Method and system for monitoring a position of an object launched from a vessel

Abstract

A method, in particular a computer-implemented method, for monitoring a position and / or displacement of an object launched, in particular submerged, from a vessel, in particular an anchor (1) lowered from said vessel, the method comprising the steps of: (c) determining an initial position xvessel,0 of the vessel, in particular by obtaining position information from a satellite navigation system, in particular GPS; (d) determining a start position xobject,start of the object, in particular from xvessel,0, in particular according to xobject,start = xvessel,0; (e) launching, in particular lowering and / or submerging the object; (f) estimating an initial position xobject,0 of the object, in particular according to xobject,0 = xobject,start.

Description

[0001]Method and system for monitoring a position of an object launched from a vessel The present invention pertains to the field of navigation. It relates to a method and system for monitoring a position of a submerged object, in particular an anchor, in accordance with the independent claims. Background of the invention Reliable anchoring is an important requirement for all kinds of water vessels, in particular rafts, boats, ships, but also floating platforms and other semi-stationary objects. If one or more anchors come loose, significant damage can result to the water vessel, other water vessels, and / or crew, passengers etc. Various methods for anchor monitoring have therefore been suggested. US patent 4,912,464 suggests an alarm system comprising a motion sensor connected to an anchor, and configured to monitor a motion signal produced by said motion sensor and raise an alarm under certain conditions, in particular when an acceleration above a threshold occurs. US patent application publication US 2003 / 0128138 A1 discloses a device that generates an alarm when a condition at an anchor or an anchor chain exceeds a set value, in particular when a jerk exceeds a predetermined measure, or when a predetermined force is exceeded. DE 10064419 A1 discloses a movement or inclination monitoring device has two or more base bodies, such as an anchor and its chain, that are directly or indirect connected, and two or more measurement elements that are used for continuous measurement of the acceleration of one or more base bodies, measurement of angles α of the base body axes relative to the gravitational force vector, a rotation β around a body axis, or a rate of rotation relative to α and / or β. The measurement elements are linked by cable or in a wireless manner. If a variation in acceleration, angle, rotation angle, or rotational velocity exceeds a predetermined threshold, an alarm signal may be displayed. DE 3810084 A1 describes an alarm device which indicates the breaking loose or slippage of an anchor, said alarm having a position encoder (displacement sensor) which is connected to the anchor and rests with a wheel on the anchor (holding) ground and transmits the breaking away or slippage of the anchor to a signaling device present in the water craft by means of a pulse generator and a transmission device, such as a cable or in a wireless fashion, e.g. by ultrasound. However, the quantities measured in the state of the art do not correlate optimally with a displacement of an anchor, und thus, in particular, do not correlate optimally with a reliability of the anchoring. In particular, anchoring may remain reliable despite the fact that very high forces or jerks occur; in particular, anchor may remain at least essentially stationary under such conditions. Under such conditions, state of the art devices may trigger false alarms. On the other hand, if an anchor has never made firm contact with ground, both boat and anchor may slowly drift, and the anchor may thus be significantly displaced, without large forces or jerks occurring on the anchor or anchor chain, or without wheels or other rotatable elements attached to the anchor being rotated. Such situations may thus go undetected with the methods and devices according to the state of the art as described above. EP 2765074 B1 and EP 3511237 describe improved methods and systems for determining displacements of an anchor based on measurements of accelerations and velocities, respectively, of the anchor, and subsequently integrating the measured values, wherein inaccuracies are reduced by measuring at least a further physical quantity associated with the anchoring, and taking into account information thus obtained when carrying out the integration. Nevertheless, it would be desirable to have alternative approaches at hand which may allow to reliably determine and / or monitor positions and / or displacements of an anchor submerged from a water vessel, or more generally, an object launched from a vessel or similar kind of platform. Such approaches could, in particular in combination with the methods and systems described in EP 2765074 B1 and / or EP 3511237, be used to provide redundant methods and / or systems, with the additional benefit of allowing for a verification of the results from each method / system by comparing the results. It would also be desirable to have an approach at hand which allows to monitor a position and / or displacement of an object other than an anchor, launched from an arbitrary floating platform or vessel, which may in particular also be an aerial vessel. Summary of the invention The above objective and other objectives are achieved by a method and system for monitoring a position of an object launched from a vessel. Preferred embodiments and / or variations of the invention are presented in dependent claims. A method for monitoring a position of an object launched from a vessel in accordance with the invention as hereinafter claimed may comprise the features of claim 1 below. The dependent patent claims specify detail related to preferred embodiments. While the invention was made with an anchor lowered from a boat or a ship and / or submerged in water in mind, the method is more generally applicable to vessels and semi-stationary platforms floating on water or airborne, and to all kinds of objects launched from such vessels or platforms. A semi-stationary platform may, e.g., be a (drilling) rig, a weather balloon, an orbiting satellite, etc. Exemplary objects may include fishing nets, submersibles, (cargo) parachutes, balloons, etc. In what follows, only the term vessel will be used for better readability, and is supposed to also include semi-stationary platforms. The aforementioned and further objectives, advantages and features of the invention will be detailed in the description of preferred embodiments below in combination with the drawings. Brief description of the drawing The invention is best understood from the following detailed description when read in connection with the accompanying drawing. It is emphasized that, according to common practice, the various features of the drawing are not to scale. On the contrary, the dimensions of the various features are arbitrarily expanded or reduced for clarity. The drawing consists of the following figure: Fig. 1 shows a schematic of an exemplary embodiment of a system for determining a displacement of an anchor in accordance with the present invention. Detailed description of the invention The present invention may, in particular, be put into practice in the form of one or more of the following numbered embodiments: 1. A method, in particular a computer-implemented method, for monitoring a position and / or displacement of an object launched, in particular submerged, from a vessel, in particular an anchor (1) lowered from said vessel, the method comprising