This paper describes the use of MET-based low-noise angular motion sensors to precisely determine azimuth direction in a dynamic-scheme method of measuring the Earth’s rotational velocity vector. The scheme includes sensor installation on a rotating platform so that it could scan the space and seek for the position of the highest Earth’s rotation vector projection on its axis. This method is very efficient provided a low-noise sensor is used. A low-cost angular sensor based on MET (molecular electronic transduction) technology has been used. The sensors of this kind were originally developed for seismic activity monitoring and are well known for very good noise performance and high sensitivity. This approach, combined with the use of special signal processing algorithms, allowed reaching the accuracy of 0.2°, while the measurement time was less than 100 seconds.
The information about body position in space is essential for the solution of a number of tasks, such as vehicles navigation, antennae positioning in communication systems and geodesy, construction of pipes and underground tunnels, target indication, and mobile objects maintenance. Herewith the body position in space is defined by two independent directions, which are gravity vector at a certain point of the Earth’s surface and azimuthal angle found from the true north heading.
The task of angle detection at which the chosen body axis is positioned relative to the Earth’s gravitational vector at a certain point in space is quite easy and can be solved successfully with the use of high precision accelerometers. High precision identification of the chosen body axis relative to the local north heading (azimuth measurement) is a much more complex task.
Azimuth measurement with certain accuracy can be performed with the help of modern magnetometers [
Azimuth measurement has been performed for a long time by the position of stars and other celestial objects. Modern astronavigation equipment is widely used at orbital vehicles and other space vehicles and missions [
The use of differential satellite signals to define the object positioning in space is the modern way to find the true azimuth. Currently, fully featured Global Navigation Satellite Systems (GNSS) feature the American Global Positioning System (GPS) and the Russian Global Navigation Satellite System (ГЛОНАСС). As a rule, GNSS uses two main positioning methods, which are absolute (direct reception of satellite signal) and relative (with the use of premounted lighthouses). The absolute method includes object coordinates reception with lower precision; that is why it is used in navigation, while the relative one provides higher precision and is used directly for positioning. The ways of defining azimuth are also classified into static and kinematic, depending on whether the satellite receiver was moving during the measurements or not. Both methods require at least two signal receivers, simultaneously observing the same satellites to provide vector calculation between the signal receivers [
The modern way to define true azimuth is based on so-called gyrocompassing, which is direct measurement of Earth’s angular velocity projection vector on horizontal plane at a given point of surface [
The possibility to use inertial measurements of Earth’s angular velocity with the dynamic method arouses considerable interest. The principle of method is to place angular motion sensor (angular accelerometer or gyroscope) on a platform which changes its position in space in a certain known way. Most frequently, the platform traverses, which is orthographic to the sensor sensitivity axis. In that case, both Earth’s angular velocity vector projection on sensor sensitivity axis and its output signal change periodically with the movement. Amplitude and phase of the corresponding changes have the information about Earth’s rotation axis, which allows defining the true north heading [
The main advantage of the dynamic method is the signal shift from 0 Hz to rotational speed, related to Earth’s rotation, which allows eliminating errors related to low-frequency driftage of the measuring equipment. The method could be quite effective if a low-noise angular motion transducer is used. With that, presently available angular motion sensors, including microelectromechanical [
Qualitative increase of the method precision can be achieved by the use of brand new, more sensitive, and exact angular motion sensor. Angular motion transducers are usually used as such sensors as they are based on the principles of molecular electronic technology which has been widely developed in recent years [
Angular motion sensors based on molecular electronic transducer (MET) exploit the electrochemical principle of mechanical signal record, as well as liquid inertial mass. MET is a system of electrodes immersed in electrolyte solution with reversible oxidation-reduction reactions on the electrodes. The transducer may use different binary electrolytes which provide reversible oxidation-reduction reactions, such as iodine-iodide, ferro-ferricyanide and so forth.
High precision of the signal record is provided by means of conflict of two charge transfer mechanisms, which are diffusion and convection ions delivery with electrolyte flow which occurs under mechanical signal influence. Electromigration does not play a key role in the charge transfer due to high concentration of so-called background electrolyte, which does not enter into reaction on electrodes.
