DE102018218231B3 - Method of navigating an underwater vehicle and underwater vehicle - Google Patents

Abstract

The present invention relates to a method for navigating an underwater vehicle and an underwater vehicle (1) which can carry out this method. At a first point in time t0, M manipulated variables u and N state variables x of the underwater vehicle (1) are measured. The N state variables x are predicted for a subsequent point in time t1. A linear relationship with a coefficient matrix is used for the prediction. The components of this coefficient matrix are calculated with the aid of a sample {y [t (k)], X [t (k)]}, which is obtained in a training phase from measured values for the manipulated variables u and the state variables x.

Description

The invention relates to a method for navigating an underwater vehicle and an underwater vehicle in which this method is used.

In particular, during a diving trip, an underwater vehicle can usually neither measure its own actual geoposition nor the actual direction of travel over the ground with sufficient reliability. Nevertheless, an underwater vehicle should be able to navigate safely through the water even when diving.

From the DE 101 53 212 A1 a navigation system for course determination, in particular an underwater vehicle, with sensors for measuring state variables and a mathematically describing vehicle model is known.

From the DE 10 2012 222 812 A1 A method for controlling a state, in particular an underwater vehicle, comprising the steps of reading in current values, reconstructing state variables, determining a working point, determining a stabilization of the working point and outputting control variables is known.

The object of the invention is to provide a method with the features of the preamble of claim 1 and an underwater vehicle with the features of the preamble of claim 11, which require less effort to carry out the prediction of the system state.

This object is achieved by a method with the features specified in claim 1 and an underwater vehicle with the features specified in claim 11. Advantageous further developments result from the subclaims, the following description and the drawings.

According to the method according to the solution, the M values u (t0) of M manipulated variables u and the values x (t0) of N state variables x of the underwater vehicle are measured at a time t0. From these measured M + N measured values, the P values of P variable quantities X for this point in time t0 derived. The N Values x (t1), which are the N state variables x at a later point in time t1 assume are at least approximately predicted and used for the further travel of the underwater vehicle. To predict x (t1), a linear relationship y = X * C ^{T is} used, where y (t0) = x (t1) - x (t0) is a difference vector between the system states at the two times t1 and t0 and C is a coefficient matrix with N rows and P columns.

The coefficients for the coefficient matrix C are calculated using a first sample. This first sample is obtained in a first training phase. In the first training phase, the manipulated variables u [t (k)] and the state variables x [t (k)] are measured at K + 1 predetermined times t (1), ..., t (K + 1). From this a first sample with K value pairs { y [t (k)], X [t (k)]} is derived (k = 1, ..., K). The coefficients c _{i, j} of the coefficient matrix C are calculated using this first sample.

In conventional methods, a predetermined physical model is used to determine the system state of the underwater vehicle at the time t1 predict. This physical model describes the system status at the time t1 as a function of the state of the system at the time t0 and the values of the M manipulated variables at the time t0 , The physical model is usually non-linear and depends on physical parameters, i.e. parameters with a physical meaning. In order to determine the values of these parameters, complex tests, for example test runs of the underwater vehicle, are often required. It may be necessary to carry out these tests again after some time, for example because parameter values may have changed after modifications to the underwater vehicle or due to aging.

The invention avoids the need to conduct such tests. Instead, the first sample that was obtained in the first training phase is used. The coefficient matrix C is calculated using this first sample. The coefficients c _{i, j} of this coefficient matrix C do not necessarily have a physical meaning and are calculated automatically using the first sample.

The first training phase can be carried out during a regular trip of the underwater vehicle. It is possible to use the coefficient matrix C after the first training phase and then to carry out a second training phase in which the coefficient matrix C is adapted. As a result, the coefficient matrix C can be adapted step by step to an ever increasing sample or to environmental conditions that can change during the journey. It is possible, but thanks to the invention, it is not necessary to carry out test drives under specific predetermined test conditions or environmental conditions in order to enable the prediction. The number of sample elements can be adapted to the time available for the first training phase and the sampling rate that can be achieved on board the underwater vehicle.

mit zunächst unbekannten Koeffizienten der Matrix C aufstellen. Um diesen linearen Zusammenhang aufzustellen, wird nicht notwendigerweise die Kenntnis eines physikalischen Modells für das Unterwasserfahrzeug benötigt. Weiterhin werden keine Werte für physikalische Parameter benötigt. Vielmehr wird lösungsgemäß der Zusammenhang zwischen Stellgrößen und Zustandsgrößen für verschiedene Zeitpunkte automatisch und in der ersten Trainingsphase unter Verwendung der ersten Stichprobe berechnet. According to the solution, P become variable sizes X ₁ , ..., X _P used. With the help of these P variable sizes, a linear connection can be made in a previous design phase $\underset{\_}{\text{y}}=\underset{\_}{\text{X}}*{\underset{\_}{\underset{\_}{\text{C}}}}^{\text{T}}$

with initially unknown coefficients of matrix C. In order to establish this linear relationship, knowledge of a physical model for the underwater vehicle is not necessarily required. Furthermore, no values for physical parameters are required. Rather, according to the solution, the relationship between manipulated variables and state variables for different points in time is calculated automatically and in the first training phase using the first sample.

Experiments have surprisingly shown that the method according to the solution makes it possible to predict for considerably longer periods of time than with conventional methods. In other words: between the measurement time t0 and the prediction time t1 can be a considerably larger time interval than in conventional methods, for example several minutes instead of several seconds.

die Koeffizienten der Matrix C zu berechnen. PLSR berücksichtigt nicht nur die maßgebliche Varianz von X, um die Varianz in y zu erklären. Vielmehr ermittelt PLSR auch automatisch diejenigen Komponenten in X, die y bestmöglich erklären, und projiziert hierfür y und X auf latente Variablen in einem gemeinsamen Raum. Das Verfahren PLSR ist insbesondere dann besonders geeignet, wenn eine hohe Multikollinearität zwischen den einzelnen Komponenten von X vorliegt, also die einzelnen Komponenten von X stark miteinander korrelieren. Dies ist bei den P veränderlichen Größen X für das Unterwasserfahrzeug häufig der Fall.The method “partial least squares regression” (PLSR) is preferably used in the first training phase using the first sample and the context $\underset{\_}{\text{y}}=\underset{\_}{\text{X}}*{\underset{\_}{\underset{\_}{\text{C}}}}^{\text{T}}$

to calculate the coefficients of the matrix C. PLSR does not only take into account the relevant variance of X to explain the variance in y . Rather, PLSR also automatically determines those components in X that best explain y and projects y and X onto latent variables in a common space. The PLSR method is particularly suitable when there is a high multicollinearity between the individual components of X , that is to say the individual components of X correlate strongly with one another. This is often the case with the P variable sizes X for the underwater vehicle.