the steps of: (a) determining an initial position x of the vessel, in particular by obtaining position information from a satellite navigation system, in particular GPS and / or GLONASS, or a radio navigation system; (b) determining a start position of the object, in particular from x , in particular according to in particular prior to launching, in particular lowering and / or submerging, the object; (c) launching, in particular lowering and / or submerging, the object; or waiting for the object to be launched, in particular to be lowered and / or submerged;(d)estimating an initial position x of the object, in particular according to in particular after launching, in particular lowering and / or submerging, the object; (e) generating an initial set P comprising a plurality of N coordinates {1, …, N}, wherein i. each coordinate p is indicative of a potential and / or hypothetical initial position of the object, and ii. a central tendency, in particular an expected value, a median, or a (weighted) average of the plurality of N coordinates equals the estimated initial position x (f) for each of a plurality of subsequent instants t ≧ 1 ℕ and / or 1 ≦ time: i. determining a subsequent position x of the vessel, in particular by obtaining position information from the satellite navigation system or radio navigation system; ii.determining a distance d between the object and the vessel, in particular by obtaining distance information from a sonar, a laser distance meter, and / or a length meter; iii. determining a manifold M of possible positions of the object based on x and d; iv. determining for at least some, in particular all, of the plurality of N coordinates p from set P a distance e from the manifold M; v. deleting a subset P comprising a number of for which the distance e is relatively large, in particular larger than a threshold from set P ; wherein, in particular, a set of coordinates to be maintained is obtained; vi. generating a set P comprising a number in particular with replacement coordinates wherein each replacement coordinate is indicative of a potential and / or hypothetical current position x of the object, in particular to obtain a (replenished / updated) set of coordinates vii. determining an estimated position x of the object from coordinates in particular from a central tendency of coordinates from P preferably P and / or from coordinates The object may, in particular, be a tracking unit or module that may be integrated with and / or attached to a second object and / or entity, a position or displacement of which is the primary monitoring target; and wherein, for practical purposes, the positions and / or displacements of the object and the second object and / or entity may be considered identical. The second entity may in particular be a person, e.g. a scuba diver or a parachutist, or an animal carrying or wearing the tracking unit or module, e.g. on a belt attached to the person’s or animal’s body. Such a tracking unit or module, may, in particular, be tightly connected to an or the anchor in order to ensure that they both will remain in close proximity, preferably in physical contact to one another to allow for exact determination of the position and / or displacement. Preferably, the tracking unit is rigidly attached to or fixed to, in particular integrated with, the anchor, so that it always maintains an identical relative position to the anchor. Alternatively, it may be rigidly attached to or fixed to, in particular integrated with, a shackle or chain element provided for linking, preferably releasably linking, the anchor with an anchor rode, thus constituting a connecting link. The method starts with a determination of an initial position of the vessel, which may be done by any method known to a person skilled in the relevant art, in particular by one or more of the various means of geopositioning as described and / or referred in Wikipedia article https: / / en.wikipedia.org / w / index.php?title=Geopositioning&oldid=116637 1797. The initial position of the vessel may, in particular, be obtained from a satellite navigation system, in particular a GPS and / or GLONASS system, installed and / or located at a first location on the vessel. Alternatively or in addition, radio navigation may exemplary be employed, in particular radio navigation methods that may be fully automated, like e.g. VHF omnidirectional range (VOR). Once the initial position x of the vessel is determined, a start position of the object is determined. x may be used as start position, in particular if dimensions of the vessel are smaller than an accuracy and / or spatial resolution of the determination of the initial position of the vessel. If, on the other hand, dimensions of the vessel are larger, in particular significantly larger, than the accuracy and / or spatial resolution of the determination of the initial position of the vessel, a distance between the first location and second location at which the object is located when the method starts may be taken into account, as well as an orientation of the vessel as, e.g., obtained from a compass. If the object is an anchor, the second location may be defined by a location of a fairlead or a hawsehole through which a mooring hawser to which the anchor is attached may be running. Once the initial position and / or start position is determined, the object is launched from the vessel. In particular, in case of a water vessel, the object may be submerged and / or lowered into water surrounding the vessel, in particular into the ocean. After being launched, the object may remain connected to the vessel, in particular through a physical connection like, e.g. provided by a rope, chain or hawse which, in particular, allows to retrieve the object. Alternatively or in addition, the object may remain connected through a communication link, which may allow signals and / or data to be sent and / or exchanged between the object and the vessel. The communication link may comprise a second physical connection like a wire or optical fibre, but may also be wireless. The object may, in particular, be launched by triggering and / or controlling means for launching the object, in particular an object launch unit configured to launch the object when triggered. Where the vessel is a water vessel and the object an anchor, the object launch unit may, in particular, be an anchor windlass which may be triggered and / or controlled to release and / or lower the anchor. When the method is implemented on a computer, launching of the object may be triggered by a triggering signal generated by the computer and / or sent to the triggering and / or controlling means by the computer. Alternatively, the computer may be configured to wait and / or pause until the has been launched; wherein the object may be launched manually or based on an external event or circumstance, and wherein the computer may receive a signal and / or an input indicative of the object having been launched, which may cause the computer to continue with the execution of the method. An (estimated) initial position x of the object may subsequently be estimated, in particular according to x = x If the object is an anchor, an estimation of where, i.e. at what position, the anchor reaches ground after having been lowered at x may be used as initial position. In obtaining such an estimation, known aquatic circumstances, in particular related to underwater currents and / or a local water or seafloor depth, may be taken into account, in particular in combination with an amount of time and / or mooring length required until the anchor reaches ground. To account for the fact that an exact initial position x^ of the object is not known, and may not be