General design of MET is schematically shown in Figure
Molecular electronic transducer. 1: ceramic or glassy pipe; 2: electrolyte; 3: porous ceramic spacers; 4: anodes; 5: cathodes;
The design of angular motion sensor based on MET is shown in Figure
Angular motion sensor design:
To solve the task of longitude direction measurement, molecular electronic angular motion sensor (2) is placed on a platform (1) which can rotate at a certain constant angular velocity
The experimental setup: 1: platform, 2: angular motion sensor, SA: angular motion sensor sensitivity axis,
With the platform rotation, the horizontal projection of Earth’s rotational velocity vector on the sensor sensitivity axis changes according to the harmonic law with frequency
To create high precision molecular electronic device to record Earth’s angular velocity and to define true north heading, several samples of angular velocity sensors (based on MET 50 mm) (see Figure
Photo of MET 50 mm.
Photo of MET 9 mm.
Table
Technical parameters of molecular electronic angular motion sensor.
Parameter | Molecular electronic angular motion sensor | Molecular electronic angular accelerometer |
---|---|---|
Transducer diameter | 50 mm | 9 mm |
Output signal type | Analog, nondifferential, proportional to angular velocity | Analog, nondifferential, proportional to angular acceleration |
Photo (Figure |
See Figure |
See Figure |
Service band | 30 sec – 20 Hz | 0–50 Hz |
Transduction coefficient | 50 B/(rad/sec) | 0.5 B/(rad/sec2) |
Maximum bandpass flatness in service band | ±0.4 dB | ±0.5 dB |
Maximum output signal | ±5 V | ±10 V |
Maximal measured signal with harmonic distortions of <2% | 0.01 rad/sec | 5.2 rad/sec2 |
Noise spectral density in the frequency range of 0.01–3 Hz [ |
7.5 · 10−7 rad/(sec2·√Hz) | 10−4 rad/(sec2·√Hz) |
Operating temperature range | −12–+55°C | −12–+55°C |
Maximum error of temperature compensation in service band | <10% | <3% |
Possible installation angle | Any | Any |
Mass | 50 g | 8 g |
Power | 12 V | 12 V |
Input | 5 mA | 1.4 mA |
During the studies of the device model to define true north heading as rotating platform, single-axis motion simulator ST 1144C produced by Actidyn SA was used. It was mounted inside the setter 750T30/4 Climats manufactured by the BLM Sinergy (Figure
The experimental installation to define true north heading based on molecular electronic angular motion sensors.
To perform the research, ST 1144C platform was brought into motion with the given speed profile (see Figure
Typically ST 1144C rotational velocity profile.
The signal of molecular electronic angular velocity or acceleration sensor modulated to the platform rotational rate and the signal of high precision sensor of the stand position were registered by 24-bit data collection system E-24 L-Card. Based on the readings of the motion simulator angular sensor, the current platform position heading north at any time point was found.
At that, the following measurement method was used, which, on the one hand, excludes the necessity to find the sensor signal initial phase, which, for a range of reasons, may be difficult to perform at the necessarily high precision, and, on the other hand, considerably increases the general precision of the method itself. The method implies alternate clockwise and contraclockwise platform rotation with consequent addition of the received signal phases at the stand rotational rate. Suppose the molecular electronic device is fixed on the platform, so the sensor sensitivity axis is aligned along some (zero) direction, azimuth of which has to be found. Start rotating the platform clockwise at a certain angular velocity and make a total number of turns
Figure
The sensor signal spectrum (MET 50 mm) at the platform rotation, log-log scale.
Below the experimental results of azimuth measurement with the device model to define true north heading with the help of molecular electronic angular velocity sensors (MET 50 mm) and angular acceleration sensors (MET 9 mm) are shown. The latitude of the laboratory device is 55.93° (Dolgoprudny, Moscow Region), while the corresponding projection of Earth’s rotational rate at the stated latitude is
The study included a set of experiments, which differed in the platform rotation rate. The duration of each measurement was 100 seconds. Eight different samples of molecular electronic angular velocity and acceleration sensors were measured. The results of the statistical study of dispersion of experimentally measured angles heading north are shown in Table
The experiments results for angular velocity sensor (MET 50 mm) and angular acceleration sensor (MET 9 mm).