• 1 ein beispielhaftes Unterseeboot mit mehreren Stellgliedern, für welches das Verfahren angewendet wird;
• 2 eine beispielhafte Fahrtroute des Unterseeboots mit zwei Trainingsphasen und zwei Tauchfahrten;
• 3 eine Ausgestaltung, bei der probeweise Stellgrößen-Werte vorgegeben werden und die Konsequenz ermittelt wird.

The method according to the invention is explained in more detail below on the basis of an exemplary embodiment shown in the drawings. Here show:

• 1 an exemplary submarine with multiple actuators, for which the method is applied;
• 2 an exemplary route of the submarine with two training phases and two diving trips;
• 3 an embodiment in which manipulated variable values are given on a trial basis and the consequence is determined.

• - Stellglieder für die Höhenruder,
• - Stellglieder für die Seitenruder,
• - Stellglieder, welche die Vortriebs-Geschwindigkeit des U-Boots durch das Wasser verändern („kommandierte Geschwindigkeit“), beispielsweise die Rotationsgeschwindigkeit einer Welle für einen Propeller oder im Falle eines elektrisch angetrieben U-Boots die Spannung, die an dem Elektromotor anliegt,
• - optional Stellglieder, die einen Trimmzustand des U-Boots im Wasser verändern, und
• - optional Stellglieder, welche die aktuelle Position eines Bestandteils, der sich ausfahren und einziehen lässt, verändern.

In the exemplary embodiment, the invention is used on board a manned submarine (submarine) which has its own drive. The submarine comprises an actuator arrangement with M actuators (M> = 1) which influence the travel of the submarine, in particular at least one of the following actuators:

• - actuators for the elevator,
• - actuators for the rudder,
• - Actuators that change the propulsion speed of the submarine through the water ("commanded speed"), for example the rotational speed of a shaft for a propeller or, in the case of an electrically powered submarine, the voltage that is applied to the electric motor,
• - Optional actuators that change the trim status of the submarine in the water, and
• - Optional actuators that change the current position of a component that can be extended and retracted.

• - eine Fahrzeughülle 10,
• - ein Steuerbord-Seitensonar 12, welches auf der Steuerbordseite an der Fahrzeughülle 10 befestigt ist,
• - ein entsprechendes nicht gezeigtes Backbord-Seitensonar,
• - ein Bug-Sonar 13, welches am Bug der Fahrzeughülle 10 befestigt ist, und
• - einen Turm 11 mit mehreren ausfahrbaren und einziehbaren Bestandteilen.

1 shows an example of a manned submarine 1 which in one direction FR drives through the water. This submarine 1 includes the following components:

• - a vehicle shell 10 .
• - a starboard side sonar 12 , which is on the starboard side of the vehicle shell 10 is attached
• a corresponding port sonar, not shown,
• - a bug sonar 13 , which is on the bow of the vehicle shell 10 is attached, and
• - A tower 11 with several extendable and retractable components.

• - einen angetriebenen Propeller 14,
• - ein vorderes Steuerbord-Höhenruder 15,
• - ein hinteres Steuerbord-Höhenruder 16,
• - zwei korrespondierende nicht gezeigte Backbord-Höhenruder,
• - ein Seitenruder 17 und
• - nicht gezeigte Stellglieder zum Ausfahren und Einziehen von Bestandteilen.

The submarine 1 includes the following actuators, which are the submarine travel 1 influenced by the water:

• - a powered propeller 14 .
• - a forward starboard elevator 15 .
• - a starboard aft elevator 16 .
• - two corresponding port elevators, not shown,
• - a rudder 17 and
• - Actuators, not shown, for extending and retracting components.

The submarine 1 extends along a longitudinal axis X , a transverse axis Y and a vertical axis Z ,

The current states of the actuators of the actuator arrangement are described by a vector with M elements. These current states of the actuators are at every sampling time t (k) (k = 1, 2, ...) and at times t0 . t1 . t2 measured, for example by means of position sensors, and are therefore known for the following method. A manipulated variable vector u [t (k)] = u ₁ [t (k), ..., u _M [t (k)] is therefore known for each time t (k).

• - die aktuelle Geoposition des U-Boots1,
• - die 3D-Lage des U-Boots 1 im Wasser, beispielsweise als die Orientierung der Längsachse X, der horizontalen Querachse Y und der Hochachse Z des U-Boots 1 in einem absoluten 3D-Koordinatensystem, welches zum Nordpol zeigt, also der Kurs (heading) des U-Boots 1, und
• - die Geschwindigkeit des U-Boots 1 relativ zum umgebenden Wasser.

So that the submarine 1 can travel through the water, the following parameters are required in particular, which vary over time and are referred to below as navigation parameters:

• - the current geoposition of the submarine1,
• - The 3D position of the submarine 1 in water, for example as the orientation of the longitudinal axis X , the horizontal transverse axis Y and the vertical axis Z of the submarine 1 in an absolute 3D coordinate system that points to the North Pole, i.e. the heading of the submarine 1 , and
• - the speed of the submarine 1 relative to the surrounding water.

• - die drei linearen Geschwindigkeiten u, v, w des U-Boots 1 in einem lokalen 3D-Koordinatensystem, welches an die aktuelle Lage des U-Boots 1 angepasst ist, wobei bevorzugt die Längsachse X des U-Boots 1 die x-Achse des lokalen 3D-Koordinatensystems definiert, die horizontale Querachse Y die y-Achse und die Hochachse Z die z-Achse,
• - die drei aktuellen Winkelgeschwindigkeiten des U-Boots 1 in diesem lokalen 3-D Koordinatensystem und
• - die Lage der drei Achsen X, Y, Z des U-Boots 1 im Wasser in einem absoluten Koordinatensystem.

During a submarine dive 1 in particular, the actual current geoposition cannot be determined exactly, or at least not at all times, because signals from a satellite are not from a receiver of the submarine 1 can be received. Therefore, the searched for and not directly measurable values of the navigation variables become dependent on the values of a temporally variable state variable x calculates which consists of N individual state variables. The value x [t (k)] = x ₁ [t (k)], ..., x _N [t (k)], x (t0), x (t1), x (t2), ... the vector-valued state variable x at the time t (k) . t0 . t1 . t2 describes a system state of the submarine at time t (k). About the individual state variables of the submarine 1 include in particular the following sizes:

• - the three linear speeds u, v, w of the submarine 1 in a local 3D coordinate system that matches the current position of the submarine 1 is adapted, preferably the longitudinal axis X of the submarine 1 defines the x-axis of the local 3D coordinate system, the horizontal transverse axis Y the y-axis and the vertical axis Z the z axis,
• - the three current angular velocities of the submarine 1 in this local 3-D coordinate system and
• - the position of the three axes X . Y . Z of the submarine 1 in the water in an absolute coordinate system.

