Sensor Data Fusion for Navigation Systems for the Extraction of Raw Materials in the Deep Sea

Copper ores are found in massive sulphide deposits in the rift zones of the oceans. For the exploration and mining of these hydrothermally formed and very small-scale heterogeneously structured deposits, exact position data of the mining equipment used and also of the individual mining tools are required. At depths of over 2,000 m, navigation has to manage without the support of established navigation systems and is carried out using inertial measurement systems. These must be designed to meet the requirements of the deep-sea environment as well as the extreme vibration stresses from the mining process. The use of robust electronic sensors requires compensation for drift and inter­ference by ­means of Kalman filtering.

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1  Growing demand for raw materials due to electrification

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The ongoing electrification of many areas of life, such as heat generation and transportation, is creating a rapidly increasing demand for the raw materials required for this. In addition to critical minerals such as lithium, cobalt and graphite, this is primarily copper, which is essential as a key raw material in large quantities for generators, transformers, motors and cables, and for which demand is projected to be around five times the currently available mining capacity by 2030. This cannot be met in the short term by developing new mines on the mainland. (1)

Due to the long service life of many electrical systems, no secondary market can be developed here in the short term, so the focus is primarily on increasing productivity, e. g. through semi-autonomization of mining equipment, in existing mines and the development of known deposits in the deep sea.

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2  Raw materials in the deep sea

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Minerals in the deep sea that are of interest for mining can be roughly divided into three groups, which are distinguished not only in terms of their origin and occurrence, but also in terms of the extraction technology used. These groups are manganese nodules, cobalt-rich crusts and massive sulphides.

The economic use of manganese nodules formed in the deep sea has been studied since the 1960s. The current debate about mining projects in the Clarion-Clipperton Zone (CCZ) off Hawaii is also increasingly part of the political discussion about the effects and consequences of deep-sea mining. Manganese nodules are mainly found in the shallow basins of the deep sea. Current projects for their exploitation rely on mobile, ground-based extraction systems.

Cobalt-rich crusts are formed by the deposition of minerals dissolved in seawater on exposed rock in areas of volcanic activity.

Massive sulphides form at the edges of rift zones as a result of the interaction of plate tectonics and water cycles. Due to the high pressure of the water column, deep water is forced into fissures in the basalt mantle at great depths, where it is heated to approximately 500 to 600 °C. As a result, minerals and other substances are released. As a result, minerals and sulphur are dissolved in the water in high concentrations and the water rises again elsewhere. When it emerges and comes into contact with the deep water, which is around 2 °C cold, the dissolved minerals suddenly precipitate, creating the visual impression of a plume of smoke (black or white smoker). The minerals are deposited at the exit point and form the typical vent-like structures of precipitated metal-sulphur and metal-silicate compounds on the one hand and a bed of fine-grained precipitated material on the other. During its active phase, the black smoker forms a so-called mound around the exit point, which mainly contains copper, copper-iron or zinc and lead sulphides. The high pressures, temperatures and extremely low pH values do not permit the decomposition of an active smoker, but provide a habitat for organisms that are specifically geared towards heat and sulphur. After the end of activity, the mound compacts through recrystallization processes and becomes accessible for exploration as life also gradually dies out due to the loss of heat.

In the case of chalcopyrite, bornite or covellite, hydrothermally formed massive sulphides are an essential basis for copper ore mining. Typically, these deposits were formed several hundred million years ago, overlaid with sediment layers several hundred to over two thousand meters thick and compacted and recrystallized by geological processes. Typical copper contents are < 1 %. Their development as open-cast mines requires the excavation of correspondingly large pits and spoil heaps. In the case of seabed massive sulphides (SMS), these ores are found relatively young and without sediment overburden; less compacted and therefore easy to dissolve, and with copper contents > 10 %, making their development interesting from many aspects of extraction and subsequent processing. On the other hand, the issues of the deep sea as a habitat – still little explored in many places – and the associated protection of the environment, the extremely high pressures and the difficult accessibility of the deposits are disadvantageous. (2, 3, 4, 5)

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3  Challenges and technical solutions

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The vertical approach to deep-sea mining is a minimally invasive procedure, similar to surgery, which attempts to limit the impact at the extraction site to the absolute minimum necessary. The sediment cloud is minimized by shielding the injection point and the negative pressure in the extraction system required by the process. Conveying within a closed system also prevents the formation of particle clouds. Due to the vertical mining direction, the topology of the deposit is met quite precisely and the generation of overburden is minimized (Figure 1). (6)

The boundary conditions for the design of equipment for the conditions in the German license area are:

• pressure: 250 to 300 bar,
• temperature: 2 °C, at the surface > 20 to 30 °C,
• no natural light,
• steep slopes of up to 30°,
• very uneven soils,
• highly variable composition of the subsoil,
• high porosity and strong scattering of geomechanical properties.