determined, at least not with reasonable effort, for fundamental reasons (e.g. due the fact that light, and electromagnetic waves in general, cannot penetrate through water beyond a certain depth; and / or that even highly accurate geopositioning methods have limited accuracy and / or spatial resolution), a plurality of N coordinates p with N ≧ i ∈ ℕ is created, wherein each of the coordinates may correspond to or reflect a potential and / or hypothetical initial position of the object, and / or may at least approximately equal the exact initial position x^ . Said plurality of coordinates, which may be considered to establish an (initial) set P of coordinates, may be generated using a random number generation process as exemplary described in Wikipedia article https: / / en.wikipedia.org / w / index.php?title=Random_number_generation&ol did=1171056194. They may, in particular, be obtained from or by means of a hardware random number generator, wherein N may typically be in a range between a few thousand and a few ten thousand. As will be understood a person skilled in the relevant art(s), i may be thought of as an (integer) index variable (sometimes simply referred to as an (integer) index for brevity), which may, inter alia, allow to distinguish each one of the plurality of coordinates p from any other one (in particular from p with i n, wherein n may be thought of as another index); wherein i (and / or n) may take on and / or assume different values, in particular between 1 and N, or, put in a more mathematical manner, i ∈ {1, …, N} (and / or n ∈ {1, …, N}), wherein N may in particular be a (positive) integer number, in particular with N ∈ ℕ, N ≧ 1000 and / or N ≧ 10000. Said plurality of coordinates may be generated such that a central tendency as exemplary described in https: / / en.wikipedia.org / w / index.php?title=Central_tendency&oldid=1169 314262 at least approximately equals the initial position x This may require post-processing and / or reshaping of a distribution of random numbers obtained in the random number generation process as known as such to a person skilled in the art of statistics. Similarly, said plurality of coordinates may be generated such that a statistical dispersion as exemplary described in Wikipedia article https: / / en.wikipedia.org / w / index.php?title=Statistical_dispersion&oldi d=1153937394 reflects an uncertainty of the initial position x^ ; wherein, in particular, a measure of the statistical dispersion as e.g. a standard deviation may equal or be proportional to a(n estimated) confidence interval for the initial position x^ , as exemplary described in Wikipedia article https: / / en.wikipedia.org / w / index.php?title=Confidence_interval&oldid=1 166902947, https: / / en.wikipedia.org / w / index.php?title=Confidence_interval&oldid=1 190931423, and / or https: / / en.wikipedia.org / w / index.php?title=Statistical_dispersion&oldi d=1153937394. Once the initial positions of the vessel and the object have been determined and the plurality of coordinates generated, an iterative and / or repetitive (second) part of the method commences, in which steps 1.(f)i.- vii. are repeated for each of a plurality of subsequent instants, in particular points, t ≧ 1 ∈ ℕ (or, put in a different way, and / or 1 ≦ t ∈ ℕ) in time. Therein, each subsequent position x of the vessel may be determined for each (numbered) instant t in time in the same way that the initial position x of the vessel was determined, in particular using the same satellite navigation system. Further, for each (numbered) instant t in time, the distance d between the object and the vessel may be determined, in particular, by measuring a time required for a signal, in particular an acoustic signal, to travel between the vessel and the object, and calculating the corresponding distance using a (known) speed the signal travels with. This may, e.g., be done by means of a sonar, which may comprise a mobile unit provided on or integrated with the object, and a main unit, which may be provided at or on the vessel – or vice versa. The mobile unit may, in particular, comprise a transmitter configured to emit an acoustic signal, in particular when triggered via the communication link mentioned further above. The main unit, on the other hand, may, in particular, comprise a receiver configured to receive an acoustic signal emitted by a remote transmitter. Transmitter and / or receiver may be part of a transceiver, which may both emit and receive signals. In a similar manner, laser distance measuring may be applied, in particular using a laser distance meter, said laser distance meter in particular configured to emit light in a visible wavelength range, for which absorption in (liquid) water is relatively weak (as compared to other wavelengths. Alternatively or in addition, the distance d may be determined by measuring a length of a physical link between the object and the vessel, in particular a wire, thread or string connected between the object and the vessel, in particular by means of a length meter, which may be configured to measure a length of unwound wire, thread or string, e.g. based on a count of revolutions of a coil or wheel. The physical link may in particular be the communication link as described further above. If the object is an anchor and the vessel a water vessel, the distance d may be determined based on an estimation involving a (used) length of the rope, chain or hawse as described above, together with information regarding a depth at which the anchor rests, as may e.g. be obtained by means of a pressure sensor attached and / or connected to the anchor, and knowledge of the shape the rope, chain or hawse may assume under gravity when attached to the vessel an one and and to the anchor at the other end. Along similar lines as laid down above for i, t may be thought of as an index (variable), in particular an integer index (variable) which may, inter alia, allow to distinguish each one of the plurality of instants, in particular points in time, t from any other one; wherein t (and / or n) may take on and / or assume different values, in particular with t ≧ 1, an / or in particular with t ∈ ℕ. As the method may, at least theoretically, be executed over an unlimited period of time, there is no need to specify an upper limit for t. In a real world situation, t may have reached a finite (integer) value tmaxwhen (execution of) the method is terminated and / or stopped, so thattmax≧ t will hold for all values t may take on and / or assume. tmax≧ 1000 and / or tmax≧ 100000 may hold. During the iterative and / or repetitive (second) part of the method, t may be incremented, in particular by 1, with each repetition of steps 1.(f)i.- vii.; in particular from a starting value of 1. Once known, the distance d together with the current (subsequent) position x for the same instant t of time defines manifold M of possible positions of the object, wherein the manifold may in particular be a sphere. For an object submerged in water from a water vessel, and, in particular, presumably resting on a ground or seafloor extending below the vessel, a shape of the manifold may correspond to a spherical zone, as defined by a virtual sphere centered at x and having a radius equal to d with spherical caps cut away at its top and bottom by the water and ground / seafloor surfaces, respectively – at least when 2d is larger than a local water depth underneath the vessel. For at least some, and in particular for all, of the current coordinates, i.e. the plurality of N coordinates p making up the set P as established prior to the determination of (subsequent) position x and distance d for instant t, a distance e from the manifold M may be determined, wherein the distance e may, in particular, be defined as the minimum of all the distances between p and an arbitrary point on the manifold M, i.e. e = ^ m ∈i Mn ^ ^ ^ p^^^,^− p ^ ^. Preferably, this may be done for all coordinates p from set P . When this step is carried out for the first time, i.e. when t=1, distance e are determined for at least some, and in particular for all, of the plurality of N coordinates p making up the set P as generated in step 1.