The current system state x [t (k)] can be measured completely at least temporarily, for example using at least one inertial navigation system on board the submarine 1 , Especially when the submarine 1 If the dive is carried out for a longer period or if a sensor of the inertial navigation system has failed or provides measured values that are physically impossible in the current situation, the submarine loses 1 the ability to link the position more precisely in the short term. The invention avoids the need for the submarine 1 therefore shows up after a short time to determine its current geoposition in a way that is only possible after surfacing, for example by the submarine that has appeared 1 Receives geoposition signals and, if necessary, repositions the sensors of the inertial navigation system.

2 shows an example of a section of the route of the submarine 1 , Those parts of the route in which the system state x can be measured at any point in time, in particular a route in the surfaced state, are each represented by a solid line. Those parts of the route in which the system state x not measured, but predicted are shown by a dashed line. The manipulated variables u can be measured during the entire route. In the example of 2 two training phases are carried out one after the other. Not only the manipulated variable vector can be used in each training phase u but also the system state x measure at any time.

In the exemplary embodiment, the system state x ( t0) at a time t0 measured. From the measured current system status x ( t0) at this time t0 the values of the navigation sizes at this time t0 derived. The values of the navigation parameters are searched for at least one future point in time t1 , for a time t1 , the time after the measurement time t0 lies, for example t1 = t0 + Δ. The values of the navigation parameters for the future point in time t1 become at least one predicted system state x ^ ( t1) for this future time t1 derived. The system state x ^ ( t1) at the time t1 is therefore not measured, but predicted. Because the system state for the time t1 is predicted and not measured, he is using x ^ (t1) and not with x (t1) designated. It is also possible to change the system status x ^ ( t1 ') for at least one other point in time t1 'to predict where t1 ' between t0 and t1 lies, and the values of the navigation variables for the time t1 depending on the two predicted system states x ^ ( t1) and x ^ ( t1 ') to calculate. For example, integration is carried out over a time sequence of system states.

The actual system state x ( t1) at a future time t1 depends on the time t0 measured system state x ( t0) and from the intervention u (t0) at this time t0 from. This dependency is described by a physical model. Such a model is, for example, in DE 102017200468 A1 and in DE 102017200470 A1 specified.

A physical constraint is that at all times the forces and moments on the moving submarine 1 work, have to be in balance. The forces in the x-axis (longitudinal axis of the submarine 1 ), in the y-axis (horizontal transverse axis) and in the z-axis (vertical axis) in equilibrium, also the torques when rolling (rotation around the x-axis), when nodding (rotation around the y-axis) and when yawing (Rotation around the z-axis). These six boundary conditions provide six nonlinear differential equations. These six boundary conditions and optionally further physical boundary conditions provide a non-linear model x ^ (t1) = x ^ (t0 + Δ) = f [ x (t0), u (t0)]. This relationship f applies to a fixed difference Δ for every point in time t0 , The notation x ^ (t1) indicates that a model naturally only approximates physical reality.

The nonlinear system relationship f contains parameters that must be known in order to be able to directly predict the system state x . These parameters of the system relationship f have physical meanings and depend on the physical properties of the submarine 1 which can be determined experimentally and / or by simulation. This determination can lead to incorrect parameter values. It is also possible that a parameter value changes over time, for example due to structural changes to the submarine 1 , new operating conditions or aging. Thanks to the invention, it is not necessary to determine these physical parameters.

The model with physical parameters mentioned above is used to determine the system state x ^ ( t1) at the time t1 to predict in a manner to be described below.

Before a system state is predicted, a design phase and then at least one training phase are carried out in advance in the exemplary embodiment. The design phase can take place anywhere. The or each training phase will be on board the submarine 1 carried out.

In the design phase, P become variable sizes X ₁ . .. ., X _P established. For every variable size X ₁ , ..., X _P a functional dependency F _j (j = 1, ..., P) is defined in each case. The functional dependency F _j describes the variable X _j (j = 1, ..., P) as a function of at least one state variable x _i (i = 1, ..., N) and / or at least one manipulated variable u _i (i = 1, ..., M). It is possible that a variable X _j of several or even all state variables x _i (i = 1, ..., N) and / or of several or even all manipulated variables u _i (i = 1, ..., M) depends.

• - Staudruck-lineare Terme - nur abhängig von Geschwindigkeitskomponenten,
• - Staudruck-lineare Terme - nur abhängig von Drehraten,
• - Staudruck-lineare Terme - abhängig von Geschwindigkeiten und Drehraten,
• - nichtlineare Partialkräfte und -Momente - nur abhängig von Geschwindigkeitskomponenten,
• - nichtlineare Partialkräfte und -Momente - nur abhängig von Drehraten,
• - nichtlineare Partialkräfte und -Momente - abhängig von Geschwindigkeiten und Drehraten,
• - Fourierglied des Rollmomentes,
• - auftriebsabhängige Kräfte und Momente als Funktion der Lagewinkel,
• - Brückenwirbelanteile, hervorgerufen von dem Turm 11 des U-Boots 1, und
• - Stellgrößenanteile in Abhängigkeit von der Stellgröße u.

For example, every variable X _j belongs to exactly one of the following ten groups of variable variables:

• - back pressure linear terms - only dependent on speed components,
• - back pressure linear terms - only dependent on rotation rates,
• - back pressure linear terms - depending on speeds and rotation rates,
• - non-linear partial forces and moments - only dependent on speed components,
• - non-linear partial forces and moments - only dependent on yaw rates,
• - non-linear partial forces and moments - depending on speeds and rotation rates,
• - Fourier element of the rolling moment,
• - buoyancy-dependent forces and moments as a function of the attitude angle,
• - parts of the bridge vortex caused by the tower 11 of the submarine 1 , and
• - Control variable shares depending on the control variable u.

For each state variable x _i (i = 1, ..., N) there is a linear functional relationship x _i (t + Δ) - x _i (t) = y _i (t) with y _i (t) = c _{i , 1} * X ₁ (t) + ... + c _{i, P} * X _P (t) and specified for the procedure described below. This relationship applies at least approximately to every time t and is used for the prediction.

