RU2444759C1 - Navigation method of underwater object by means of hydroacoustic navigation system - Google Patents

Abstract

FIELD: radio engineering.

SUBSTANCE: navigation method of underwater object is implemented by means of hydroacoustic navigation system containing navigation base of M hydroacoustic transmitters-responders with various response frequencies and hydroacoustic receiver-transmitter arranged on navigation object. Hydroacoustic transmitters-responders are arranged on drifting stations along water surface and bottom stations at sea bottom. Measurement results are processed as per spatial-time observations. During calculation of coordinates there performed is minimisation of error as per distribution of measured coordinates; at that, to calculation device there introduced are local Cartesian coordinates for the considered spatial-time area in which drifting station, bottom responding beacons and underwater object is arranged.

EFFECT: higher reliability during navigation of underwater objects.

11 dwg

Description

The invention relates to the field of sonar navigation systems and can be used for navigation support of underwater vehicles of increased range, for example, operating in ice conditions, making it difficult for the supply vessel to access them, and can also be used for seismic and geological exploration on the seabed.

Known methods and devices designed to solve the problems of navigation and positioning through sonar systems (RU 2032187 C1, 03/27/1995 [1], RU 2158431 C1, 10/27/2000 [2], RU 34020 U1, 11/20/2003 [3], RU 2289149 C2, 12/10/2006 [4], US 2008008045 A1, 01.10.2008 [5], US 4024491 A, 05.17.2007 [6]).

The well-known sonar synchronous rangefinder navigation system [1], contains a bottom navigation base of M hydroacoustic transponders with different response frequencies and a hydroacoustic transmitter, a clock generator, an M-channel receiver, M meters of propagation time of hydroacoustic signals to and from transponders located on the navigation object, M · N blocks for converting time intervals in the distance by N in each of the channels from M, M blocks for selecting the maximum value of the distance from N beginnings and a coordinate calculator of the navigation object, in which each of the M channels is entered according to the number of ray paths N-1 of additional measuring instruments for the propagation time of hydroacoustic signals, N-1 multivibrators of delay, N-1 multivibrators of the strobe pulse, N-1 selectors, the first inputs N-1 propagation meters are connected to the output of the clock generator, the second inputs are connected to the first outputs of the corresponding selectors, and the outputs are connected to the M · N inputs of the block for converting time intervals to distances, the first input of each of the selectors is connected to the output of the corresponding multivibrator of the strobe pulse, the second input is connected to the output of the corresponding receiver channel, the input of the first delay multivibrator is connected to the output of the corresponding receiver channel, and the output of each subsequent delay multivibrator is connected to the second output of the corresponding selector, to each of M channels introduced N (N-1) additional blocks for converting time intervals into distances, N-1 additional blocks for selecting the maximum distance value and a distance averager, and the inputs of each of the N-1 sets of N blocks for converting time intervals into distances are connected to the corresponding outputs of N-1 additional time interval meters, and the outputs are connected to the inputs of N-1 additional blocks for selecting the maximum value, the outputs of all blocks the choice of the maximum distance values are connected to N inputs of the distance averager, and the output of the distance averager is connected to the input of the coordinate calculator of the navigation object.

This system implements a method for navigating an underwater object, including placing hydroacoustic transponders at the bottom of a reservoir, creating a navigation base of M hydroacoustic transponders with different response frequencies, calibrating using external means to provide a navigation base, and using the hydroacoustic transmitter located on an underwater object, measure time intervals propagation of signals with their subsequent conversion in the distance between the underwater object and sonar receivers vetchikami. To obtain reliable measurement results, the measured distances are averaged.

The navigation base of such systems, pre-installed at the bottom of the water area, as a rule, consists of 12-16 beacon transponders and is pre-calibrated in relative and geographical coordinates (relative and absolute calibrations) using a support vessel equipped with an on-board complex of satellite and sonar navigation systems. After developing their energy resource, the transponder beacons are replaced, and a new calibration of the bottom navigation base is performed. This method allows for the geographic location of the underwater vehicle within an area of up to 100 square kilometers and a length of up to 50 kilometers.

Using the known method for navigating underwater vehicles requires a significant amount of ship time, a large number of bottom transponder beacons with a long autonomy, limits the range of the underwater vehicle to the communication range with the bottom navigation base. Considering that underwater stations are subject to the influence of hydrological and lithodynamic factors, in order to obtain reliable results of navigation of underwater objects, calibration work is required to be performed not only when installing and removing underwater stations, but also during their operation when external factors change.

When conducting research work using autonomous underwater manned vehicles, performing operational and tactical tasks by underwater vehicles at sea ranges of up to thousands of kilometers and an area of tens of thousands of square kilometers, operational highly reliable provision of these works without the use of a support vessel is of particular importance.

There is also known a method for navigating an underwater object using a sonar navigation system containing a navigation base of M hydroacoustic transponders with different response frequencies and a sonar transceiver located on the navigation object, by which the signal propagation time intervals are measured with their subsequent conversion in the distance between the underwater object and sonar transponders.

According to this method, hydroacoustic transponders are placed at drifting stations on a water surface, the navigation parameters of an underwater object relative to a drifting station or base from drifting stations are determined in a mode with a long and / or ultrashort base, and / or in a combined mode (long + ultrashort base), and / or in the direction-finding system, in this case, two navigation bases are formed from receivers with a common center of the base, placing them in a plane parallel to the plane of the deck of the underwater object, while one base X is directed along the axial line of the underwater object, and the axis of the other base Y is directed along the beam to the right ([7] patent RU No. 2365939).

When implementing this method, unlike the known devices [1-6], a drifting station equipped with appropriate equipment is located on the sea surface, and which, while in a drift, has the ability to continuously receive signals from medium-orbit satellite navigation systems, process them with the determination of high-precision eigen coordinates at any given time. At a certain point in time (according to a request signal from an underwater object or according to the work program of a drifting station) this information is transmitted via a hydroacoustic channel in the form of a noise-like encoded signal of a certain format to an underwater object. Having determined its coordinates relative to the drifting station and having information about the geographical coordinates of the latter, the underwater object performs its own coordination in the geographical coordinate system.

A common disadvantage of the known devices, which are sonar navigation systems [1-7], is a significant error in determining the coordinates associated with the variability of the speed of sound in sea water. Moreover, the error in determining the distance and coordinates increases significantly when working in the shallow sea, when the time delays between the individual rays are reduced, and the rays themselves cannot be identified and identified separately.

To reduce the measurement error by means of computing, as a rule, methods based on formula dependencies are used, which partially allows minimizing the error in estimating the arithmetic mean of the hydroacoustic characteristic from spatio-temporal arrays of observations.

In known methods, the arithmetic average for any task is calculated by direct summation of all measured values falling into the considered spatio-temporal volume and divided by the total number of measurements.

In fact, this method of calculating the arithmetic mean of the hydrological characteristic does not allow us to obtain the minimum possible error in estimating the mean. The reason for this is that in the adopted method, the distribution of observation points over the spatio-temporal volume is ignored. Moreover, the accuracy of estimating the average value of the applied method decreases with increasing dimension of the space of observation coordinates.