(e). In the determination of the manifold M, and / or the a distance e , it may again be assumed that the main unit or mobile unit – whichever of the two is provided at or on the vessel – is located at x . However, if, in particular, dimensions of the vessel are larger, in particular significantly larger, than the accuracy and / or spatial resolution of the determination of d, a distance between x and a third location at which the main or mobile unit is located may be taken into account, as well as the orientation of the vessel as, e.g., again obtained from a compass. Once (all) the distances e have been determined, some coordinates, in particular coordinates p with j ∈D ⊂{1, …,N } corresponding to relatively larger distances e may be deleted from set P , whereas other coordinates, in particular coordinates p with k ∈{1, …,N }\D corresponding to relatively smaller distances e may be maintained. The deleted coordinates may thus constitute a (first) subset P of P with | P | = N < N ; the maintained coordinates a (second, disjunct) subset P = P \ P . In this manner, coordinates from set P that may be considered to relatively less likely correspond to or reflect a (current) position of the object at instant t, in particular a (current) exact position x^ , are deleted; whereas coordinates that may be considered to relatively more likely correspond to or reflect a (current) position of the object at instant t, in particular a (current) exact position x^ , are maintained. In embodiments, a dynamic threshold S or a fixed threshold S (with ∀ t : S = S) for e may be applied in determining which coordinates are to be deleted, and which ones to be maintained. A dynamic threshold may, in particular, be determined in dependence on d and / or x - x , in particular | x - x |. Alternatively, N may be (pre-)determined for each or all (according to ∀ t :N = N ), and N coordinates corresponding to the largest distances be deleted. Subsequently, set P comprising a number | P | = N , of replacement coordinates p may be created, wherein N may in particular be chosen according to N = but may also be larger or smaller. The set of replacement coordinates together with the set of coordinates that were maintained in step 1.(e).v constitute and / or may be aggregated to form an an updated and / or replenished set P = N coordinates, which may be regarded as current coordinates for the next iteration or repetition of steps 1.(f)i.- vii. at instant t+1. Finally, an estimated and / or expected position the object at instant t may be obtained by determining a central tendency of coordinates p from P preferably of (all) coordinates p with p and / or from (all) coordinates The central tendency may be an average, in particular a weigthed average, wherein coordinatesphaving relatively smaller distances e from the manifold M are given higher weights than coordinates having relatively larger differences, and wherein, in particular, l ≠ m with l,m ∈{1, …,N }, preferably with l,m ∈{1, …,N }\D. 2. The method according to embodiment 1, further comprising, for each of the plurality of subsequent instants t ≧ 1 ∈ ℕ and / or 1 ≦ t ∈ ℕ in time, the step of: (a) determining a distance d from the position x of the vessel for at least some, in particular each of the plurality of N coordinates p In addition to the distances e , a distance d from the position x of the vessel at instant t may be determined for at least some of the coordinates, which distance may inter alia be considered indicative of whether coordinate is located within a space delimited and / or enclosed by the manifold, or outside such space, as will be explained in more detail below. 3. The method according to embodiment 2, further comprising, for each of the plurality of subsequent instants t ≧ 1 ∈ ℕ and / or 1 ≦ t ∈ ℕ in time, the steps of: (a) comparing each of the distances d with d, in particular (b)determining for each of the distances d whether it is larger than d or at least equal to d. In particular, when d is larger than d, coordinate may be considered to be located outside the space delimited and / or enclosed by the manifold. 4. The method according to embodiment 2 or 3, further comprising, for each of the plurality of subsequent instants t ≧ 1 ∈ ℕ in time, the step of determining: (a) for each of the distances d a difference δ with δ = d - d, and, in particular (b) a coefficient c = δ / |δ |. To allow for fast and simple discrimination of coordinates located inside and outside of the space delimited and / or enclosed by the manifold, respectively, coefficients may be introduced, which equal +1 for coordinates located outside, and -1 for coordinates inside the space delimited and / or enclosed by the manifold, and are thus indicative of whether p is inside the sphere / circle or outside The method according to one of the preceding embodiments, wherein the step of generating replacement coordinates comprises copying coordinates, in particular in particular with To obtain at least some, in particular all, of the replacement coordinates, selected ones of the coordinates that were maintained in step 1.(e)v. may be copied in a copy operation. The copy operation thus yields a plurality of pairs of identical coordinates, wherein the set P of replacement coordinates will comprise exactly one of the coordinates of each pair (with the set maintained coordinates comprising the other one). While, generally, all of the replacement coordinates may be obtained by copying, generation of at least some of the replacement coordinates following a different approach is also conceivable, e.g. using a random number generation process in a similar manner as described above with respect to the generation of the initial set of coordinates. 6. The method according to embodiment 5, further comprising the step of modifying, in particular translating, at least some, in particular all, of the replacement coordinates, in particular those replacement coordinates that were obtained by copying coordinates from Replacement coordinates, in particular (all) replacement coordinates obtained by means of the copy operation, may subsequently be modified, inter alia to avoid having duplicate coordinates in the updated and / or replenished set P = P described above. More specifically, (only) one of the coordinates of each pair may be modified. In a practical implementation of the method, this may, for each or all of the coordinates copied in the copy operation, either be done by modifying a source coordinate of said copy operation, or a target coordinate thereof; and may in particular be done before the maintained coordinates and the replacement coordinates are aggregated to form the updated and / or replenished set P = 7. The method according to embodiment 5 or 6, wherein the coordinates to be copied are selected based on their respective distances e from the manifold M, wherein, in particular, those coordinates corresponding to the N smallest distances e are chosen. In this manner, those coordinates, in particular in particular N coordinates, in particular with N = N , from set P that may be considered to most likely correspond to or reflect a (current) position of the object at instant t are copied. 