These relationships contain N * P initially unknown coefficients c _{i, j} , in which N the number of state variables and P the number of variable variables is these coefficients c _{i, j} , do not necessarily have a physical meaning and are not calculated by tests or simulations, but automatically using at least one sample, which is described below. These N * P coefficients c _{i, j} are combined into a coefficient matrix C with N rows and P columns. The P variable sizes X ₁ . .. ., X _P become a vector X summarized with P components. The N Difference quantities y ₁ , ..., y _N become a vector y summarized with N components. The linear functional relationship can then also be expressed as y = Write X * C ^T , where C ^{T is} the matrix transposed to C , which has P rows and N columns.

For the first training phase, a sequence with K + 1 sampling times t (1), t (2), ..., t (K + 1), for example equidistantly arranged sampling times, is specified, cf. 2 , These K + 1 sampling times preferably cover the first training phase. At each sampling time t (k) the current system state x [t (k)] = x ₁ [t (k)], ..., x _N [t (k)] is measured (k = 1, .. ., K + 1). A system state difference vector y [t (k)] = x [t (k + 1)] - x [t (k)] is derived from two successive system states, which N components y _i [t (k)] = x _i [t (k + 1)] - x _i [t (k)] has (i = 1, ..., N, k = 1, ..., K). This provides K system state difference vectors y [t (1)], ..., y [t (K)].

Furthermore, the current manipulated variable vector u [t (k)] = u ₁ [t (k)], ..., u _M [t (k)] is measured at each sampling time. The P Predefined functional dependencies F ₁ , ..., F _P are applied to the measured system states x and measured manipulated variable vectors u . This will change for every size X ₁ , ..., X _P each calculated K + 1 values X _j [t (k)], which is the variable size X _j assumes at time t (k) (j = 1, ..., P, k = 1, ..., K). This provides K size vectors X [t (1)], ..., X [t (K)]. The K System state difference vectors and the K size vectors form a sample with K vector value pairs { y [t (k)], X [t (k)]} (k = 1, ..., K).

In the context of y = X * C ^T gives the first sample K Values for y and x . Using the first sample, the P * N components c _{i, j} the coefficient matrix C is automatically determined. This defines the coefficient matrix C.

At the end of the or each training phase, the coefficients of the coefficient matrix C are thus determined automatically and using a sample obtained in the training phase, which is described below using the example of the first sample. In the exemplary embodiment, the method “partial least squares regression” (PLSR) is used, which is described in the following publication for applications of chemical analysis (chemometrics): S. Wold, M. Sjöström, L. Eriksson: “PLS regression: a basic tool of chemometrics ”, Chemometrics and Intelligent Laboratoy Systems 58 (2001), pp. 109-130.

In the present embodiment, PLSR is applied to the coefficients c _{i, j} (i = 1, ..., N; j = 1, ..., P) of the coefficient matrix C and calculate the linear relationship y = X * C ^T and the first sample { y [t (1) ], X [t (1)], ..., y [t (K)], X [t (K)]}. The difference vector y has N components (number of state variables), the vector X has P components (number of variable variables), the coefficient matrix C has N rows and P columns and the transposed C ^T thus P rows and N columns.

The first sample contains a vector X [t (k)] with P elements and a vector y [t (k)] with N elements for each measurement time t (k) (k = 1, ..., K) , The K Measured values X _j [t (1), ..., X _j [t (K)] for a variable X _j form a measured value vector which is designated X _j '(j = 1, ..., P ). According to the PLSR, A so-called X-scores s ₁ , ..., s _{A are} calculated, whereby A is usually significantly smaller than P, each vector s _a K has elements (a = 1, ..., A) and K is the number of measurement times. The number A can be specified, for example depending on the computing capacity on board the submarine 1 , It is also possible to use different values for A on a trial basis in the course of the method. Everyone X -Score s _a is calculated as a weighted summary, i.e. as a linear combination, of the P measured value vectors of X (a = 1, ..., A), i.e. as follows: $${\underset{\_}{\text{s}}}_{\text{a}}={\text{w}}_{\text{a}\mathrm{,1}}*{\underset{\_}{\text{X}}}_1\text{'}+...+{\text{w}}_{\text{a}.\text{P}}*{\underset{\_}{\text{X}}}_{\text{P}}\text{'},$$

Die Gewichtsfaktoren w_a,j (a=1,...,A; j=1,...,P) werden so bestimmt, dass die AX-Scores s ₁, ..., s _A paarweise senkrecht (orthogonal) aufeinander stehen. Ein weiteres Kriterium, um die Gewichtsfaktoren w_a,j zu bestimmen, ist das, dass die so genannten X-Residuen e ₁, ..., e _P minimiert werden (möglichst nahe bei Null), beispielsweise durch eine multiple lineare Regression. Die zu minimierenden X-Residuen sind die Abweichungen zwischen den Messwerte-Vektoren für X und der bestmöglichen linearen Kombination aller X-Scores: $${\underset{\_}{\text{e}}}_{\text{j}}={\underset{\_}{\text{X}}}_{\text{j}}\text{'}-\left\{{\text{p}}_{\mathrm{1,}\text{j}}*{\underset{\_}{\text{s}}}_1+\dots +{\text{p}}_{\text{A},\text{j}}*{\underset{\_}{\text{s}}}_{\text{A}}\right\}\left(\text{j}=\mathrm{1,}\dots ,\text{P}\right).$$

Hierbei sind p_a,j die Gewichtsfaktoren, die zu den kleinstmöglichen Residuen e _j führen. In Komponenten-Schreibweise: $${\underset{\_}{\text{e}}}_{\text{j}}\left(\text{k}\right)={\underset{\_}{\text{X}}}_{\text{j}}\left[\text{t}\left(\text{k}\right)\right]-\left\{{\text{p}}_{\mathrm{1,}\text{j}}*{\underset{\_}{\text{s}}}_1\left(\text{k}\right)+\dots +{\text{p}}_{\text{A},\text{j}}*{\underset{\_}{\text{s}}}_{\text{A}}\left(\text{k}\right)\right\}.$$

Möglich ist auch, dass die Anzahl A der X-Scores vergrößert wird, wenn einzelne Residuen auch bei bestmöglichen Gewichtsfaktoren noch zu weit von Null entfernt sind.In component notation: $${\underset{\_}{\text{s}}}_{\text{a}}\left(\text{k}\right)={\text{w}}_{\text{a}\mathrm{,1}}*{\text{X}}_1\left[\text{t}\left(\text{k}\right)\right]+...+{\text{w}}_{\text{a}.\text{P}}*{\text{X}}_{\text{P}}\left[\text{t}\left(\text{k}\right)\right]\left(\text{k}=\mathrm{1,}....\text{K}\right),$$