In navigational practice, when determining an observation by three or more distances or / and bearings, the point of location of the underwater object refers to the center of the error triangle. The question arises of the degree of reliability of such a rule. This question is important, for example, for the validity of the assertion that the area of the error triangle serves as a measure more accurately than the observation - the larger the area of the error triangle, the more accurate the observation. This statement makes sense only if it is known that the observation point lies inside the compared error triangles.

In this case, when processing the obtained data by means of a hydroacoustic system, the arcs of circles are drawn on the navigation map, the centers of which are images of landmarks (bottom beacons), and the radii are equal to the measured distances on the map scale, and the observable location (coordinates) of the underwater object is determined at the intersection of the arcs . Moreover, if the circles at one point do not intersect, then the observable place is taken in the middle of the figure of errors. Moreover, if the error is large (its sides on the map are more than 5 mm), then check the accuracy of identification of landmarks, measurements and laying (Reference officer / Pronichkin A.P., Chuprikov M.K., Skvortsov M.I. and others . - M.: Military Publishing, 1975, p.205-206). Moreover, the processing of measurement results is burdened by significant laboriousness, due to numerous operations to verify the accuracy of identification of landmarks, measurements and laying, and ultimately there is a relatively low reliability of determining the coordinates.

In well-known sonar navigation systems, the problem of estimating a place by known distances is solved on the basis of the linear method (Kolomiychuk ND Hydrography. L .: Publishing House of the Navy, 1975, 470 p.). The basis of this method is the well-known dependence valid for geometry on the plane that the sought place lies at the intersection of circles with centers at reference points (landmarks) and radii corresponding to the measured distance to them. This dependence, valid for small distances, for large distances requires the introduction of special corrections that take into account the position of reference points in three-dimensional space and the speed of sound propagation in water at different horizons, which leads to the complexity of the known methods. In addition, with a linear formulation of the solution to this problem, it is impossible to obtain an estimate of the accuracy of the coordinates obtained, as well as errors due to the laying of position lines on the navigation map.

The relative coordinates in known systems are determined by the azimuthally rangefinding method (measured parameters of bearings and distance), or by the method consisting in the fact that the bearing and the moment of arrival of the signal from the beacons of the transponders are simultaneously recorded on an underwater moving object. The distance measurement is based on the measurement of the time interval from the moment the transponder emits the signal from the beacon (information on this is contained in the encoded signal) until it is received on the underwater moving object. It is also possible to use the direction finding method, in which only the bearings are measured, or the combined method, which consists in measuring distances and / or bearings and taking into account the distance traveled during this time along the standard lag of an underwater object (mainly an absolute lag measuring speed relative to the ground) .

In the first version, the determination of coordinates requires highly accurate knowledge of the speed of sound propagation in water, which affects the accuracy of determining the distance, as well as the presence of errors in the measurement of distance due to refraction. The second option is also characterized by the introduction of errors in the measurement of distance due to refraction. The main condition for the implementation of the third option, by monitoring the distance traveled through the lag, from the point of view of ensuring the required accuracy, is to achieve maximum accuracy in measuring the vector of the distance traveled during the observation, which requires the use of measurements of the distance traveled by the absolute sonar lag during the observation period, the main component of the error which is also due to a change in the speed of sound in the aquatic environment.

When conducting research work using autonomous underwater manned vehicles, performing operational and tactical tasks by underwater vehicles at sea ranges of up to thousands of kilometers and an area of tens of thousands of square kilometers, operational highly reliable provision of these works without the use of a support vessel is of particular importance. The well-known system consisting of placed bottom beacons responders to ensure subsequent geographical location of the underwater vehicle has significant limitations both in terms of the range of the landfill and the complexity of performing calibration work and work related to the placement and installation of bottom stations with each replacement of power sources having a limited life.

When implementing each of the known methods for determining coordinates from landmarks, a necessary condition for obtaining the required accuracy is that the measured parameters characterizing the position lines when building them on the navigation map intersect at one point, which is only ensured if observations, calculations, and laying did not contain any errors. Moreover, in practice, the bearing lines form a triangle of errors, and if the size of the sides of the triangle of errors is small, then the probable place of the vessel is taken in the center of the triangle. Finding these lines and, consequently, the place of the vessel is a minimax optimization problem. Its direct immediate solution is a difficult task, so when solving it by known methods it is very difficult to obtain the necessary accuracy in determining the coordinates of moving marine objects relative to landmarks. Achieving acceptable accuracy requires laborious calculations even when using automated tools. This is due to the fact that existing standards for the representation of numbers in computers do not support all the necessary properties for ensuring arithmetic operations.

For example, when performing arithmetic operations in a floating-point format, the laws of commutativity, associativity and distributivity, which are mandatory in arithmetic, are not fulfilled (Akritas A. Fundamentals of computer algebra with applications. - M .: Mir, 1994. - 544 p.). This circumstance does not allow us to find straight lines intersecting at one point for which the sum of deviations from bearings is minimal.

The construction of an error triangle also does not completely solve the problem of obtaining reliable coordinates, since when finding errors, an interval analysis is used, which is based on the surrounding of real numbers characterizing the coordinates by intervals, which leads to the need to solve the problem of numerical data (a contradiction between continuous and discrete). Geographic coordinates are abstractly defined in continuous space and are represented as real numbers. Further, real numbers are represented (approximated) by rational numbers - a discrete set. In turn, rational numbers are most often written in decimal form, which further distorts the model of continuity of geographical coordinates. This leads to divergence in the estimation of the coordinates obtained, due to a mismatch between the actual measurement accuracy and the digital representation of this measurement, i.e. a mismatch between the number of significant digits provided with accuracy and the number of significant digits in the presented result, and a mismatch in the accuracy of two or more compared coordinate values.

To obtain reliable data, the measurement results are presented in digital form with the number of significant digits corresponding to the measurement error. This leads to an excess of significant figures, which, when presenting the measured information, leads to an increase in the volume of processed information, an increase in the required volumes of read-only memory for its storage and main memory during its processing and the processing time itself. The source of the variability of the measured data is the procedure for the exchange of information between computers and measurement tools. In known methods, floating point numbers are used to represent the values of geographical coordinates. Therefore, the geographical coordinates recorded initially in degree measure (rational numbers), when entered into a computer, are translated into decimal notation. To store the measured geographical coordinates, the format with the maximum bit depth available for the computer used is used, which leads to numbers with a large number of decimal digits that are not provided with measurement accuracy. When representing geographical coordinates in a computer in a floating point format, the corresponding numerical values have unreasonably high accuracy, and the actual error is usually not determined. All measured values of geographical coordinates are represented by decimal numbers with the same number of decimal places. The number of bits is determined not by the measurement error of geographical coordinates, but by the capacity of the processor used by the computer. The same bit depth of the representation of geographical coordinates creates the illusion of the legitimacy of performing cartometric tasks using sets of measured data having different accuracy of geographical coordinates.

