Читать книгу Pedestrian Inertial Navigation with Self-Contained Aiding - Doruk Senkal, Andrei M. Shkel - Страница 12

The operation of inertial navigation relies on the measurements of accelerations and angular rates, which can be achieved by accelerometers and gyroscopes, respectively. In a typical Inertial Measurement Unit (IMU), there are three accelerometers and three gyroscopes mounted orthogonal to each other to measure the acceleration and angular rate components along three perpendicular directions. To keep track of the orientation of the system with respect to the inertial frame, three gyroscopes are needed. Gyroscopes measure the angular rates along three orthogonal directions. Angular rates are then integrated, and the orientation of the system is derived from these measurements. The readout of the accelerometers is called the specific force, which is composed of two parts: the gravity vector and the acceleration vector. According to the Equivalence Principle in the General Theory of Relativity, the inertial force and the gravitational force are equivalent and cannot be separated by the accelerometers. Therefore, the orientation information obtained by the gyroscopes is needed to estimate the gravity vector. With the orientation information, we can subtract the gravity vector from the specific force to obtain the acceleration vector, and revolve the acceleration vector from the system frame to the inertial frame before performing integration. Given the accelerations of the system, the change of position can be calculated by performing two consecutive integrations of the acceleration with respect to time.

The earliest concept of inertial sensor was proposed by Bohnenberger in the early nineteenth century [6]. Then in 1856, the famous Foucault pendulum experiment was demonstrated as the first rate‐integrating gyroscope [7], whose output is proportional to the change of angle, instead of the angular rate as in the case of most commercial gyroscopes. However, the first implementation of an inertial navigation system did not occur until the 1930s on V2 rockets and the wide application of inertial navigation started in the late 1960s [8]. In the early implementation of inertial navigation, inertial sensors are fixed on a stabilized platform supported by a gimbal set with rotary joints allowing rotation in three dimensions (Figure 1.1). The gyroscope readouts are fed back to torque motors that rotates the gimbals so that any external rotational motion could be canceled out and the orientation of the platform does not change. This implementation is still in common use where very accurate navigation data is required and the weight and volume of the system are not of great concern, such as in submarines. However, the gimbal systems are large and expensive due to their complex mechanical and electrical infrastructure. In the late 1970s, strapdown system was made possible, where inertial sensors are rigidly fixed, or “strapped down” to the system. In this architecture, the mechanical complexity of the platform is greatly reduced at the cost of substantial increase in the computational complexity in the navigation algorithm and a higher dynamic range for gyroscopes. However, recent development of microprocessor capabilities and suitable sensors allowed such design to become reality. The smaller size, lighter weight, and better reliability of the system further broaden the applications of the inertial navigation. Comparison of the schematics of algorithmic implementations in gimbal system and strapdown system is shown in Figure 1.2.

Figure 1.1 A schematic of gimbal system.

Source: Woodman [5]

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Figure 1.2 Comparison of (a) gimbal inertial navigation algorithm and (b) strapdown inertial navigation algorithm.

Inertial navigation, as a dead reckoning approach to navigation, also suffers from error accumulations. In the inertial navigation algorithm, not only accelerations and angular rates are integrated but all the measurement noises are also integrated and accumulated. As a result, unlike the position fixing type of navigation, the navigation accuracy deteriorates as navigation time increases. Noise sources include fabrication imperfections of individual inertial sensors, assembly errors of the entire IMU, electronic noises, environment‐related errors (temperature, shock, vibration, etc.), and numerical errors. Thus, inertial navigation imposes challenging demands on the system, in terms of the level of errors, to achieve long‐term navigation. This partially explains why inertial navigation systems were developed around 100 years later than the development of inertial sensors. It has been shown that without an error‐suppressing algorithm, the position error accumulates without bound and approximately proportional to time cubed. For example, for navigation grade IMUs, which cost a few hundred thousand dollars per axis, the navigation error will reach about one nautical mile after an hour of navigation, or equivalently less than 0.01 m of navigation error within a minute of navigation. However, for consumer grade IMUs, which cost a few dollars, the navigation error will exceed a meter of error within a few seconds of navigation [9]. Therefore, aiding techniques are necessary to limit the navigation error propagation in inertial navigation, especially in the case of pedestrian inertial navigation, where the cost and size of the system are limited.