The weighting factors w _{a, j} (a = 1, ..., A; j = 1, ..., P) are determined in such a way that the AX scores s ₁ , ..., s _{A in} pairs are perpendicular (orthogonal) stand on each other. Another criterion for determining the weighting factors w _{a, j} is that the so-called X residuals e ₁ , ..., e _{P are} minimized (as close as possible to zero), for example by a multiple linear regression. The X residuals to be minimized are the deviations between the measured value vectors for X and the best possible linear combination of all X scores: $${\underset{\_}{\text{e}}}_{\text{j}}={\underset{\_}{\text{X}}}_{\text{j}}\text{'}-\left\{{\text{p}}_{\mathrm{1,}\text{j}}*{\underset{\_}{\text{s}}}_1+...+{\text{p}}_{\text{A}.\text{j}}*{\underset{\_}{\text{s}}}_{\text{A}}\right\}\left(\text{j}=\mathrm{1,}....\text{P}\right),$$

Here p _{a, j are} the weighting factors that lead to the smallest possible residuals e _j . In component notation: $${\underset{\_}{\text{e}}}_{\text{j}}\left(\text{k}\right)={\underset{\_}{\text{X}}}_{\text{j}}\left[\text{t}\left(\text{k}\right)\right]-\left\{{\text{p}}_{\mathrm{1,}\text{j}}*{\underset{\_}{\text{s}}}_1\left(\text{k}\right)+...+{\text{p}}_{\text{A}.\text{j}}*{\underset{\_}{\text{s}}}_{\text{A}}\left(\text{k}\right)\right\},$$

It is also possible that the number A the X-Score is increased if individual residuals are still too far from zero even with the best possible weight factors.

In Komponenten-Schreibweise: $${\underset{\_}{\text{f}}}_{\text{i}}\left(\text{k}\right)={\underset{\_}{\text{y}}}_{\text{i}}\left[\text{t}\left(\text{k}\right)\right]-\left\{{\text{b}}_{\text{i}\mathrm{,1}}*{\underset{\_}{\text{s}}}_1\left(\text{k}\right)+\dots +{\text{b}}_{\text{i},\text{A}}*{\underset{\_}{\text{s}}}_{\text{A}}\left(\text{k}\right)\right\}\left(\text{k}=\mathrm{1,}\dots ,\text{K}\right).$$

After the X-scores are determined, N * A are regression coefficients b _{i, a} (i = 1, ..., N; a = 1, ..., A), where N is the number of state variables and A is the number of X scores. These N * A regression coefficients b _{i, a} are determined so that the N so-called Y residuals f ₁ , ..., f _{N are} minimized: $${\underset{\_}{\text{f}}}_i={\underset{\_}{\text{y}}}_{\text{i}}\text{'}-\left\{{\text{b}}_{\text{i}\mathrm{,1}}*{\underset{\_}{\text{s}}}_1+...+{\text{b}}_{\text{i}.\text{A}}*{\underset{\_}{\text{s}}}_{\text{A}}\right\}\left(\text{i}=\mathrm{1,}....\text{N}\right),$$

In component notation: $${\underset{\_}{\text{f}}}_{\text{i}}\left(\text{k}\right)={\underset{\_}{\text{y}}}_{\text{i}}\left[\text{t}\left(\text{k}\right)\right]-\left\{{\text{b}}_{\text{i}\mathrm{,1}}*{\underset{\_}{\text{s}}}_1\left(\text{k}\right)+...+{\text{b}}_{\text{i}.\text{A}}*{\underset{\_}{\text{s}}}_{\text{A}}\left(\text{k}\right)\right\}\left(\text{k}=\mathrm{1,}....\text{K}\right),$$

From the N * A regression coefficients b _{i, a} (a = 1, ..., A; i = 1, ..., N) and the P * A weighting factors w _{a, j} (a = 1, ..., A; j = 1, ..., P) become the N * P coefficients c _{i, j} of the coefficient matrix C is determined as follows: $${\text{c}}_{\text{i}.\text{j}}={\text{b}}_{\text{i}\mathrm{,1}}*{\text{w}}_{\mathrm{1,}\text{j}}+....{\text{b}}_{\text{i}.\text{A}}*{\text{w}}_{\text{A}.\text{j}},$$

After the first training phase, the coefficient matrix C is applied at least once. As already stated, will be at a time t0 the system state x ( t0 ) with N components and the manipulated variable vector u ( t0 ) measured with M components. In the exemplary embodiment, this point in time t0 at the end of the first training phase or after the first training phase. In the example of 2 is the time t0 after the first training phase and is, for example, the last time before a dive at which the system status can still be measured.

From these two vectors x (t0) and u (t0) becomes the vector X (t0) calculated with P components. The linear relationship y = X * C ^T with the coefficient matrix C calculated in the first training phase is based on the vector obtained by the measurements X (t0) applied and returns a vector y ( t0 ) = x ^ ( t1 ) - x ( t0 ). The searched system state x ^ (t1) for the time t1 according to x ^ ( t1 ) = y ( t0 ) + x ( t0 ) calculated and thus predicted. From this predicted system state x ^ ( t1 ) at the time t1 are the navigation sizes at the time t1 derived and thus predicted.

It is possible that this prediction is carried out several times. A sequence of times is specified t1 . t2 . .. , The respective system status should be predicted for each point in time. The manipulated variable vector u is measured at each prediction time, so that the measured values u (t1) . u (t2) , ... are available. The system state x ^ (t1) for the time t1 is predicted as just described. Then the functional relationships F ₁ , ..., F _P reapplied to the measured manipulated variable vector u (t1) and the predicted system state x ^ ( t1 ). This application provides a vector X (t1) with the P values of the P variable sizes X ₁ , ..., X _P for the time t1 , The linear relationship y = X * C ^T is applied again and yields a vector y (t1) = x ^ (t2) - x ^ ( t1 ). From this, the system state to be predicted is sought x (t2) calculated. This procedure is used for the subsequent prediction times t4 . t5 , ... carried out accordingly.

In the example of 2 is first measured using the vectors x (t0) and u (t0) the system state x ^ (t1) for the time t1 predicted. Then using the measured manipulated variable vector u (t1) and the predicted system state vector x ^ (t1) the system state vector x ^ (t2) for a subsequent point in time t2 predicted.

In one embodiment, a first training phase and a second training phase are carried out in succession. In the first training phase, the steps are carried out as just described, so that a sample is determined using K vector-valued sample elements and the P * N components c _{i, j} of the coefficient matrix C can be determined. In a subsequent application period, the respective system status will be as just described x (t1) . x (t2) , ... for several prediction times t1 . t2 , ... calculated.