8. The method according to one of embodiments 5 to 7, wherein at least some, in particular all, of the replacement coordinates are shifted by a random distance in a random direction, in particular by a vector v with |v | ≪d, wherein distance and / or direction are, in particular, governed by artificial noise, in particular when at least one of the distances e is smaller than d and / or one of the c is negative. Replacement coordinates, in particular (all) replacement coordinates obtained by means of the copy operation, may, in particular, be modified by adding (artificial) noise, in particular Gaussian noise. This may be achieved by adding a vector v to the respective coordinates, where j ∈C ⊂{1, …,N } with |v |, and, in general, v ≠ v for s with r, s ∈C, and wherein C identifies the (sub-)set of replacement coordinates that are modified at instant t. This may, in particular, be done when at least some, in particular at least 10% or at least 20%, of the distances d are smaller than d and / or at least some, in particular at least 10% or at least 20%, of the c are negative. 9. The method according to one of embodiments 5 to 8 wherein at least some, in particular all, of the replacement coordinates are shifted at least approximately by x - x , in particular when all or almost all of the c are positive and / or all or almost all the distances e are larger than d. Replacement coordinates, in particular (all) replacement coordinates obtained by means of the copy operation, may, in particular, be shifted by a vector at least approximately equaling a displacement x - x of the vessel between previous and current instances of time t and t-1, respectively. If the vessel is a ship, this may, in particular, reflect the fact that it is dragging its anchor (representing the object). This may, in particular, be done when at least a majority, in particular at least 75% or at least 90%, of the distances d are larger than d and / or at least 75%, in particular at least 90%, of the c are positive. Shifting as just described may be done alternatively or in addition to adding noise as described further above. 10. The method according to one of embodiments 5 to 8 wherein at least some, in particular all, of the replacement coordinates are shifted at least approximately by (x - p ) / |(x - p ) | * e , in particular when all or almost all of thecand / or the distances e are larger than d. Replacement coordinates, in particular (all) replacement coordinates obtained by means of the copy operation, may, in particular, be shifted in the direction of the x at instant t until they are at least approximately located on the manifold M of the vessel between previous and current instances of time t and t-1, respectively. This may, in particular, be done when at least a majority, in particular at least 75% or at least 90%, of the distances d are larger than d and / or at least 75%, in particular at least 90%, of the c are positive, wherein the shift may in particular exclusively be applied to coordinates p for which d > d. Again, shifting as just described may be done alternatively or in addition to adding noise as described further above. 11. The method of any preceding embodiment, wherein all coordinates, positions, vectors and / or distances are defined and / or determined with respect to a two-dimensional coordinate system, in particular a Cartesian coordinate system the axes of which are at least essentially parallel to a water surface at x . The vessel and the object to which the method embodiments as described above relates may normally move in three-dimensional space, and the description of the method embodiments was formulated with three- dimensional space, in particular three-dimensional positions, vectors, and distances in mind. A practical implementation of the method may, however, be carried out in two-dimensional space, in particular based on a projection, in particular a vertical projection, of positions, coordinates, vectors and / or distances etc. onto an (imaginary) plane parallel to a surface of water on which the vessel is located and / or may move, which surface of water may in particular be the sea surface. Notably, in such a two-dimensional implementation, the manifold M for each instant t may reduce to a circle, in particular a circle around x . 12. The method of embodiment 11, wherein (a) a true distance ^^^between the object and the vessel, said true distance in particular corresponding to a distance between the object and the vessel in three-dimensional space, is determined, in particular obtained through a travel time measurement carried out with a sonar; (b) a depth s of the object is determined, in particular by obtaining depth information from a depth gauge provided on and / or integrated with the object; and (c) d is determined according . To obtain the correct d for a two-dimensional implementation, in particular as described above for a water vessel located and / or moving on a water surface, with the object, in particular being an anchor, lowered into and / or submerged in water, true distance ^^^, corresponding in particular to a distance between the object and the vessel, in three-dimensional space, may be obtained in a first step in a manner as described above, in particular using a sonar. Subsequently, depth s of the object at instant t may be determined, in particular based on depth information obtaining by means of a depth gauge provided on and / or integrated with the object, which depth gauge may, in particular, comprise a pressure sensor. Such pressure sensor may allow to determine the depth s based on known relations between depth and pressure in and / or under water. The correct value corresponding to ^^^for d to be used in the two- dimensional implementation may then be obtained using Pythagoras’ theorem as described above. 13. The method of embodiment 9 or 10, wherein all coordinates and / or positions are specified by a longitude and a latitude. Using coordinates and / or positions specified by longitude and latitude may allow to work directly with the coordinates provided by the satellite navigation system, and / or within the coordinate system established by said coordinates. 14. A tracking system for monitoring a position and / or displacement of an object launched, in particular submerged, from a vessel, in particular an anchor (1) lowered from said vessel, the system comprising: (a) a central unit configured to remain, in particular be installed, on the vessel; (b) a tracking unit configured to be attached to, integrated with and / or carried or worn by the object; (c) the central unit and the tracking unit configured to cooperate to determine, in particular repeatedly determine, a distance d between the central unit and the tracking unit, in particular by means of a sonar, laser distance meter or length meter comprised by the system, in particular by the central unit and / or the tracking unit; (d) means adapted to execute the steps of any one of the preceding method embodiments. A system for carrying out the method as described in the embodiments further above may, in particular, comprise a tracking unit as described further above, which may be the object whose position and / or displacement is to be monitored, and / or which may be attached to, integrated with and / or carried or worn by a second object and / or entity, thus allowing for monitoring a position and / or displacement of said second object and / or entity. The tracking unit may, in particular, be configured to be attached to and / or tightly connected to an anchor, inter alia as described further above. The system may further comprise a central unit which may be configured to remain on the vessel while the method is carried out. The central unit may further comprise data processing means adapted to execute the steps of any