The objective of this technical proposal is to increase reliability while ensuring the navigation of underwater objects while reducing labor intensity.

The problem is solved due to the fact that in the method of navigating an underwater object using a hydroacoustic navigation system, which includes placing a navigation base of M hydroacoustic transponders with different response frequencies and placing a hydroacoustic transceiver on an underwater navigation object, by which the signal propagation time intervals are measured with their subsequent conversion in the distance between the underwater navigation object and sonar transponders, times placement of hydroacoustic transponders at drifting stations on the water surface and bottom stations on the seabed, determining the navigation parameters of the underwater navigation object relative to the bottom and / or drifting station or base from drifting stations, which are determined in the mode with a long and / or ultrashort base, and / or in the combined mode (long + ultrashort base), and / or in the direction finding system, while forming two navigation bases from the receivers with a common center of the base, placing them in a plane parallel the plane of the deck of the underwater navigation object, while the axis of one base X is directed along the axial line of the underwater navigation object, and the axis of the other base Y is directed along the beam to the right, processing the measurement results from spatio-temporal arrays of observations, determining the coordinates of the underwater navigation object by calculations When calculating the coordinates, the invention minimizes the error in the distribution of the measured coordinates, while the local Cartesian coordinates d I considered the spatio-temporal region in which the drifting station, bottom transponder beacons and the underwater object are located, while determining the temporal course of the hydroacoustic characteristics for the obtained time series, the extreme values of the hydroacoustic characteristics in each obtained series of measurements using the Gerst statistic, and the arithmetic mean values of the hydroacoustic characteristic for spatio-temporal arrays of observations are performed by calculations using multidimensional quadrature Haar formulas and functions.

The determination of the temporal course of the hydroacoustic characteristics for the obtained time series, by determining the extreme values of the hydroacoustic characteristics in each obtained series of measurements by the Gerst statistics method, and the estimation of the arithmetic mean value of the hydroacoustic characteristics by spatio-temporal arrays of observations by calculations using multidimensional quadrature formulas and Haar functions allows minimizing errors in measuring the coordinates of the underwater object ..

The proposed method is implemented as follows.

In the research area, a navigation base is formed by placing bottom transponder beacons on the seabed, and on the water surface - drifting stations, which are a device consisting of a polyurethane housing, on which a mast is installed with a satellite antenna and, if necessary, meteorological sensors. Inside the case, equipment for measuring, processing and storing information is installed. The design of devices for implementing the proposed method and the principle of their operation are similar to the devices of the prototype.

When installing a large group of drifting stations, communications equipment may also include a repeater that receives the radio signal from the drifting station in the UHF band (401-403 MHz), combining with the signals of other drifting stations and bottom beacon responders located in the area of the drifting station, in a common group signal and simultaneous transmission to ground-based reception points in two trunks of the SMB range (4/6, 7/8 GHz), and, if necessary, the communication facility may also include a coastal satellite communication station, which It accepts the emitted group signal of the repeater and contains message recovery equipment including a decoder and a message processing and recovery device, a storage device, and a control device.

Message processing includes error-correcting coding, breaking each message into packets with a duration depending on the state of the excited surface, transmitting message packets to the repeater according to an algorithm automatically generated depending on sea waves, which is determined by the satellite navigation system in accordance with known algorithms (description of RF patent No. 2254600).

The use of drifting buoy stations (drifters) equipped with a GPS receiver and equipment for a hydroacoustic communication channel as navigation beacons located on the sea surface in combination with bottom transponder beacons allows for high-precision navigation for underwater objects.

Obviously, the location of the navigation drift beacon on the sea surface does not require relative and absolute calibration of the landfill, which is necessary when using bottom sonar transponder beacons, since the drifter's GPS receiver allows it to “know” its geographical coordinates in real time with high accuracy (for example, the accuracy of determining coordinates using a satellite navigation measuring module of the SNIM type developed by the Russian company Navis is no worse than 5 meters s). Navigation of an underwater object relative to a drifting station or a base of drifting stations can be carried out both in the mode with a long, ultrashort base (DB and UKB), and in the combined DB / UKB mode.

The underwater object is equipped with hydroacoustic transmitting and receiving antennas corresponding to the operating mode, a navigation controller, and navigation mathematical software. The drifter beacon operates in the request-response mode and in the pinger mode (beacon). In the long base mode, to determine the coordinates of the underwater object, signals from at least 3-4 drifting beacons are used (similar to satellite GPS) and the triangulation problem is solved. In this case, the area or extent of the system coverage area depends on the energy range of hydroacoustic communication, the number of drifters, the depth of the underwater object, hydrology, noise of the underwater object and the sea surface. At the same time, unlike navigation using only the bottom navigation base, navigation using drifters, which does not require calibrations, significantly expands the functionality of the underwater object, makes it possible to quickly equip a training ground of any area and length with the required number of drifters, and allows the underwater object determine your coordinates in real time, quickly change your tactical tasks without losing navigation information, receive data on your coordinates any necessary time or permanently in the automatic mode.

When navigating an underwater object while operating at depths of more than one kilometer, it is advisable to work at frequencies in the range from 8 to 15 kHz, while the energy range of communication with the drifting beacon will reach 10-14 km, and the error in determining the coordinates of the device will be 7-10 meters in the DB mode and 0.3% of the range in the UKB mode and 0.5 degrees in the direction finding angle. At a working depth of less than one kilometer, it is advisable to use operating frequencies in the range of 25-35 kHz and work in the UHF mode. In this case, the maximum communication range will reach about 3 km.

A special purpose is the ability of an underwater object to determine its coordinates using beacons drifters in passive mode. In this case, the drifter beacons are switched to the automatic periodic emission of sonar signals (pinger mode) with high accuracy of synchronization, and the underwater object, receiving these signals and using the special algorithm and mathematical software for processing, determines its geographical coordinates relative to coordinates of the drifting beacon or navigation base from drifting beacons. It should be noted at the same time that each signal of the drifting beacon has a special format and encoding and carries information about the geographical coordinates of the drifting beacon, its individual number, direction and speed of its movement on the surface.

The algorithm of the navigation system using drifters has a flexible structure and can be easily adapted both to a pre-laid route of an underwater object at the range, and to determine the coordinates of the underwater object at any specific time of its operation at the range under various hydrological conditions, noise conditions. Additional opportunities for providing operational navigation of an underwater object are provided by the installation (launch) of a drifting beacon directly from the underwater object at the right time.

At the same time, during the ascent to the surface, the lighthouse-drifter can measure the sound velocity profile and hydrological parameters, which is necessary when calculating the exact coordinates of the underwater object. After the drifter is raised to the surface, it enters the GPS satellite signal reception mode and sonar signals are transmitted to the underwater object in the “request-response” mode or “pinger” mode. The underwater object records the distance and bearing to the drift lighthouse (UKB mode) and calculates its exact geographical coordinates using information received from the drift lighthouse via the sonar communication channel. The sonar transmission rate may be 9600-12400 baud. The most optimal communication range in UKB mode with an underwater object depth of up to 500 meters is 1 km. Accuracy of determination of coordinates to 5 meters.