Platform rotational rate, Hz | Earth’s rotational rate projection on completion of measurements, rad/sec | Azimuth average value and root-mean-square | ||
---|---|---|---|---|
MET 50 mm | MET 9 mm | MET 50 mm | MET 9 mm | |
0.05 | 4.12 · 10−5 | 5.6 · 10−5 | 254.22° ± 0.24° | 253.3° ± 1.2° |
0.1 | 4.02 · 10−5 | 4.6 · 10−5 | 254.33° ± 0.17° | 257.4° ± 2.1° |
0.2 | 4.16 · 10−5 | 4.2 · 10−5 | 254.36° ± 0.28° | 259.5° ± 2.8° |
True values of quantities | 4.084 · 10−5 | 254.23° |
For miniature MET 9 mm, the error in measurement of north heading may reach several degrees. Thus, miniature MET 9 mm does not possess the necessary sensitivity for high precision finding of north heading; however, due to its cost and mass-dimensional parameters it can be used in cheap household systems. At the same time, in the conditions of the performed experiments for MET 50 mm, root-mean-square error of a single measurement is 0.2°-0.3°. With that, these errors may have completely different nature. Therefore, depending on the dominating mechanisms, approaches to reduce the errors must be different. The errors of random nature can be reduced by averaging the signal and by sensors noise characteristics optimization. Inaccuracy in sensor sensitivity axis positioning can be found at calibration and it can be taken into account at data processing. That is why the further analysis was performed to identify the certain sources of errors.
In the present study, a very accurate mechanical system was used. Thus, there were no errors connected with nonideality of the mechanical system in this study. Generally speaking, the following factors may affect the accuracy of measurement: Irregularity of the platform rotation may lead to errors if the angle between the ME sensor sensitivity axis and the platform rotation axis is different from 90 degrees. In fact, the sensor, does not only measure the Earth’s rotation angular velocity, but also the angular velocity projection of unevenly rotating platform on its sensitivity axis. The platform rotation axis inclination relative to the gravity acceleration causes a change in the gravity projection on the sensor axis, which results in spurious signal due to the presence of some sensor sensitivity to linear acceleration. Fluctuations of the rotation axis due to the bearing beats result in a change of the sensor angular position, with the angular velocity component along sensors sensitivity axis.
To increase the measurements accuracy and to find the main sources of errors and to develop the methods to decrease their influence, numeric modelling was performed. The modelling studied to what type of error in the studied signal phase molecular electronic angular motion sensor self-noise led. Further modelling was performed for molecular electronic angular velocity sensor based on MET 50 mm.
For further comparison with the experimental data, calculation experiment was performed. It modelled the described above measurements on the assumption that the only source of errors was sensor noise. Software was used to create sine wave corresponding to the number of rotations made by the real azimuth measurer, to the frequency equal to the platform rotation rate, to the amplitude equal to the Earth’s rotational rate projection registered in the experiment, and to the initial phase corresponding to the initial angle of sensor sensitivity axis rotation relative to the known direction of true north heading. Later, the signal was processed by bandpass Butterworth filter with decline order completely corresponding to the sensor technical parameters from Table
What is more, noise signal of molecular electronic sensor was modelled. For that, standard distribution noise signal was modelled, which is known to have frequency independent spectrum. Noise spectral power density of molecular electronic angular velocity sensor was recognized not to depend on the frequency in units of applied angular acceleration [
During modelling the spectral behavior of the virtual signal was similar to the real sensor signal spectrum. So in modelled signals both the signal of projection from Earth’s rotation and the contribution from the sensor self-noise existed (see Figure
Spectra of real and imitating signals at modelling of azimuth measurement error, determined by the sensor self-noise (dark is the real experimental signal, light is the modelled signal, and the peak of the corresponding registered Earth’s rotational rate projection is highlighted), log-log scale.