• - die N Werte x₁[t1(k)], ..., x_N[t1 (k)], welche die N Zustandsgrößen zum Zeitpunkt t1(k) jeweils annehmen, und
• - die M Werte u₁[t1(k)], ..., u_N[t1(k)], welche die M Stellgrößen zum Zeitpunkt t1(k) jeweils annehmen,

gemessen (k=1,..., K1+1). K1 Differenz-Werte y_i[t1(k)] = x_i[t1(k+1)] - x_i[t1(k)] werden berechnet (i=1,..., N, k = 1,..., K1). Für jede veränderliche Größe X_j werden jeweils K1 Werte X_j[t1(k)] berechnet, welche die veränderliche Größe X_j zum Zeitpunkt t1(k) annimmt (j=1,..., P, k=1,..., K1). Aus den berechneten K Differenz-Werten und den berechneten P * K Werten der P veränderlichen Größen X₁ , ..., X_P wird eine zweite Stichprobe mit K1 vektor-wertigen Wertepaaren { y[t1(k)], X[t1(k)] } abgeleitet. Unter Verwendung der zweiten Stichprobe wird die Koeffizienten-Matrix C die in der ersten Trainingsphase bestimmt wird, an die zweite Stichprobe angepasst. Möglich ist, dass in der zweiten Trainingsphase alle Elemente der zweiten Stichprobe oder auch nur einige automatisch ausgewählte Stichproben-Elemente verwendet werden. Möglich ist, die Koeffizienten-Matrix C aus der ersten Trainingsphase anzupassen oder auch die vollständige Berechnung der Koeffizienten-Matrix C erneut „von Null an“ durchzuführen.Then a second training phase is carried out, in which the system state is again x can be measured and, for example, in particular the current geoposition of the submarine can be measured. A sequence with K1 + 1 sampling times t1 (1), t1 (2), ..., t1 (K1 + 1) is specified for the second training phase. K1 can be equal to K or different from K. Anytime t1 (k) are each

• - the N values x ₁ [t1 (k)], ..., x _N [t1 (k)], which each take on the N state variables at time t1 (k), and
• - the M values u ₁ [t1 (k)], ..., u _N [t1 (k)], which each take the M manipulated variables at time t1 (k),

measured (k = 1, ..., K1 + 1). K1 Difference values y _i [t1 (k)] = x _i [t1 (k + 1)] - x _i [t1 (k)] are calculated (i = 1, ..., N, k = 1, .. ., K1). For each variable size X _j are each K1 Values X _j [t1 (k)] calculated, which the variable size X _j assumes at the time t1 (k) (j = 1, ..., P, k = 1, ..., K1). From the calculated K difference values and the calculated P * K values of the P variable quantities X ₁ , ..., X _P is using a second sample K1 vector value pairs { y [t1 (k)], X [t1 (k)]} are derived. Using the second sample, the coefficient matrix C determined in the first training phase is passed to the second Sample adjusted. It is possible that all elements of the second sample or only some automatically selected sample elements are used in the second training phase. It is possible to adapt the coefficient matrix C from the first training phase or to perform the complete calculation of the coefficient matrix C again "from zero".

In one embodiment, an overall sample is generated. This total sample is generated using the first sample, which was determined in the first training phase, and using the second sample, which was determined in the second training phase. This total sample can contain all elements of the first sample and all elements of the second sample or only automatically selected elements of the first and / or the second sample. In the second training phase, the overall sample is used to calculate the coefficient matrix C redetermine or around the already determined coefficient matrix C adapt.

In the applications described so far, the M manipulated variables u ₁ , ..., u _M measured at each sampling time. It is also possible to give test values for the manipulated variables on a trial basis and to determine which system status the submarine has by means of a prediction 1 at a subsequent time t5 would have if the M manipulated variables were actually set to the values given on a trial basis. This is referred to below 3 explained. Point of time t5 can be the same time t1 be or deviate from it.

The submarine 1 is located near an area Ar and is not allowed in this area Ar drive. At the time t0 As a test, M manipulated variable values are specified, which together form a vector u '( t0 ) form. The system state at the time t0 is measured, whereby a state quantity vector x (t0) is delivered. As just described, the system state x ^ ( t5 ) at a later time t5 predicted. In one embodiment, several system states are created one after the other at intermediate times t2 . t3 , ... predicted. To the system state x ^ (t5) at the time t5 to predict, in this embodiment the same predetermined manipulated variables each time become vector u '(t0) or also a sequence of manipulated variable vectors that have been predetermined on a trial basis u '(t0) . u '(t1) , ... used. The predicted system state x ^ (t5) is compared with a given criterion. For example, the geoposition is predicted, which, according to the prediction, is given in this sequence of trial-and-error manipulated variable vectors u '(t0) . u '(t1) , and the predicted system states x ^ (t1) , ..., x ^ (t5) at the time t5 is achieved. In the in 3 The example shown would be the submarine 1 then in the area Ar what is prohibited. Therefore, instead of the control variable vector that is given as a test u '(t0) a changed manipulated variable vector u (t0) used. This leads to a route that leads to the area Ar passes.

LIST OF REFERENCE NUMBERS

1

manned submarine

10

Submarine vehicle hull 1

11

Submarine tower 1

12

Starboard side sonar, on the starboard side of the vehicle hull 10 assembled

13

Bow sonar, on the bow of the vehicle hull 10 assembled

14

Submarine propeller 1

15

forward starboard elevator of submarine 1

16

aft starboard elevator of submarine 1

17

Submarine rudder 1

A

Number of X-scores s _a (a = 1, ..., A)

Ar

Area in which the submarine 1 shouldn't drive

b _{i, a}

Regression coefficients (i = 1, ..., N; a = 1, ..., A)

C

Coefficient matrix, has N rows and P columns and the coefficients c _{i, j}

c _{i, j}

Coefficients of the coefficient matrix C (i = 1, ..., N; j = 1, ..., P)

e ₁ , ..., e _P

X residuals to be minimized each have K components

f ₁ , ..., f _P

Y residuals to be minimized each have K components

FR

Direction of travel of the submarine 1

M

Number of manipulated variables, number of components of the vector u

N

Number of state variables, number of components of the vectors x and y

P

Number of variable sizes, number of components of the vector X

s ₁ , ..., s _A

X-scores, each with K components, are orthogonal in pairs

t0

Time at which the M manipulated variables and the N state variables are measured

t1, t2, ...