Massive sulphide deposits formed by black smokers are often referred to as mounds because of their shape – mounds several hundred meters in diameter and tens to 30 m high. The smokers form vents that collapse again and again over time, forming a kind of debris cone that is subject to geological transformation processes. As a result, in contrast to layers formed by sedimentation processes, e. g., the structure and mineralogical composition of the subsurface is very undefined.

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4  Navigation system

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4.1  Positional representations in space

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Euler angles define three rotations in Euclidean space. These include the rolling motion ϕ (roll), i. e. the rotation around the x-axis, the pitch movement θ (pitch) with the rotation around the y-axis and the yaw movement ψ (yaw), a rotation around the z-axis. If these movements are carried out one after the other, the new coordinates of the rotated body in three-dimensional space can be defined by multiplying the respective rotation matrices. (7, 8)

Due to the commutative law of matrix multiplication, a fixed rotation sequence must be observed. In addition to the six possibilities, the z-y-x convention according to DIN 9300 and DIN ISO 8855 is chosen in this work (Figure 2):

If a rotation of ± 90° occurs during the second rotation step, the pitching, this leads to a gimbal lock, as the x-axis of the body shares the same axis as the z-axis of the reference system and therefore one degree of freedom is lost. The independently selected angles ψ and ϕ lead to a transformation that only has one parameter. To avoid this error, the positional representation can also be calculated using quaternions, an extension of the complex numbers. However, Euler angles are used in parallel for simpler visualization and better understanding. (9, 10, 11, 12, 13)

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4.2  Coordinate systems

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Different coordinate transformations are necessary so that the geographical coordinates can be determined with an alternative mobile measuring device, similar to the global navigation satellite system. The corresponding transformation matrix is multiplied by the known spatial coordinates. Due to the orthogonality of the matrix, a reverse transformation is possible using both the inverse and the transposed mapping matrix:

The body-fixed coordinate system (b-frame) is fixed to the object to be tracked, which means that the axes of the system are always in the same orientation relative to the body, regardless of the rotation or acceleration applied. The origin of the navigation coordinate system (n-frame) or local Cartesian coordinate system is identical to the body-fixed coordinate system. The xⁿ– and yⁿ-axes always point in an easterly or northerly direction and are parallel to the tangential plane of the simplified earth model. The zⁿ-axis is correspondingly parallel to the gravitational acceleration. The navigation coordinate system can either be oriented as local east-north-up (ENU) coordinates or local north-east-down (NED) coordinates. The present work refers to the ENU system. The inertial coordinate system (i-frame) is located at the center of the Earth model, with the coordinate axes fixed in relation to the fixed stars and disregarding the Earth’s rotation. The zⁱ-axis of the internal coordinate system corresponds to the Earth’s rotation, while the xⁱ– and yⁱ-axes lie in the equatorial plane. The origin and the vertical axis of the earth-fixed coordinate system (e-frame) are identical to the inertial coordinate system, which rotates at the angular velocity of the earth. The x^e-axis is determined by the intersection of the equatorial plane and the plane of the prime meridian. Due to the aforementioned properties of the Earth-fixed coordinate system, it is also referred to as a geographic or geocentric coordinate system (Earth-Centered, Earth-Fixed (ECEF)) (Figure 3). (14, 15, 16, 17)

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4.3  Geodetic datum

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A reference model of the earth must be defined so that the target coordinates p can be determined using the geographical coordinate system. A distinction must be made between the spherical and the ellipsoidal geodetic model. While the spherical model is spherical, the actual shape of the earth can be represented more precisely using a rotational ellipsoid. In addition to the world systems, e. g. the Geodetic Reference System 1980 or the World Geodetic System of 1984 (WGS 84), the choice of reference ellipsoid can also vary from region to region, as the geometric calculation surface differs from the existing geoid to varying degrees. In Europe, e. g., the Bessel ellipsoid serves as a suitable regional datum, while the global datum WGS 84 is used as a uniform basis for the Global Positioning System (GPS), among other things. (15)

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4.4  Calculation of Cartesian coordinates from geographical coordinates

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Similar to the rotation sequence for the Euler angles, a rotation matrix must be defined for the calculation of the coordinates in the geographical coordinate system, taking into account the longitude and latitude:

However, it should be noted that, taking into account the tangency of the navigation coordinate system, the latitude of the spherical coordinate system is not the same as that of the ellipsoidal coordinate system. Also, in the last model, the intersection point on the z-axis is no longer in the coordinate origin (Figure 4). (15, 18, 19)

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4.5  Definition of altitude

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In addition to the longitude and latitude, the total height or depth resulting from the earth radius b or the curvature radius N and the ellipsoidal height h is relevant for determining the exact position data. It is important to distinguish h from the normal height and geoid height.