The presence of a hydro-acoustic communication channel between the drifter and the underwater object also allows the transmission of service information from the ground center to the underwater object via a satellite telemetric communication channel through a drift station located in the hydro-acoustic communication zone with the underwater object.

In the proposed method, a combined hydroacoustic navigation system with a long and ultrashort base is used, which allows the use of a direction finding system for solving the problem of an underwater object reaching the drift station installation point. In this case, the hydroacoustic antenna of the underwater object is two having a common center of the base of the receivers. Moreover, if two receiving bases are located in a plane parallel to the deck plane and are orthogonal, the axis of one base is directed along the axial line of the underwater object, and the axis of the other base is directed to the right along the beam.

Two having a common center base of receivers allow you to determine the direction to the signal source as the line of intersection of two conical surfaces with matching vertices.

Since the plane of the deck almost never coincides with the plane of the horizon, the influence of heel and trim angles is also taken into account.

Information on the coordinates of the drifting station relative to the underwater object allows us to solve the problem of the underwater object reaching the reference point, since it can easily be converted into heading angle and distance. Solving the inverse problem makes it possible to determine the coordinates of an underwater object on a map or tablet on which a reference point is previously applied. In the case where the inclined distance to the drifting station is also determined, the third position surface is a sphere with a radius equal to the inclined distance.

Components of an underwater object include a receiving hydroacoustic antenna consisting of four hydrophones. The antenna section consists of two single-channel and one two-channel module, located on a linear carrier bracket. The distance between the receiving hydrophones of the two-channel module is 50 mm. The maximum spacing of the extreme receivers on the bracket is 1000 mm. The bracket is perforated, which allows the receivers to be located in close proximity to each other for phase calibration and with arbitrary spacing for measuring the direction of arrival of the acoustic signal. Piezoceramic spheres with a diameter of 30 mm are used as hydrophone receivers, inside of which preliminary amplifiers with a gain of 30 dB are placed. The spheres are placed on a steel plate measuring 145 × 145 × 10 mm, equipped with fasteners and an acoustic plug on the back side. The suppression ratio of the audio signal from the back is at least 30 dB.

The antenna complex consists of an 8-channel 2-section receiving hydroacoustic antenna and a hydroacoustic emitting antenna.

Each section of the receiving antenna is a 4-element non-equidistant hydrophone module designed to measure the projection of the acoustic signal arrival vector onto one of the horizontal axes in the ultrashort base mode, in the direction finding mode, or for receiving signals in the long base mode at 4 operating frequencies. Sections of the receiving antenna are located in a horizontal plane perpendicular to each other.

Thus, when all hydrophones receive at the same working frequency, the mode for determining the delay and direction of arrival of the response from a fixed drifting station in ultra-short base mode is implemented, and when each of the hydrophones is tuned to its working frequency, a mode for measuring delays from drifting stations in long base mode. A similar device has bottom beacons responders.

The system for transmitting information through a sonar channel at an underwater object is implemented using standard sonar communication equipment. At the same time, as the devices for generating and processing signals, both the hydroacoustic equipment available in the composition, providing the hydroacoustic communication mode, and additional devices in the form of consoles connected to their transmitting and receiving paths can be used.

As location signals, tonal signals with a frequency of 3 kHz are used, emitted both in automatic mode according to a special program and in a request mode.

The satellite communications module is designed to form packets and control algorithms for transmitted information.

As a result of direction finding, an array of data (distances and / or bearings) is obtained. Put on the navigation map the position of the landmarks (figure 1) p ₁ , p ₂ , p ₃ and the measured bearings d ₁ , d ₂ , d ₃ . To determine the coordinates of a moving marine object, constructs are performed on the dual plane (Fig. 2), where the points of the landmarks p ₁ , p ₂ , p ₃ correspond to the dual straight lines p ₁ , p ₂ , p ₃ , the coordinates of which are determined by the formula d: у = ax + b → d (a, -b). The direct bearings of d ₁ , d ₂ , d ₃ will correspond to the dual points d ₁ , d ₂ , d ₃ , the coordinates of which are determined by the formula p (a, b) → p: ax-b. If bearings on the main plane do not intersect at one point, then on the dual plane, points d ₁ , d ₂ , d ₃ do not lie on one straight line. The least squares method is used to find a straight line po, the least deviating from the points d ₁ , d ₂ , d ₃ . This straight line on the dual plane corresponds to the desired location point ro of the marine moving object on the main plane (O is the point in Fig. 1). The straight line po in the dual plane intersects all three lines p ₁ , p ₂ , p ₃ . In figure 2, the intersection points are indicated by circles (O). These intersection points correspond to such bearings on the main plane (dashed lines in figure 1), which intersect at one point po.

Further, the numerical values of the obtained coordinates are presented in the form of symbols, the number of which corresponds to the representation of the number with a given accuracy, which is almost equal to the number of bits in the binary representation of this number with the same accuracy. Moreover, the record of the number in the symbol system contains information not only about the measured value, but also contains information about the error in representing the number. This operation is carried out by means of a computer, which, along with means for measuring distances and bearings and a plotter, forms an automated system for determining the location of a moving marine object. The symbolic representation of numbers characterizing the measured coordinate values is carried out by constructing the Stern-Brock binary tree (Graham R., Knut D., Patashnik O. Concrete mathematics. - M .: BINOM. Laboratory of Knowledge, 2006. - 703 p.) .

The sequence of characters in the representation of the number characterizing the coordinates is determined by all the corresponding nodes in the Stern-Broco tree. For the lowest node, its neighbors are found both vertically and horizontally, which allows us to evaluate the accuracy of the representation of the number and, if necessary, switch to the representation of this number with a different (required) accuracy.

In the problems of taking into account the influence of hydrological phenomena on the speed of sound propagation in the aquatic environment, the choice of the distribution function of hydrological characteristics is important for evaluating extreme values that determine the degree of influence of hydrological conditions on the speed of sound propagation at different horizons of the aquatic environment.

Due to the fact that the extreme values of hydrological and hydroacoustic characteristics are distributed not according to the exponential law, as is characteristic of normally distributed random variables, but according to a power law, this leads to the fact that the damage from the extreme values is much higher than what is usually estimated using normal distribution law. The rationale for this is the classical theory of extrema (Leadbetter M., Rotsen X., Lindgren G. Extremums of random sequences and processes. - M .: Mir, 1989. - 392 p.), Which considers the distribution of the maximum:

where n are independent and identically distributed random variables ξ with the distribution function F (x) for large values of n.

The main result of this theory states that if for some sequences of normalizing constants a _n > 0, b _{n the} random variable a _n (M _n -b _n ) has a non-degenerate limit distribution function G (x), then this function G (x) should have one of three possible forms

Type 1: G (x) = exp (-e ^-x ), -∞ <x <∞,

Type 2:

Type 3:

In particular, it is proved that the “tails” of all distribution functions F (x) have only two types:

- exponential (e ^-x ) for type 1 (for example, for the normal distribution law);

- power law (х ^-α , α> 0) for types 2 and 3.