During modelling, statistic study of the influence of the additional interfering signal equal to low-frequency noise of molecular electronic angular velocity sensor on the error in measuring the phase of the registered signal and the azimuth, respectively, was performed. The statistic study included both the influence of the measurement duration and the platform rotation frequency on the precision of phase finding for the developed model and for the real experiment and the comparison of the obtained data. The experimental data received in a large number of experiments with the use of one measurer was used to process the information. At that, only the platform rotation frequency and the duration of record varied. Other conditions, such as temperature, type of sensor fixation on the platform, testing frequency, and the recording equipment, remained the same.
The study results are shown in Table
The results of mathematical modelling of sensor self-noise contribution into the phase error of the studied signal compared to the experimental results of studying the possibility of high precision azimuth measurement.
Platform rotation rate (Hz) | Record duration (seconds) | Mean-root-square error in the modelling signal phase finding by 15 productions (degrees) | Mean-root-square error in experimental true north heading determination (degrees) | Experiment systematic error (degrees) |
---|---|---|---|---|
0.05 | 400 | 0.13 | 0.13 | 0.07 |
0.05 | 200 | 0.18 | 0.16 | 0.06 |
0.05 | 100 | 0.20 | 0.21 | 0.06 |
0.1 | 400 | 0.07 | 0.08 | 0.06 |
0.1 | 200 | 0.09 | 0.1 | 0.08 |
0.1 | 100 | 0.16 | 0.13 | 0.06 |
0.2 | 400 | 0.04 | 0.09 | 0.02 |
0.2 | 200 | 0.05 | 0.1 | 0.03 |
0.2 | 100 | 0.08 | 0.13 | 0.05 |
The presented experimental results, as well as the data of numeric modelling of angular sensor self-noise contribution into the error of azimuth finding, suggest the following conclusions.
Miniature molecular electronic angular acceleration sensor based on MET 9 mm does not have high precision of azimuth finding (2°-3°) but considering its small parameters can be treated as an alternative to portative household compasses.
The precision of true north heading determination for molecular electronic angular velocity sensor based on MET 50 mm is 0.2°-0.3° at the studied latitude (
The best precision in the stated experiment conditions is achieved at the platform rotation rate of 0.1 and 0.2 Hz. If the rotation rate decreases, the precision falls down, which can be apparently described by the increase of molecular electronic angular velocity sensor self-noise at low frequencies. At the platform rotation rate of 0.05 Hz and 0.1 Hz, the modelling results, in assumption that the only source of errors is angular rotation sensor self-noise, fully correspond to the experimental data. This result brings us to the conclusion that in this case the main error factor in true north heading determination is molecular electronic angular rotation sensor self-noise. Consequently, the methods of errors eliminating must include reduction of sensor self-noise, which can be achieved, for example, by increase of its size and by reduction of hydrodynamic resistance of the transductive element.
At the higher platform rotation rate, the modelling predicts lower value of azimuth finding error, which could be observed in a real experiment. That is apparently connected to low, achievable for this type of equipment, data sampling rate and the resulting decrease of measurements resolution for rotation angle at high rotation rate of movement simulation platform. Detailed study of the mechanisms responsible for the measurements errors at higher rotation rates must be a topic of a separate study.
Systematic error in true north heading determination in this case is lower than accidental error and is apparently conditioned by the combined effect of nonorthogonality of sensor sensitivity axis to the mounting platform, lack of perpendicularity in rotation axis, influence of angular motion sensor sensitivity to linear acceleration, and so forth. At the same time, as compared to the data from Table
On the whole, the obtained data demonstrate that the manufacturing of the equipment based on these principles, which can provide the precision of true north heading determination at 0.2 degrees or even several times better, is quite a real task.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The results presented in this paper were partly obtained under the projects supported by The Russian Ministry of Education and Science—Project ID RFMEFI57514X0017 and State Assignment no. 14.575.21.0017.