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4.6  Inertial measuring unit

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4.6.1  Conceptual design and sensor selection

Various sensors are used to ensure that a location-independent measuring system can be used without restriction in real time to determine position and orientation, even without satellite reception. The sensors essentially include acceleration and angular rate sensors, which are also referred to as an inertial measurement unit (IMU). Dead reckoning is used to continuously determine the direction of movement, speed and distance traveled. While in the early days of inertial navigation the sensors were still mounted on a gimbal-mounted stabilized platform, which meant that the x^b y^b-plane was always parallel to the xⁿ yⁿ-plane respectively the z^b– and zⁿ-vectors were parallel, advanced strapdown systems now make it possible to connect the IMU firmly to the outer frame of the body. If the body to be observed is at rest and aligned horizontally to the earth’s surface, only the acceleration due to gravity of 1 g is recorded along the z^b-, respect. the zⁿ-axis. If the sensor is now tilted, a proportion of the normal gravity is also detected by x^b and y^b. As long as the absolute acceleration of 1 g is not exceeded or fallen short of, the roll- and pitch angles can be calculated with the exception of the yaw angle:

The angular rate sensor, on the other hand, measures independently of the gravitational acceleration of the earth, which means that the position angles can be determined numerically over the measurement duration t, even during an acceleration or deceleration process of the body.

To determine the exerted velocity v^b and position p^b, the recorded gravitational acceleration component g^b must be substracted not only from the z^b-axis, but also from the x^b– and y^b-axes of the recorded acceleration data, in contrast to the gimbal-mounted IMUs:

Although microelectromechanical systems (MEMS) are among the comparatively less accurate measuring devices, they are very small in size and considerably cheaper due to mass production, which is why they are used in numerous computer-based mobile devices or as safety and control systems in vehicles. Compared to mechanical models, the MEMS design dominates in acceleration sensors in terms of compactness and robustness, low energy consumption, low maintenance, low costs and easy handling. (15, 20, 21, 22, 23)

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4.6.2  Sensor model and calibration

Ideally, the three sensor axes are orthogonal to each other and measure with the same sensitivity according to the aforementioned properties. As this is not the case in practice and the inertial sensors used have a high measurement deviation due to the MEMS design, the following model function for the discrete time step k can be generally established:

b   bias

N   non-orthogonality of the axes

S   scale factor

u^b_k actual measured value

y^b_k raw data

ε^b_k measurement noise

The aim is to find out the actual measured values u^b_k. In order to define the faulty influencing variables specifically for the sensors used, a practical investigation is required in addition to the manufacturer’s specifications. However, it should be noted that each sensor must be considered individually. As mentioned above, the absolute acceleration in any stationary position is 1 g. If the measuring device is rotated within a cardanic suspension with the sensor center at the intersection of the three supported axes, the recorded point cloud can be used to determine not only the zero offset, i. e. the bias, but also the scale factor. Ideally, the point cloud corresponds to a spherical shape with a radius of 1 g. With extreme measurement inaccuracies, however, the point cloud is more like an ellipsoid. This structure can be converted into the ideal, calibrated spherical shape using a singular value decomposition. It should be noted that the gravitational acceleration of 1 g on the earth varies depending on the position and must be taken into account for the calibration, taking the selected earth model into account.