We show that the extreme values of hydroacoustic characteristics are distributed according to a power law. The logic of the proof is as follows.

Direct statistical estimates of the series of observations cannot evaluate the behavior of the “tail” of the distribution due to the rarity of extreme events. We use an indirect technique, namely, that the behavior of the “tails” of the distributions splits the entire set of non-degenerate distributions of random variables into two equivalence classes - power and exponential. Moreover, linear statistics do not violate this partition. We choose such statistics L (a _n , b _n ) for the time course of the hydrological characteristic ξ (n), which leads to a random variable η (n) distributed according to some law F ^* (y), for which the distribution type is known from the classical theory of extrema her tail. Then the same type of tail distribution will be for the extrema of the sonar characteristic.

As linear statistics we use the statistics of Gerst, which has the form (Feder E. Fractals. - M .: Mir, 1991. - 260 p.):

Where

Let us estimate the distribution function F ^* (y) of the random variable η obtained using this transformation.

Processing time series of hydrological characteristics leads to the following power law

F ^* (y) ~ τ ^H ,

where 1/2 <H <1.

Therefore, Gerst statistics determines a random function distributed according to a power law, which, as proved in the theory of extrema, has a power distribution of the tail. This means that the “tails” of hydroacoustic characteristics have a power-law distribution.

The damage from the extreme value of the hydroacoustic characteristic is obviously a certain power function of the magnitude of the extremum

Q ~ x ⁿ , n <1.

If we use the mathematical expectation of damage as a quantitative assessment of the influence of extreme values of hydroacoustic characteristics during design

where f (x) is the density function of the "tail" of the hydroacoustic characteristic, we obviously get:

при любом n. Для наблюдаемых гидроакустических процессов α~1, и вероятнее всего большое влияние "хвоста" распределения на величину ущерба от возникновения экстремального значения гидроакустической характеристики.For the normal distribution law

for any n. For the observed sonar processes, α ~ 1, and most likely a large influence of the “tail” of the distribution on the amount of damage from the occurrence of the extreme value of the sonar characteristic.

The error in determining the coordinates from bearings is evaluated in the following sequence.

The estimation of the error in determining the coordinates by bearings is illustrated by the drawings.

Figure 3. The location of the bearings relative to the true bearing. Landmark 1, true observation point 2, true bearing 3, left measured bearing 4, right measured bearing 5.

Figure 4. Classes of geometric configurations of three landmarks and observation points. Landmarks 1, true observation point 2, figa - observation point 2 is in a triangle with vertices at points of landmarks 1, fig. 4b - observation point 2 is outside the triangle with vertices at points of landmarks 1.

Figure 5. Classes of configurations. Solid lines are measured bearings, dotted lines are true bearings.

Figa. A class of configurations in which observation point 2 is inside a triangle with vertices at landmark points.

Fig.6b. A class of configurations in which observation point 2 is located outside the vertices of a triangle with vertices at landmark points 1.

7. Charts of the probability of the location of observation point 2 inside the error triangle.

Figa, b, c. Examples of graphs of the total probability of finding the observation point in the error triangle.

Theoretically, the determination of the error is based on a quantitative assessment of this degree of reliability in the form of the probability of finding the observation point inside the error triangle. The solutions to this problem lie in the field of combinatorial probability with some natural assumptions regarding the probabilistic properties of geometric objects. First, we give a few technical clarifications for the sake of uniqueness of the further presentation.

We assume that the measured bearing for a landmark always has a random error with respect to the true bearing. The measured bearing can lie on the left or right relative to the true bearing (figure 3). If the measured bearing lies to the right of the true, then this event will be denoted by the symbol R, and if to the left, then L.

Let us make the following assumptions regarding the probabilistic properties of the deviation of the measured bearing relative to the true one.

1. The density distribution function of the deviation of the measured bearing relative to the true exists, but is unknown. Let, in accordance with this density distribution function, the probability of finding the measured bearing to the left relative to the true one is equal to P _L , then the probability of finding the measured bearing to the right relative to the true one will be equal to P _R = 1-P _L.

2. When observing along three bearings, a lot of errors are pairwise independent random events with their distribution density functions and, therefore, with their P _L (n) and P _R (n), n∈ (1, 2, 3).

Thus, when measuring one bearing, there are only two incompatible events: R and L. This pair of events forms in the considered problem a complete group of events of measuring one bearing Ω ₁ = {R ₁ , L ₁ }. When measuring three bearings, we will have Ω _N = {R ₁ , L ₁ , R ₂ , L ₂ , R ₃ , L ₃ }.

In view of the foregoing, the solution of the problem is reduced to the following steps:

1. To identify all possible combinations of finding the measured bearings on the left or on the right with respect to the true M = {ε ₁ , ε ₂ , ε ₃ }, where ε = {R, L}.

2. Define among the list of combinations M the subset of m combinations for which the observation point will lie in the error triangle.

3. Calculate the total probability P (m) of the appearance of a subset of combinations for which the observation point will lie in the error triangle.

To simplify the presentation, we assume that P _L (n) = P _R (n) = 0.5 (the requirement is equal to probability) for all n = 1, 2, 3 (this restriction will be removed in the future).

Landmarks will be numbered clockwise relative to the observation point. The choice of the first reference point is arbitrary. The reference numbers are in no way related to the bearing measurement order.

The implementation of the first stage of the decision. The number of possible combinations (elements of the set M) is 2 ³ . Table 1 lists all possible combinations.

At the second stage of solving the problem, all geometric configurations have two classes of geometric configurations of three landmarks and an observation point, which have different types of combinations m for which the observation point will lie in the error triangle. This is determined by the fact that the distances from the observation point to the landmarks do not matter (therefore, we will depict the positions of the landmarks on the circle of a unit radius centered at the observation point, taking into account the bearing).

Table 1 The list of possible combinations of finding the measured bearings on the left or on the right relative to the true when observing on three bearings Bearing number 1 (item 6 in FIG. 5) 2 (item 7 in FIG. 5) 3 (item 8 in FIG. 5) Combination number 1 to R R R 2k R R L 3k R L R 4k R L L 5k L R R 6k L R L 7k L L R 8k L L L

One class, denoting its class-A, consists of configurations in which the observation point lies in a triangle with vertices at landmark points (figa), and another class, denoting its class-B, consists of configurations in which the observation point lies outside the triangle with vertices at the points of reference (fig.4b).

Typical situations of finding the measured bearings on the left or on the right relative to true for all combinations of table 1 are presented for configurations of class A in figa, for class B in fig.5b.

From these figures it follows that for class-A configurations for which the observation point will lie in the error triangle consists of combinations corresponding to numbers 1 and 8 of table 1 (m _A = {{R, R, R}, {L, L, L }}), and for class-B configurations it consists of combinations corresponding to numbers 3 and 6 (m _B = {{R, L, R}, {L, R, L}}).

Thus, the result of the second stage consists in proving that when observing in three bearings, the observation point lies in the error triangle with only two combinations in each of the two classes of configurations.