Points in time at which the M manipulated variables are measured and for which the N state variables are predicted

u ₁ , ..., u _M

measurable manipulated variables for the actuator arrangement

x ₁ , ...,

State variables, measured or predicted, form together

x _N

the system state

K

Scope of the first sample

K + 1

Scope of the second sample

x (t1), x (t2), ...

actual system status at the time t1 . t2 , ...

x ^ (t1), x ^ (t2), ...

for the times t1 . t2 , ... predicted system states (vectors of the state variables x )

X

Longitudinal axis of the submarine 1

X

Vector of variable sizes, has P components

X ₁ , ..., X _P

variable variables, each depend on state variables and / or manipulated variables

y

Difference vector from the system states at two successive points in time

Y

horizontal transverse axis of the submarine 1

y (t)

Difference from the system states at two successive points in time is equal to x (t + Δ) - x (t)

Z

vertical vertical axis of the submarine 1

Claims (11)

Method for navigating an underwater vehicle (1), the underwater vehicle (1) comprising an actuator arrangement (14, 15, 16, 17) with at least one actuator, the actuator arrangement being adjustable and measurable manipulated variables u ₁ ,... ., u _{M can be changed} with M> = 1, a system state comprising N time-variable state variables x ₁ , ..., x _N and being correlated with the movement of the underwater vehicle (1) through the water is predetermined, N > = 1, and wherein the method comprises the steps that - the N values x ₁ (t0), ..., x _N (t0), which represent the N state variables x ₁ , ..., x _N at a time t0 assume, be measured, - the M values u ₁ (t0), ..., u _M (t0), which assume the M manipulated variables u ₁ , ..., u _M at time t0, are measured or specified, - under Use of the N state variable values x ₁ (t0), ..., x _N (t0), the M manipulated variable values u ₁ (t0), ..., u _M (t0) and a specified functional relationship the N values x ^ ₁ (t1), ..., x ^ _N (t1), which assume the N state variables x ₁ , ..., x _N at a predetermined later time t1, are at least approximately predicted, and - the predicted N state variable values x ^ ₁ (t1), ..., x ^ _N (t1) are used for navigating the underwater vehicle (1), characterized in that P variable variables X ₁ , ..., X _P and for each variable X ₁ , ..., X _{P there} is a functional dependency F _j , which shows the variable X _j (j = 1, ..., P) as a function of at least one state variable x _i (i = 1, ..., N) and / or at least one manipulated variable u _i (i = 1, ..., M) describes, are given a linear functional relationship for each state variable x _i (i = 1, ..., N) x _i (t + Δ) - x _i (t) = y _i (t) with y _i (t) = c _{i, 1} * X ₁ (t) + ... + c _{i, P} * X _P (t ) is specified, whereby the initially unknown coefficients c _{i, j} form a coefficient matrix C with N rows and P columns, the P variable quantities X ₁ , ..., X _P form a vector X and the N difference quantities y ₁ , ..., y _{N are combined} into a vector y , so that $\underset{\_}{\text{y}}=\underset{\_}{\text{X}}*{\underset{\_}{\underset{\_}{\text{C}}}}^{\text{T}}\text{glit}\text{.}$

in a first training phase, the steps are carried out such that - the underwater vehicle (1) is moved through the water, - K + 1 times t (1), ..., t (K + 1) are specified, - for each point in time t (k) (k = 1, ..., K + 1) the N values x ₁ [t (k)], ..., x _N [t (k)] are measured, which are the N state variables x ₁ , ..., x _N each assume at time t (k), - for each time t (k) (k = 1, ..., K) the M values u ₁ [t (k)], ... , u _M [t (k)] are measured, which each assume the M manipulated variables u ₁ , ..., u _M at time t (k), - K difference values y _i [t (k)] = x _i [t (k + 1)] - x _i [t (k)] can be calculated (i = 1, ..., N, k = 1, ..., K), - by applying the functional dependence F _j for each variable X _j K + 1 values X _j [t (k)] are calculated, which the variable X _j assumes at time t (k) (j = 1, ..., P, k = 1,. .., K), - from the calculated K difference values and the calculated P * K values of the P variable quantities X ₁ , ..., X _P a first sample with K vector value pairs {y [t (k)], X [t (k)]} is derived (k = 1, ..., K) and - using the first sample and the relationship $\underset{\_}{\text{y}}=\underset{\_}{\text{X}}*{\underset{\_}{\underset{\_}{\text{C}}}}^{\text{T}}$

the coefficient matrix C is calculated and in the step of predicting the values x ^ ₁ (t1), ..., x ^ _N (t1) of the N state variables for the later time t1, the steps are performed that - using the functional dependencies F ₁ , ..., F _P , the N state variable values x ₁ (t0), ..., x _N (t0) measured at time t0 and the M manipulated variable values u ₁ (t0) ,. .., u _M (t0) the P values X ₁ (t0), ..., X _P (t0) are calculated, which assume the P variable quantities X ₁ , ..., X _P at time t0, - under Use of the coefficient matrix calculated in the first training phase $\underset{\_}{\underset{\_}{\text{C}}}$

and the P values X ₁ (t0), ..., X _P (t0) N difference values y _i (t0) = c _{i, 1} * X ₁ (t0) + ... + c _{i, P} * X _P (t0) (i = 1, ..., N) are calculated and - the N state quantity values x ^ ₁ (t1), ..., x ^ _N (t1) for the later time t1 using the for the earlier state t0 measured N state variable values x ₁ (t0), ..., x _N (t0) and the calculated N difference values y ₁ (t0), ..., y _N (t0) can be predicted. Procedure according to Claim 1 , characterized in that at the step using the first sample the coefficient matrix $\underset{\_}{\underset{\_}{\text{C}}}$

