Application of the Principle of Rational Approximations for Measuring Dynamic Frequency Values Generated by an IMU

Introduction

For aerial vehicles, like aircrafts, unmanned aerial vehicles (UAV) or drones (Sabatini et al., 2015), the estimation of position, also known as georeferencing (Schwarz, 1996), and velocity are some of the most important tasks that are done during “the fly”. For most flying systems, such parameters are calculated using combined data from Global Positioning System (GPS) and the Inertial Navigation System (INS). Since the INS is located inside the vehicle, navigation information can be generated in situ without external references. At the same time, within the INS, the desired parameters are calculated by the Inertial Measurement Unit (IMU), as it is illustrated in Fig. 1. In the case of GPS outage, aircraft positioning depends from INS. In such a case, positional and attitude precision degrades rapidly due to INS sensor errors (Zhao et al., 2011). For this reason, the functioning of sensors incorporated in IMU can be improved by means of sensors construction, operation and signal processing. Accelerometers and gyroscopes are the primary source of information for an IMU (Ahmad et al., 2013). As stated by Sankar et al. (2009), there are many types of accelerometers, which include piezoelectric, piezoresistive, capacitive, tunneling, vibrating/resonating beam. This work focus on the accelerometers that generate a frequency output signal, this value is a function of the experienced acceleration. For some applications it is enough if the frequency output is interpreted as voltage or electrical current, which is easily achievable using well known frequency to voltage converters. Nevertheless, an accelerometer with a frequency output offers desirable characteristics such as quasi-digital signals, high sensitivity, high resolution, wide dynamic range, anti-interference capacity and good stability (Huang et al., 2013). For these reasons, from a metrological point of view, the use of the signal with frequency variations is better than a frequency to “something” conversion. From the measured frequency value, the IMU can directly estimate the acceleration magnitude. Additionally, by dead reckoning the velocity and position (or displacement) can be calculated. In other words, using initial conditions, after one integration of acceleration, the velocity is obtained; the position can be obtained after a second integration (Noureldin et al., 2013). Since position, velocity and acceleration depend of the frequency domain output from the accelerometer, fast and accurate frequency measurement is required. Usually, there are three accelerometers, one per each axis.

Figure 1.

Elements of an INS

Some accelerometers that are commercially available are Vernier 3D-BTA (Vernier, 2019), Honeywell HG4930 (Honewywell, 2019), Ellipse2 (SBG Systems, 2019) or Endevco 773 (MEGGITT Endevco, 2019). Some of their operating parameters are offered in Table 1. These sensors have a frequency domain output; for this reason, in order to use such sensors, proper frequency measurement is required. Besides of data in Table 1, the accelerometers based on MEMS are actively being researched and developed (Eling et al., 2015, Gao et al., 2017; Li et al., 2017, Li et al., 2019; Sekiya et al., 2016).