A stationary investigation is not sufficient for the angular rate sensor, as this would only record the bias and, in the case of very precise sensors, the earth’s rotation. However, if the angular rate sensor is rotated around a defined axis at a known angular velocity, the actual angular rate can be compared with the target angular rate. As the calibration unit is also subject to measurement deviations, the applied angular velocity is checked, e. g. by outputting a square-wave signal using an incremental encoder (Figure 5). (16, 17, 24, 25, 26, 27)

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4.7  Temperature compensation

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In addition to the IMU raw data, the temperature experienced during the measurement must also be recorded, as this is largely responsible for the size of the measurement deviations. In order to be able to derive a correction function accordingly, the IMU is loaded at rest over a specified temperature range, which is the maximum it can experience during its use. In addition to the temperature, the air pressure, humidity, mechanical vibration and also the supply voltage of the IMU have a negative influence on the measuring device. (23)

The Allan variance can be used to investigate the error characteristics and the behavior of the measuring device over a longer period of use under stationary conditions and thus to better assess the performance of the sensors used. The Allan variance is a measure of frequency stability and measures the square deviation of the individual measurements from the mean value. It is particularly useful for evaluating the stability and noise behavior of sensors. (14, 16, 21, 28, 29)

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4.8  Digital filters

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Due to its design with its narrow moving comb structures, the MEMS accelerometer has a particularly high measurement noise, which is still present in an attenuated form even after calibration. A low-pass filter can be used to further attenuate the noise behavior, but the response varies depending on the size of the weighting factor. The stronger the weighting, the more slowly the system reacts to changes in angle.

With the angular rate sensor, on the other hand, the error component, which is still minimized after calibration, leads to a summation of the measurement deviation due to the recursive angle function, which increases steadily over the measurement period. Although a high-pass filter forces the measurement signal back to its origin, the Euler angles cannot be maintained and slow rotations cannot be mapped.

To compensate for the disadvantages with the advantages of the other sensor, it is possible to merge the measured IMU data using sensor data fusion. The simplest option here is the complementary filter, in which the low-pass filter of the acceleration sensor is combined with the high-pass filter of the angular rate sensor. The disadvantage is that the weighting factor is still fixed and remains the same over the measurement period. This is in contrast to the Kalman filter, which is also a recursive data processing algorithm, but determines the state vector probabilistically rather than heuristically. After the initialization of the variables, a prediction of the state vector is made and, after the subsequent calculation of the Kalman gain, the estimate is corrected. (14, 16, 30, 31, 32, 33)

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4.9  Support methods

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To ensure that the remaining measurement deviation can be corrected by other means despite complex calibration, it is possible to supplement the measuring device with additional sensors.

A magnetic field sensor can be used to implement a digital compass by detecting the earth’s magnetic field, whereby a defined north direction can be output, taking into account the declination, i. e. the deviation of the geographic north pole from the magnetic north pole. The sensor can therefore cooperate with the angular rate sensor in determining the yaw angle during sensor data fusion and is also referred to as the Attitude Heading Reference System (AHRS) in conjunction with the IMU. A disadvantage, however, is the very high calibration effort, as the sensors react very sensitively to metallic elements. (14, 16)

So that the height and zⁿ-position in relation to the calibrated zero plane can be supported in addition to the dual numerically integrated acceleration data, the height and depth information can be determined via the vertically variable ambient pressure.

As the information from vertical pressure changes is not sufficient for horizontal position support, the position is calculated via triangulation using acoustic distance and direction measurements with the help of runtime-based underwater positioning systems. The lack of light and the turbidity that arises during the milling process not only has a detrimental effect on the measurement method presented, but also on optical measurement methods. Due to the very limited installation space and space ratio in the compact diaphragm wall milling machine, the installation of large-scale measuring equipment is also extremely difficult. In addition, the high ambient pressures of up to 300 bar, the changing temperature conditions with strong vibrations and high forces acting on the system cannot be neglected, which is why the focus is on compact and robust sensors that are controlled via an intelligent algorithm with precise calibration and active monitoring in real time.

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5  Applications, status and outlook

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As part of the Deep Sea Sampling (DSS) project of the Maritime Research Program of the Federal Ministry for Economic Affairs and Climate Protection (BMWK), four construction stages of the measuring device were developed and tested under stationary conditions, starting with a concept prototype. The aim of the next construction stages is to develop prototypes for pressure tests to ensure pressure stability under temperature changes as well as the technical further development and calibration of the compensation mechanisms, particularly for the not inconsiderable vibration excitations from the working system of the mining machine.

In the subsequent application, the data is to be used both for navigation of the template – a unit weighing approximately 60 t – and the movement data of the milling head for determining the direction of excavation. Precise position data is particularly important for controlling the milling head, both by manual remote control and as semi-autonomous control.

Thinking further, robust and inexpensive sensors can be used to control mining processes under water, underground or even in extraterrestrial applications. Precise positioning data of the milling head and the excavation unit, even without additional support from GPS, is essential, particularly for rapid reaction to changing conditions and exact measurement of rapidly changing ground formations.

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