended Kalman Filter (EKF) as a pseudo‐measurement to compensate for IMU biases, thus reducing the navigation error growth in the system. In this architecture, not only the navigation errors but also IMU errors can be estimated by the EKF. The limitation of this approach is that the IMU needs to be mounted on the foot.
In order to avoid the integral step in the pedestrian inertial navigation and also relax the requirement of IMU mounting position, a Step‐and‐Heading System (SHS) is an alternative. It is composed of three main parts: step detection, step length estimation, and step heading angle estimation [13]. Unlike the first approach, this approach can only be applied in the pedestrian inertial navigation. In this approach, the step length of each stride is first estimated based on some features of motion obtained from the IMU readouts. Methods based on biomechanical models and statistical regression methods are popular for the estimation. Some commonly used features include the gait frequency, magnitude of angular rate, vertical acceleration, and variance of angular rate. Then, the heading angle is estimated by the gyroscope readout, which is typically mounted at the head. This step can also be aided by magnetometers to improve the accuracy. In this way, the total displacement can be estimated combining the traveled distance and the heading angle. However, two major challenges exist for this approach. First, the gazing direction needs to be aligned with the traveling direction, implying that the subject needs to look at the traveling direction all the time, which is not practical. Second, the step length estimation remains difficult. The average value of the estimated step length may be accurate when median value generally less than 2%, but the estimate precision is generally low, with the Root Mean Square Error (RMSE) about 5% [14]. With a wide adaption of hand‐held and fitness devices, this is currently an active area of research.
1.3.2 IMU Mounting Positions
In pedestrian inertial navigation, depending on the approaches to be taken and the application restrictions, the IMU can be mounted on different parts of body to take advantage of different motion patterns, such as head, pelvis, foot, wrist, thigh, and foot. Pelvis, or lower back, was the first explored IMU mounting position in the literature, because these parts of the body experience almost no change of orientation during walking, which greatly simplifies the modeling process for both strapdown inertial navigation and SHS [15]. In subsequent studies, thigh and shank were explored, such that IMU can directly measure the motion of the leg, which is directly related to the step length by the biomechanical models [16,17]. More recently, in order to integrate pedestrian inertial navigation with smart phones and wearable devices, such as smart watches and smart glasses, pocket, wrist (or hand hold), and head are becoming the IMU mounting positions of interest [18–20]. The foot‐mounted IMU has also been demonstrated for SHS, but this placement of sensors is mostly used in the ZUPT‐aided pedestrian inertial navigation, instead of SHS.
Head‐mounted IMUs are usually used for heading angle estimation, since it experiences lowest amount of shock and almost no change of orientation. Besides, it is usually convenient to mount the IMU on the helmet for first responders and military applications [21]. However, the low amplitude of angular rate and acceleration during walk makes it hard for step length detection. In addition, the gazing direction may not be aligned with walking direction during navigation. Pelvis‐mounted IMUs have the ability of estimating the step length for both legs with one single device, compared to the IMUs mounted on the legs. It is also more convenient to align the IMU to the walking direction compared to the head‐mounted IMUs. Pocket‐mounted IMUs and hand‐held IMUs are mostly developed for pedestrian inertial navigation for use with smart phones. In this approach, the IMU is not fixed to a certain part of the body, and its orientation may change over the navigation applications due to different hand poses and different ways to store the smart phone in the pocket. It makes the SHS algorithm more complicated than other IMU mounting positions. Foot‐mounted IMUs will experience the highest amount of shock and vibration due to the heel shocks during walking [22]. As a result, a more stringent requirement on the IMU performance will be necessary, such as high shock survivability, high bandwidth and sampling rate, low g‐sensitivity, and low vibration‐induced noise [23]. However, with foot‐mounted IMUs, a close‐to‐stationary state of the foot during the stance phases will greatly reduce the navigation errors in the ZUPT‐aided pedestrian inertial navigation.
1.3.3 Summary
Between the SHS and the ZUPT‐aided strapdown inertial navigation, the latter is the more widely used approach for precision pedestrian inertial navigation. The main reasons are:
ZUPT‐aided strapdown inertial navigation has demonstrated a better navigation accuracy compared to the SHS. For example, in a navigation with the total walking distance of 20 km, position estimation error on the order of 10 m was demonstrated, corresponding to a navigation error less than 0.1% of the total distance [24]. The navigation error for SHS, however, is typically about 1% to 2% of the total walking distance.
ZUPT‐aided strapdown inertial navigation is more universal compared to SHS, with only one assumption that the velocity of the foot is zero during the stance phase. As a result, it can be applied to many pedestrian scenarios, such as walking, running, jumping, and even crawling. In the case of SHS, it has to classify different motion patterns, if the system has been trained with such patterns, and correspondingly fit the data to different models.
SHS is user‐specified and needs to be calibrated or trained according to different subjects, while ZUPT‐aided strapdown inertial navigation in principle does not need any special calibration for different users.
Even though IMU will experience high level of shock and vibration when mounted on the foot in the ZUPT‐aided strapdown inertial navigation, the developed MEMS technologies are able to reduce the disadvantageous effects. For example, it has been demonstrated that IMU with gyroscope maximum measuring range of and bandwidth of 250 Hz would be able to capture most features of the motion without causing large errors [25].
In this book, we will mainly focus on the ZUPT‐aided strapdown inertial navigation.
1.4 Aiding Techniques for Inertial Navigation
Many aiding techniques have been developed to fuse with inertial navigation to improve the navigation accuracy. They can be roughly categorized into self‐contained aiding and aiding that relies on external signals (non‐self‐contained aiding). We start with non‐self‐contained aiding.
1.4.1 Non‐self‐contained Aiding Techniques
According to the property of the external signals, non‐self‐contained aiding techniques can be divided into two categories. In the case where the external signals are naturally existent, such as the Earth's magnetic field and the atmospheric pressure, no extra infrastructure is needed, but the signals may be subject to disturbance since their sources are not controlled. However, in the other case where man‐made signals are used, implementation of infrastructures is needed with the benefit that the signals are engineered to facilitate the navigation process.