one of the method embodiments as laid out further above. The system may comprise a sonar, laser distance meter or length meter for determining the distance d between the central unit and the tracking unit. In particular, the central unit may comprise the main unit of the sonar as described further above; and / or the tracking unit may comprise the mobile unit of the sonar as described further above. The system may further comprise communication means which allow data to be exchanged and / or signals, in particular communication signals, to be send back and / or forth between the central unit and the tracking unit, which communication means may comprise a first communication unit integrated with the central unit and a second communication unit integrated with the tracking unit. The communication means may comprise a communication link which may in turn comprise a wire, optical fibre etc. (physically) connecting the first and second communication units. Alternatively or in addition, the communication means may comprise means that allow the first and second communication units to exchange data and / or signals wirelessly. Such signals may, in particular, be used to trigger an emission of an acoustic signal by the mobile unit. An amount of time elapsed until the acoustic signal is received and / or detected by the main unit may the be used to determine, in particular compute, a distance between the mobile and main units of the sonar. 15. The tracking system according to the preceding embodiment, further comprising a satellite navigation system and / or radio navigation system, said satellite and / or radio navigation system in particular integrated with the central unit. 16. The tracking system according to the preceding embodiment, further comprising means for launching the object, and / or configured to be connected to means for launching the object; and / or means for receiving an indication, in particular a signal or an input indicating that the object has been launched. The system may further be connectable or connected to means for launching the object, in particular to an object launch unit. Alternatively, it may comprise such means. The central unit may not necessarily be constituted by a single and / or discrete physical unit, but may be a distributed and / or logical unit comprising a plurality of sub-units, which sub-units may be located at different locations on the vessel, and may in turn be part of and / or integrated with other systems comprised by and / or provided on the vessel. 17. A data processing apparatus, in particular a computer, comprising means for carrying out the method of any one of the preceding method embodiments. 18. A computer program product comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method of any one of the preceding method embodiments. 19. A computer program comprising instructions to cause the tracking system of any of numbered embodiments 14 to 16 to execute the steps of any one of the preceding method embodiments. 20. A computer-readable medium having stored thereon the computer program of numbered embodiment 19. Fig. 1 shows a schematic of an exemplary application of a system for monitoring a position and / or displacement of an object in form of an anchor 1 in accordance with the present invention. As an exemplary (water) vessel, a yacht 2 is anchored by means of anchor 1 resting on a seafloor at a current position. The anchor 1 is attached to an anchor rode 3. Tracking unit 11 is also attached to the anchor 1. The anchor rode is further attached to yacht 2 at an end remote from the anchor 1. Central unit 20 is installed on yacht 2 and comprises main unit 21 of a sonar, a first communication unit as detailed above, and a display unit 22 configured to display information related to the monitoring of the position and / or displacement of the anchor. Tracking unit 11 comprises a mobile unit of a sonar and a second communication unit as detailed above. A touchdown location at which the anchor first touched the seafloor upon lowering is indicated by reference symbol 1'. A displacement between anchor 1 at its actual position and the touchdown location of 3.5m as determined by the method in accordance with the invention may be displayed by display unit 22. This description and any accompanying drawings that illustrate aspects and embodiments of the present invention should not be taken as limiting the claims defining the protected invention. In other words, while the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive. Various mechanical, compositional, structural, electrical, and operational changes may be made without departing from the spirit and scope of this description and the claims. In some instances, well-known circuits, structures and techniques have not been shown in detail in order not to obscure the invention. Thus, it will be understood that changes and modifications may be made by those of ordinary skill within the scope and spirit of the following claims. In particular, the present invention covers further embodiments with any combination of features from different and / or individual embodiments as described above and below. Embodiments in accordance with the invention may, in particular, include further and / or additional features, elements, aspects, etc. not shown in the drawings or described above. The disclosure also covers all further features shown in any Figure, individually, although they may not have been described in the afore or following description. Also, individual alternatives of the embodiments described in any Figure and the description and individual alternatives of features thereof can be disclaimed from the subject matter of the invention or from disclosed subject matter. The disclosure comprises subject matter consisting of the features defined in the claims or the exemplary embodiments as well as subject matter comprising said features. The present disclosure also includes embodiments with any combination of features which are mentioned or shown above and / or below, in various embodiments or variants. It also includes individual features as shown in the Figures, even if they are shown there in connection with other features and / or are not mentioned above or below. The disclosure comprises embodiments which exclusively comprise the features described in the claims or the exemplary embodiments, as well as those which comprise additional other features. The steps of any method disclosed above or claimed below may preferably be carried out according to the order in which they are presented, but may also be carried out in a different order. Furthermore, in the claims the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality. A single unit or step may fulfil the functions of several features recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. The terms "essentially", “substantially”, "about", "approximately" and the like in connection with an attribute or a value particularly also define exactly the attribute or exactly the value, respectively. The term "about" in the context of a given numerate value or range refers to a value or range that is, e.g., within 20%, within 10%, within 5%, or within 2% of the given value or range. Components described as coupled or connected may be electrically or mechanically directly coupled, or they may be indirectly coupled via one or more intermediate components. Any reference signs in the claims should not be construed as limiting the scope. Unless stated otherwise, it shall be assumed throughout this entire document that a statement a ≈ b may imply that |a-b| / (|a|+|b|) < 0.2, preferably |a-b| / (|a|+|b|) < 0.05, wherein a and b may represent arbitrary quantities, parameters and / or variables