The third step involves calculating the total probability P (m) of finding the observation point in the error triangle. Earlier assumptions about the probabilistic properties of bearing measurement errors allow us to use the theory of combinatorial probability. We get:

в каждом из двух классов конфигураций. Ясно, что всякая конкретная обсервация относится только к одному из двух классов конфигураций.Thus, under the condition of equiprobability (0.5) of obtaining the measured bearing value from the left or from the right with respect to the true value, the probability that the observation point will lie in the error triangle is

in each of two classes of configurations. It is clear that any particular observation refers to only one of two classes of configurations.

Weaken the requirement is equal to probability. We assume that P _R (n) = P ₀ assumes a certain value in the interval zero - unity, and the same for all n = 1, 2, 3. n.

Then (4) and (5) can be written as

и достигается в точке Р₀=1/2.The values of function (3) as P ₀ tends to zero or to unity tend to unity. Indeed, if P ₀ tends to zero, then the first term in (6) tends to zero, and the second to unity, and if P ₀ tends to unity, then the first term in (6) tends to unity, and the second to zero. Since (6) is a continuous non-constant function having a maximum value equal to unity, then (6) should have a minimum. He is equal

and is reached at the point P ₀ = 1/2.

и достигается в точке Р₀=1/2.Values of function (7) tend to zero when P ₀ tends to zero or to unity. Indeed, if P ₀ tends to zero or unity, then the first and second terms in (4) tend to zero. Since (7) is a continuous non-constant function having a minimum value equal to zero, then (6) should have a maximum. He is equal

and is reached at the point P ₀ = 1/2.

Graphs for expressions (6) and (7) are presented in Fig.6.

и для класса-А и для класса-В. Однако при этом для класса-А это точка минимума, а для класса-В - точка максимума (фиг.6).Thus, in the case of P _R (n) = P _{0, the} probability that the observation point lies inside the error triangle substantially depends on the configuration class. An increase in the asymmetry in finding the measured bearing on the left or on the right relative to true for class A increases the likelihood of finding an observation point in the error triangle, and for class B, on the contrary, it decreases. When P ₀ = _^1/2, the probability of finding a point of observation errors of the triangle is equal to

for both Class A and Class B. However, for class A this is the minimum point, and for class B it is the maximum point (Fig. 6).

We assume that P _R (n) has any value in the interval zero - unity, and its own for each n = 1, 2, 3. Then (6) and (7) take the form

The value of function (8) will be maximum (one) if all P _R (n) (n = 1, 2, 3) are equal to one or zero at the same time. The value of function (8) will be minimal (zero) if one of P _R (n) is equal to one, and any other is equal to zero. Hence, since function (8) is continuous, the values of (8) lie in the interval zero - unity.

The value of function (9) will be maximum (one) if P _R (1) and P _R (3) are equal to one, and P _R (2) is equal to zero, or if P _R (1) and P _R (3) are equal to zero , and P _R (2) is equal to one. The value of function (9) will be minimal (zero) if P _R (1) or P _R (3) is equal to zero and P _R (2) is equal to zero, or if P _R (1) or P _R (3) are equal to one and P _R (2) is equal to one. Hence, since the function (9) is continuous, the values of (9) lie in the interval zero - unity.

Some examples of graphs for (8) are presented in Fig.7.

Thus, in the case when P _R (n) has any value in the interval zero - unity, and its own for each n = 1, 2, 3, the probability that the observation point lies inside the error triangle also significantly depends on the configuration class. For Class-A, an increase in the asymmetry in finding each measured bearing by one side (left or right) relative to the true one increases the probability of finding the observation point in the error triangle. For class-B, the probability of finding an observational point in the error triangle is achieved by increasing large (small) values of P _R (1) and P _R (3) and simultaneously small (large) values of P _R (2).

As a result of theoretical analysis, it was found that:

1. The probability of finding the observation point inside the error triangle depends on two classes of relative location (configuration) of the observation point and landmarks, namely the class (class-A), when the observation point is inside a triangle with vertices at the landmark points, and class (class-B ), when the point lies outside the triangle with vertices at the points of reference.

2. Assuming that during one observation the probability that each measured bearing is located on a fixed side from the true bearing is equal to one fixed value P ₀ ∈ [0,1] for this observation, the probability that the observation point lies inside the triangle errors is equal to:

;- for class A not less than

;

.- for class-B no more than

.

3. Under a weaker assumption, if P _R (n) has any value in the interval zero - one, and its own for each n = 1, 2, 3, the probability that the observation point lies inside the error triangle can have any value in the interval zero is one. Moreover, by artificially introducing a “systematic” error into the measured values of bearings, one can obtain a triangle of errors, which, with a probability close to unity, contains an observation point.

The practical implementation of the method is as follows.

Compass bearings are measured for landmarks that are visible and plotted on the navigation map, starting from landmarks lying closer to the diametrical plane of the underwater object.

Correct compass bearings by compass correction. Lay on the navigation map from the corresponding landmarks the lines of the calculated bearings, the intersection of which is the place of the underwater object. In this case, if, when determining from three reference points, the bearing lines at one point do not intersect, forming a triangle of errors, a triangle of errors is constructed, including the observation point in the following sequence.

The obtained values of the three measured bearings {φ ₁ , φ ₂ , φ ₃ } are numbered in order.

The value of the angle α is set, comparable in magnitude with the assumed value of the absolute error when measuring bearings, corresponding to the magnitude of the compass correction.

The class of configurations formed by the observation point and landmarks is determined.

The bearing values {ϕ ₁ , ϕ ₂ , ϕ ₃ } are calculated taking into account the magnitude of the compass correction in this case:

- for a class-A situation: add (or subtract) the values {φ ₁ , φ ₂ , φ ₃ } and α;

- for a class-B situation: add (or subtract) the values {φ ₁ , φ ₃ } and α and subtract (or add) the values {φ ₂ } and α;

- build a triangle of errors on the values of bearings {ϕ ₁ , ϕ ₂ , ϕ ₃ }.

The error value is set according to the values of the observation points located inside the triangle.

In the practice of processing sonar observations, there is the task of estimating the average value of the sonar characteristic in a certain spatio-temporal volume from discrete observations. Each discrete observation is fixed by four coordinates: time, latitude, longitude, and depth (height). In other words, the value of the hydroacoustic characteristic in the general case is a function defined in the four-dimensional coordinate space. In special cases, this dimension can take smaller values. The dimension is determined by the number of coordinates of the observation points, the values of which change in the array of observations. For example, for typical tasks of calculating the average value of the sonar characteristic from discrete observations:

1) by time-discrete measurements at a geographical point with fixed coordinates at a fixed depth;

2) by simultaneous observations in a certain spatial region at a fixed depth;

3) according to observations in a certain area at different points in time and at different points at a fixed depth;

4) according to observations in a certain fixed region for a certain time interval in a certain interval of depths.

The numbering of tasks corresponds to the dimension of the task space of the hydroacoustic characteristics.