To calculate, at least one of the following methods is used: - a linear regression analysis, - a principal component analysis, - the method "Partial Least Squares Regression (PLSR)". Method according to one of the preceding claims, characterized in that the underwater vehicle (1) along - a longitudinal axis (X), - a horizontal transverse axis (Y) perpendicular to the longitudinal axis (X) and - one perpendicular to the longitudinal axis (X) and the transverse axis (Y) standing vertical axis (Z) and measuring at least one of the following variables and used as a state variable x _i : - the speed of the underwater vehicle (1) over the ground in a direction parallel to the longitudinal axis (X), - the Speed of the underwater vehicle (1) above the ground in a direction parallel to the transverse axis (Y), - the speed of the underwater vehicle (1) above the ground in a direction parallel to the vertical axis (Z), - the angular speed of the underwater vehicle (1) above the ground by one Axis parallel to the longitudinal axis (X), - the angular velocity of the underwater vehicle (1) above the ground about an axis parallel to the transverse axis (Y), - the angular velocity ability of the underwater vehicle (1) over the ground about an axis parallel to the vertical axis (Z). Method according to one of the preceding claims, characterized in that the underwater vehicle (1) has a drive (14) which is designed to move the underwater vehicle (1) through the water, at least one manipulated variable u _{i being} a variable which with the driving speed of the Underwater vehicle (1) correlated relative to the surrounding water. Method according to one of the preceding claims, characterized in that the underwater vehicle (1) comprises - a vehicle body (10), - a change of direction element (15, 16, 17) and - a drive for moving the change of direction element , at least one manipulated variable u _{i being} a variable which correlates with the position of the direction change element (15, 16, 17) relative to the vehicle body (10). Method according to one of the preceding claims, characterized in that the M values u ₁ (t1), ..., u _m (t1), which assume the M manipulated variables u ₁ , ..., u _M at the subsequent time t1, are measured or predetermined and the values x ^ ₁ (t2), ..., x ^ _N (t2) of the N state variables are predicted for a subsequent time t2, which is after the time t1, the prediction for the time t2 the steps comprises that - using the functional dependencies F ₁ , ..., F _P , the N state variable values x ^ ₁ (t1), ..., x ^ _N (t1) and the predicted for the time t1 M manipulated variable values u ₁ (t1), ..., u _M (t1) for the time t1 the P values X ₁ (t1), ..., X _P (t1) are calculated, which are the P variable variables X ₁ , ..., X _P at time t1, - using the coefficient matrix C calculated in the first training phase and the P values X ₁ (t1), ..., X _P (t1) N difference values y _i (t1) = c _{i, 1} * X ₁ (t1) + ... + c _{i, P} * X _P (t1) (i = 1, ..., N) are calculated and - the N state variable values x ^ ₁ (t2), ..., x ^ _N (t2 ) for the subsequent time t2 using the N state variable values x ^ ₁ (t1), ..., x ^ _N (t1) predicted for the time t1 and the calculated N difference values y ₁ (t1), .. ., y _N (t1) can be predicted. Method according to one of the preceding claims, characterized in that after the prediction of the N values x ^ ₁ (t1), ..., x ^ _N (t1), which the N state variables x ₁ , ..., x _N for subsequent Assume time t1, in a second training phase the steps are carried out, that at K1 + 1 predetermined times t1 (1), ..., t1 (K1 + 1) - the N values x ₁ [t1 (k)], .. ., x _N [t1 (k)], which each assume the N state variables at time t1 (k), and - the M values u ₁ [t1 (k)], ..., u _N [t1 (k)] , which each assume the M manipulated variables at time t1 (k), K difference values y _i [t1 (k)] = x _i [t1 (k + 1)] - x _i [t1 (k)] are calculated (i = 1, ..., N, k = 1, ..., K1), for each variable X _j K1 values X _j [t1 (k)] are calculated, which change the variable X _j to Time t1 (k) assumes (j = 1, ..., P, k = 1, ..., K1), from the calculated K difference values and the calculated P * K1 values of the P variable quantities X ₁ ,. .., X _P a z wide sample with K1 vector value pairs { y [t1 (k)], X [t1 (k)]} is derived, the coefficient matrix $\underset{\_}{\underset{\_}{\text{C}}}$

C is adapted to the second sample and a prediction is then carried out again, in which the steps are carried out that - the N values x ₁ (t3), ..., x _N (t3), which represent the N state variables x ₁ , ..., x _N at a subsequent time t3, are measured, - the M values u ₁ (t3), ..., u _m (t3), which increase the M manipulated variable u ₁ , ..., u _M accept, measure or specify the time t3, - using the N state variable values x ₁ (t3), ..., x _N (t3), the M manipulated variable values u ₁ (t3), ..., u _M (t3) and the adjusted coefficient matrix $\underset{\_}{\underset{\_}{\text{C}}}$

the N values x ^ ₁ (t4), ..., x ^ _N (t4), which assume the N state variables x ₁ , ..., x _N at a predetermined later time t4, are at least approximately predicted and - the predicted N state variable values x ^ ₁ (t4), ..., x ^ _N (t4) can be used for further navigation of the underwater vehicle (1). Procedure according to Claim 7 , characterized in that the step, the coefficient matrix $\underset{\_}{\underset{\_}{\text{C}}}$

C to adapt to the second sample, which comprises the steps that - in the second training phase using the first sample and the second sample, an overall sample is generated and - using the overall sample and the context $\underset{\_}{\text{y}}=\underset{\_}{\text{X}}*{\underset{\_}{\underset{\_}{\text{C}}}}^{\text{T}}$

the coefficient matrix $\underset{\_}{\underset{\_}{\text{C}}}$

is recalculated. Method according to one of the preceding claims, characterized in that M values u ₁ (t0), ..., u _M (t0) of the M actuating variables for the time t0 are given as a test, using the N state variables measured for the time t0 Values x ₁ (t0), ..., x _N (t0), the M manipulated variable values u ₁ (t0), ..., u _M (t0) and the linear dependencies F _j for the time t0 P values X ₁ (t0) ..., X _P (t0) are calculated, which are the P variable quantities X ₁ , ..., Accept X _P according to the specification for the time t0, using the N measured state variable values x ₁ (t0), ..., x _N (t0), the P calculated values X ₁ (t0) ..., X _P (t0) and the coefficient matrix $\underset{\_}{\underset{\_}{\text{C}}}$

the N values x ^ ₁ (t5), ..., x ^ _N (t5) are at least approximately predicted, which have the N state variables x ₁ , ..., x _N at a predetermined point in time t5, if the trial-prescribed control variables -Values u ₁ (t0), ..., u _M (t0) are actually used, the N state variable values x ^ ₁ (t5), ..., x ^ _N (t5) predicted for the time t5 with a predefined criteria are compared and, depending on the result of the comparison, a decision is made as to whether the test values M ₁ u ₁ (t0), ..., u _M (t0) of the M actuating variables are actually used for navigating the underwater vehicle (1). Method according to one of the preceding claims, characterized in that the geoposition of the underwater vehicle (1) is measured or specified at time t0 and using at least one predicted value for a state variable a geoposition of the underwater vehicle (1) is predicted at a future time. Underwater vehicle (1) with - an actuator arrangement (14, 15, 16, 17) with at least one actuator, - a manipulated variable sensor arrangement - a state variable sensor arrangement and - a computer, the actuator arrangement (14 , 15, 16, 17) can be changed by M adjustable and measurable manipulated variables u ₁ , ..., u _M with M> = 1, the manipulated variable sensor arrangement being designed to measure the M manipulated variables u ₁ , ... to measure u _M , the state variable sensor arrangement being designed to measure N state quantities x ₁ ,..., _{N of} a system state, where N> = 1, the system state with the movement of the underwater vehicle (1) correlated by the water and the computer being designed to automatically carry out a method according to one of the preceding claims.

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