as described and / or defined anywhere in this document, or as otherwise known to a person skilled in the art. Further, a statement that a is at least approximately equal or at least approximately identical to b may imply that a ≈ b, and not exclude that a = b. Further, unless stated otherwise, throughout this entire document, a statement a ≫ b may imply that a > 5b, preferably a > 10b; and statement a ≪ b may imply that 5a < b, preferably 10a < b. A statement that a is significantly larger than b may imply that a ≫ b. A statement that a is significantly smaller than b may imply that a ≪ b. ℕ may designate the set of natural numbers, which is generally understood to comprise all positive integer numbers (i.e. with 0 excluded). Letters typeset in bold face may designate variables representing vector values, whereas variables representing scalar values are generally represented by letters typeset using normal (as opposed to bold face) and / or plain fonts. Along similar lines as laid down for i further above, m, j, r and / or s may be thought of as (integer) index variables (sometimes also referred to as (integer) indices for brevity) which may, inter alia, allow to clearly and / or uniquely identify each (individual) one of a plurality of quantities, in particular coordinates, and / or to distinguish each one of such a respective plurality of quantities from any other one. As will be understood a person skilled in the relevant art(s), in the common notation for such a plurality of quantities, the index variable, in particular the letter representing the index variable, will be written as a subscript after and / or to the right of the symbol representing the quantity. As will likewise be understood a person skilled in the relevant art(s), in the common notation for such a plurality of quantities, when more than one index is used to identify each (individual) one of the plurality of quantities, the various indices or index variables may be separated by commas. Embodiments of the invention may involve one or more electronic or computing devices, and / or involve the use of such devices. Said devices typically include a processor, processing device, or controller, such as a general purpose central processing unit (CPU), a graphics processing unit (GPU), a microcontroller, a reduced instruction set computer (RISC) processor, an application specific integrated circuit (ASIC), a programmable logic circuit (PLC), a field programmable gate array (FPGA), a digital signal processing (DSP) device, and / or any other circuit or processing device capable of executing the functions described herein. In particular, the battery management system, the control system may, and / or the control system settings update unit may be partially or fully implemented on such electronic or computing devices, individually or jointly. The methods described herein may be partially or fully implemented as or in the form of software, which may in turn be encoded as executable instructions embodied in a non-transitory computer readable medium, including, without limitation, a storage device and / or a memory device. Such instructions, when executed by a processing device, cause the processing device to perform at least a portion of the methods described herein, preferably in real-time. The above examples are exemplary only, and thus are not intended to limit in any way the definition and / or meaning of the term processor and processing device. As used herein, the terms “processor”, “computer” and related terms, e.g., “data processing apparatus”, “processing device,” “computing device,” and “controller” are not limited to just those integrated circuits referred to in the art as a computer, but broadly refers to a microcontroller, a microcomputer, a programmable logic controller (PLC), and application specific integrated circuit, and other programmable circuits, and these terms are used interchangeably herein. In the embodiments described herein, memory may include, but it not limited to, a computer-readable medium, such as a random access memory (RAM), a computer-readable non-volatile medium, such as a flash memory. Alternatively, a floppy disk, a compact disc – read only memory (CD- ROM), a magneto-optical disk (MOD), and / or a digital versatile disc (DVD) may also be used. Also, in the embodiments described herein, additional input channels may be, but are not limited to, computer peripherals associated with an operator interface such as a mouse and a keyboard. Alternatively, other computer peripherals may also be used that may include, for example, but not be limited to, a scanner. Furthermore, in the exemplary embodiment, additional output channels may include, but not be limited to, an operator interface monitor. Further, as used herein, the terms “software” and “firmware” are interchangeable, and include any computer program storage in memory for execution by personal computers, workstations, clients, and servers. As used herein, the term “non-transitory computer-readable media” is intended to be representative of any tangible computer-based device implemented in any method of technology for short-term and long-term storage of information, such as, computer-readable instructions, data structures, program modules and sub-modules, or other data in any device. Therefore, the methods described herein may be encoded as executable instructions embodied in a tangible, non-transitory, computer-readable medium, including, without limitation, a storage device and / or a memory device. Such instructions, when executed by a processor, cause the processor to perform at least a portion of the methods described herein. Moreover, as used herein, the term “non-transitory computer-readable media” includes all tangible, computer-readable media, including, without limitation, non-transitory computer storage devices, including without limitation, volatile and non-volatile media, and removable and non-removable media such as firmware, physical and virtual storage, CD- ROMS, DVDs, and any other digital source such as a network or the Internet, as well as yet to be developed digital means, with the sole exception being transitory, propagating signal. The steps of any method disclosed above or claimed below may preferably be carried out according to the order in which they are presented, but may also be carried out in a different order. Features, properties, etc. mentioned in the description but placed in parentheses may, but do not necessarily have to, be present and / or required, and are thus to be regarded as optional in principle. Such features, properties, etc. may serve the better understanding of the invention by hiding implicit, but non-essential aspects of the invention. Such features, properties, etc. may, in articular, be preferred and / or advantageous. The present disclosure also includes embodiments with any combination of features which are mentioned or shown above and / or below, in various, individual embodiments, variants and / or claims. It also includes individual features as shown in the Figures, even if they are shown there in connection with other features and / or are not mentioned above or below. The disclosure comprises embodiments which exclusively comprise the features described in the claims or the exemplary embodiments, as well as those which comprise additional other features. The steps of any method disclosed above or claimed below may preferably be carried out according the order in which they are presented, but may also be carried out in a different order. All documents mentioned and / or referred to in this patent application, in particular all patent documents and any Wikipedia articles, are included by reference in their entirety.