In known methods, the arithmetic average for any task is calculated by direct summation of all measured values falling into the considered spatio-temporal volume and divided by the total number of measurements.

In fact, this method of calculating the arithmetic mean of the sonar characteristic does not allow us to obtain the minimum possible error in estimating the mean. The reason for this is that in the adopted method, the distribution of observation points over the spatio-temporal volume is ignored. Moreover, the accuracy of estimating the average value of the applied method decreases with increasing dimension of the space of observation coordinates.

In the inventive method, an adequate method is used to calculate the arithmetic mean of the hydroacoustic characteristic, minimizing the error.

From the mathematical point of view, the task of determining the average value of the hydroacoustic characteristic from the values of the characteristic at discrete space-time points is the problem of estimating the arithmetic mean of a continuous function in a space-time volume from its values at discrete points. The error in the estimation of the arithmetic mean, subject to the isotropy of the variability of the function, is determined by the structure of the "unevenness" of the location of the measurement points in the spatio-temporal volume. The smallest error is given by points uniformly distributed over the volume under consideration. Points are called uniformly distributed in an n-dimensional unit cube if in any hypercube the number of points is proportional to the volume of the hypercube (I. M. Sobol. Multidimensional quadrature formulas and Haar functions. - M .: Nauka, 1969. - 288 p.).

Formally, this is defined as follows. We denote by K ^{n the} unit cube in n-dimensional space: K ⁿ consists of all points P with Cartesian coordinates P = (x ₁ , ..., x _n ) that satisfy the inequalities 0≤x _j ≤1 (j = 1, 2, ..., n). Consider a sequence of points P ₀ , P ₁ , ..., P _i , ... belonging to a cube K ^{n of} dimension n, and denote by S _N (G) the number of points P _i with numbers 0 <i <N-1 belonging to G. The sequence points P ₀ , P ₁ , ..., P _i , ... is called uniformly distributed in K ⁿ (abbreviated pp), if for any nth box π with edges parallel to the coordinate axes,

where V _π is the volume of the parallelepiped π. It can be proved that if G is an arbitrary domain located in K ⁿ and having volume V _G , then it follows from (10) that

Thus, for large N, the number of points of a p.p. sequence belonging to any domain G is proportional to the volume G.

By Weyl theorem (Sobol IM Multidimensional quadrature formulas and Haar functions -. M .: Nauka, 1969. -. 288) to {P _i} was pp, it is necessary and sufficient that any integrable by Riemann, the function f (P) satisfies the relation

Expression (11) is an estimate of the arithmetic mean. The error estimate (11) is determined by the expression

where C is a constant different for functions with different variability, D is the deviation of the distribution of points from p.p.

Deviation D is defined as follows. Consider in K ^{n a} grid consisting of N arbitrary points P ₀ , P ₁ , ..., P _N-1 . To each point P of K ⁿ we associate a parallelepiped π _P with the diagonal OP (O is the origin). The volume V _{P of} this parallelepiped is equal to the product x ₁ ... x _{n of the} coordinates of the point P. The grid deviation P ₀ , P ₁ , ..., P _N-1 is the number

where the upper bound is taken over all P∈K ⁿ .

For the sequence of points to be p.p., it is necessary and sufficient that, as N → ∞

The characteristic D (P ₀ , ..., P _N-1 ) is a very complex function of the structure of the points. The upper bound is D≤N, its lower bound is still not known (with the exception of the case n = 1, when inf D = 1/2). There is an assumption that the best possible estimate of D for an n-dimensional grid consisting of N points is

It should be noted that in hydrometeorology, researchers mistakenly believe that cubic grids (they are called “regular”, “uniform”, etc.) are always very “good” and the purpose of collecting information is to obtain measurements on such a grid.

The cubic grid for N = M ² points is specified by the coordinates

where i ₁ , i ₂ , ..., i _n - independently run through the values 1, 2, ..., M. Figure 9 shows a cubic grid with n = 2, M = 4.

будет максимальным, например, в точке P'=(1/2M,1,1,…,1), когда S_N(π_p')=0, NV_P'=N/2M=M_n ^-1/2. Следовательно,It is easy to verify that for such grids the value

will be maximum, for example, at the point P '= (1 / 2M, 1,1, ..., 1), when S _N (π _p' ) = 0, NV _{P '} = N / 2M = M _n ^-1 / 2. Hence,

- такой же порядок соответствует случайным сеткам, состоящим из N независимых случайных точек, равномерно распределенных в Kⁿ. Значит при n≥3 сетки (16) асимптотически хуже случайных.It follows from formula (17) that for n = 1, cubic grids are optimal. However, with increasing n, the uniformity of the grids (16) worsens and the orders in formula (17) approach the worst, equal to N. Already at n = 2, order (17) is equal

- the same order corresponds to random grids consisting of N independent random points uniformly distributed in K ⁿ . Therefore, for n≥3, grids (16) are asymptotically worse than random ones.

, которое образует сетку с наибольшей степенью равномерного распределения. Решение этой задачи будем искать следующим образом. Определим подходящую опорную сеть точек, имеющую p.p. Сравнивая координаты точек наблюдений с координатами точек опорной p.p. сетки, найдем искомое подмножество

, которое будет давать минимальную ошибку в оценке среднего арифметического, в соответствии с (12).Let K ⁿ set a set of observation points for the sonar characteristic P ₀ , P ₁ , ..., P _N-1 . This set of points is far from pp. It is necessary to define such a subset of points

which forms the grid with the greatest degree of uniform distribution. We will seek a solution to this problem as follows. We define a suitable reference point network with pp. Comparing the coordinates of the observation points with the coordinates of the points of the reference pp grid, we find the desired subset

, which will give a minimal error in the estimation of the arithmetic mean, in accordance with (12).

In computational mathematics, many variants of grids close to pp are constructed. For our task, it is advisable to choose a grid with a sequence of points Q ₀ , Q ₁ , ..., Q _i , ... that satisfies three requirements:

1) the uniformity of the distribution of the grid should be asymptotically optimal;

2) uniform distribution of points should be observed not only as N → ∞, but already for small N;

3) the algorithm for calculating the points Q _i should be quite simple.

These requirements are satisfied, for example, by the so-called LP _τ - sequences (I. Sobol. Multidimensional quadrature formulas and Haar functions. - M.: Nauka, 1969. - 288 p.).

Without setting out a theoretical justification for p.p. properties of these sequences, we present a simple calculation algorithm.

In this algorithm, the coordinates (q _i1 , ..., q _in ) of the point Q _i from the LP _T - sequence are calculated by the formula

- двоично-рациональные числа вида

, числители которых табулированы.where i = e _m ... e ₂ e ₁ is the representation of i in the binary system,

- binary rational numbers of the form

whose numerators are tabulated.

для 1≤s≤20 и 1≤j≤4, что позволяет легко вычислять точки Q_i размерности n≤4 в количестве N≤2²⁰.Table 2 presents

for 1≤s≤20 and 1≤j≤4, which makes it easy to calculate points Q _{i of} dimension n≤4 in the amount of N≤2 ²⁰ .

The deviations of D for the LP _τ sequence in the double logarithmic scale, respectively, for the one-dimensional (A), two-dimensional (B), three-dimensional (C) and four-dimensional (G) LP _τ- sequences are presented in Fig. 10.

table 2

Value table

s n one 2 3 four one one one one one 2 one 3 one 3 3 one 5 7 one four one fifteen eleven 5 5 one 17 13 31 6 one 51 61 29th 7 one 85 67 81 8 one 255 79 147 9 one 257 465 433 10 one 771 721 149 eleven one 1285 823 719 12 one 3855 4091 3693 13 one 4369 4125 3841 fourteen one 13107 4141 11523 fifteen one 21845 28723 16641 16 one 65535 45311 49925 17 one 65537 53505 16671 eighteen one 196611 250113 83229 19 one 327685 276231 515921 twenty one 983055 326411 482707

For example, in Fig. 11, the position of the LP _τ sequence for the first 16 points is shown for a two-dimensional unit region. The position of the points indicates that it is significantly different from the "regular location" shown in Fig.10. The algorithm for selecting representative points can be represented as follows:

Given: a set of N observation points P ₀ , P ₁ , ..., P _N-1 in an n-dimensional cube K ⁿ , n = 1, 2, 3, 4. Each observation point is represented by the normalized coordinates P = (x ₁ , ... , x _n ), 0≤x _j ≤1, j = 1, 2, ..., n.

, которые дают наименьшую ошибку в оценке среднего арифметического функции, измеренной в этих точках (т.е наиболее репрезентативный набор точек измерений для оценки среднего или, что тождественно, образуют сетку с наибольшей степенью равномерного распределения).Required: Define a subset of points

which give the smallest error in the estimation of the arithmetic mean function measured at these points (i.e., the most representative set of measurement points for estimating the mean or, identically, form a grid with the greatest degree of uniform distribution).

Initiation: T _k = T ₀ = ⌀ - a set of candidate points at the k step.

Solution flow:

1. Calculate N points of Q _k (k = i, ... N) LP _τ -sequences by formula (18).

2. Consistently for each k from 1 to N:

среди множества точек {Р₁, …, Р_N}\Т_k-1,

, и добавить ее в набор точек-кандидатов на k, образуя

.2.1. For each point Q _k find the nearest point in the Euclidean metric

among the set of points {P ₁ , ..., P _N } \ T _k-1 ,

, and add it to the set of candidate points on k, forming

.

Calculate the deviation D _k = D (T _k ) for the point P _i according to the formula (7).

5. Sequentially for each k from 1 to N find D _0k = max (D ₁ , ..., D _k ).

6. Find k ₀ for which there is a minimum value of D _0k .

является искомым множеством точек наблюдений, дающим минимальную ошибку в оценке среднего арифметического.Result: point set

is the desired set of observation points giving a minimal error in the estimation of the arithmetic mean.

Thus, when calculating the arithmetic mean of the hydroacoustic characteristic from discrete observations in a certain spatio-temporal volume, in order to minimize the error, it is necessary to take into account the distribution of measurement coordinates. For the calculation to be correct, local Cartesian coordinates are introduced into the computing device for the considered spatio-temporal region, in which the drifting station, bottom transponder beacons and the underwater object are located.

A method for navigating an underwater object using a hydroacoustic navigation system is implemented through a navigation base of M hydroacoustic transponders with different response frequencies and a hydroacoustic transceiver located on the navigation object, which measures the propagation time intervals of the signals with their subsequent conversion into the distance between the underwater object and hydroacoustic transponders.

Hydroacoustic transponders are placed at drifting stations on the water surface and bottom stations on the seabed, the navigation parameters of the underwater object relative to the bottom and / or drifting station or base from the drifting stations are determined in a mode with a long and / or ultrashort base, and / or in a combined mode ( long + ultrashort base), and / or in the direction finding system, in this case, two navigation bases with a common center of the base are formed from receivers, placing them in a plane parallel to the plane of the underwater deck object, wherein the one base axis X is directed along the center line of the underwater object, and another base Y axis is abeam the right.

When processing the measurement results, the arithmetic mean value of the hydroacoustic characteristic is estimated from the spatio-temporal arrays of observations by calculation.

When calculating the coordinates, the error is minimized by the distribution of the measured coordinates, while the local Cartesian coordinates are introduced into the computing device for the considered spatio-temporal region, in which the drifting station, bottom transponder beacons and the underwater object are located, while determining the time course of the hydroacoustic characteristics for the received time series, while determining the extreme values of the hydroacoustic characteristics in each obtained series of measurements using the st Gerst's atistics, and the arithmetic mean value of the hydroacoustic characteristic is estimated from spatio-temporal arrays of observations by calculations using multidimensional quadrature formulas and Haar functions.

Using the proposed method allows you to effectively carry out the required operations of comparing the coordinates by eliminating the processing of different exact data when determining the coordinates of a moving marine object.

The industrial implementation of the method is not of technical complexity, since standard ship direction finding devices are used for its implementation.

Information sources

1. Patent RU No. 2032187 C1, 03/27/1995.

2. Patent RU No. 2158431 C1, 10.27.2000.

3. Patent RU No. 34020 U1, 11.20.2003.

4. Patent RU No. 2289149 C2, 12/10/2006.

5. Application US No. 2008008045 A1, 01/10/2008.

6. US patent No. 4024491 A, 05.17.2007.

7. Patent RU No. 2365936 C1, 03.06.2008.

Claims (1)

A method for navigating an underwater object using a hydroacoustic navigation system, comprising placing a navigation base of M hydroacoustic transponders with different response frequencies and a hydroacoustic transceiver located on an underwater navigation object, by which the signal propagation time intervals are measured with their subsequent conversion into the distance between the underwater navigation object and hydroacoustic transponders placing sonar transponders on drifting stations on the water surface and bottom stations on the seabed, determining the navigation parameters of the underwater navigation object relative to the bottom and / or drifting station or base from drifting stations, which are determined in the mode with a long and / or ultrashort base, and / or in a combined mode ( long + ultrashort base), and / or in the direction finding system, in this case, two navigation bases with a common center of the base are formed from receivers, placing them in a plane parallel to the plane of the deck of the underwater object, at the axis of one base X is directed along the axial line of the underwater object, and the axis of the other base Y is directed along the traverse to the right, processing the measurement results from spatio-temporal arrays of observations, determining the coordinates of the underwater navigation object by calculation, characterized in that when calculating the coordinates, the error is minimized according to the distribution of the measured coordinates, while the local Cartesian coordinates for the considered spatio-temporal region, in which the drifting station, bottom beacons, transponders and an underwater object are located, while determining the temporal course of the hydroacoustic characteristics for the obtained time series, while determining the extreme values of the hydroacoustic characteristics in each measurement series by the Gerst statistics, and estimating the arithmetic mean of the hydroacoustic characteristics by spatio-temporal observation arrays are performed by calculations using multidimensional quadrature formulas and Haar functions.

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