Claims

Claims 1. A method, in particular a computer-implemented method, for monitoring a position and / or displacement of an object launched, in particular submerged, from a vessel, in particular an anchor (1) lowered from said vessel, the method comprising the steps of: (a) determining an initial position x of the vessel, in particular by obtaining position information from a satellite navigation system, in particular GPS; (b)determining a start positionof the object, in particular from x , in particular according to(c) launching, in particular lowering and / or submerging the object; (d) estimating an initial position x of the object, in particular according(e) generating an initial set P comprising a plurality of N coordinateswherein i.each coordinate p is indicative of a potential and / or hypothetical initial position of the object, and ii. a central tendency, in particular an expected value, a median, or an average of the plurality of N coordinates equals the estimated initial position(f) for each of a plurality of subsequent instants t ≧ 1 ∈ ℕ and / or 1 ≦ t ∈ ℕ in time: i. determining a subsequent position x of the vessel, in particular by obtaining position information from the satellite navigation system; ii. determining a distance d between the object and the vessel, in particular by obtaining distance information from a sonar; iii. determining a manifold M of possible positions of theobject based on x and d; iv. determining, for at least some, in particular all, of the plurality of N coordinatesfrom set P a distance e from the manifold M; v. deleting a subsetcomprising a number ofN coordinates p for which the distance e is relatively large, in particular larger than a threshold S, from set P ; wherein, in particular, a setof coordinates to be maintained is obtained; vi. generating a set P comprising a number N , in particular with N =of replacement coordinates p wherein each replacement / new coordinate is indicative of a potential and / or hypothetical current position x of the object, in particular to obtain a set of coordinates P = Pvii. determining an estimated position x of the object from coordinates p and / or p , in particular from a central tendency of coordinates p from P preferably P and / or from coordinates2. The method according to claim 1, further comprising, for each of the plurality of subsequent instants t in time, the step of: (a)determining a distance d from the position x of the vessel for at least some, in particular each of the plurality of N coordinates p 3. The method according to claim 2, further comprising, for each of the plurality of subsequent instants t in time, the step of: (a) comparing each of the distances d with d, in particular (b) determining for each of the distances d whether it is larger than d or at least equal to d.

4. The method according to one of the preceding claims, wherein the step of generating replacement coordinates comprises (a) copying coordinates, in particular N coordinates, in particular with N = N , from P ; (b) modifying, in particular translating, at least some, in particular all, of the replacement coordinates.

5. The method according to claim 4, wherein the coordinates to be copied are selected based on their respective distances e from the manifold M, wherein, in particular, those coordinates corresponding to the N smallest distances are chosen.

6. The method according to one of claims 2 to 5, wherein at least some, in particular all, of the replacement coordinates are shifted by a random distance in a random direction, in particular by a vector v with |v | ≪ d, wherein distance and / or direction are, in particular, governed by artificial noise, in particular when at least one of the distances e is smaller than d and / or one of the c is negative.

7. The method according to one of claims 2 to 6 wherein at least some, in particular all, of the replacement coordinates are shifted at least approximately by x - x , in particular when all or almost all of the c are positive and / or all or almost all the distances e are larger than d.

8. The method according to one of claims 2 to 6 wherein at least some, in particular all, of the replacement coordinates are shifted at least approximately by (x - p ) / |(x - p ) | * e , in particular when all or almost all of the c and / or the distances e are larger than d.

9. The method of any preceding claim, wherein all coordinates, positions, vectors and / or distances are defined and / or determined with respect to a two-dimensional coordinate system, in particular a Cartesian coordinate system the axes of which are at least essentially parallel to a water surface at x .

10. The method of any preceding claim, wherein (a) a true distance ^^^between the object and the vessel is determined, in particular obtained through a travel time measurement carried out with a sonar; (b) a depth s of the object is determined, in particular by obtaining depth information from a depth gauge provided on and / or integrated with the object; and (c) d is determined according to^^^^^− ^^^.

11. The method of any preceding claim, wherein all coordinates and / or positions are specified by a longitude and a latitude.

12. The method of any preceding claim, further comprising, for each of the plurality of subsequent instants in time, the step of determining: (a)for each of the distances d a difference δ with δ = d - d, and, in particular (b) a coefficient c|δ |.

13. A tracking system for monitoring a position and / or displacement of an object launched, in particular submerged, from a vessel, in particular an anchor (1) lowered from said vessel, the system comprising: (a) a central unit configured to remain, in particular be installed, on the vessel;(b) a tracking unit configured to be attached to, integrated with and / or carried or worn by the object; (c) the central unit and the tracking unit configured to cooperate to determine, in particular repeatedly determine, a distance d between the central unit and the tracking unit, in particular by means of a sonar comprised by the system, in particular by the central unit and / or the tracking unit; (d) means adapted to execute the steps of any one of the preceding method claims.

14. A data processing apparatus comprising means for carrying out the method of any one of the preceding method claims.

Images