CN108303715B - Beidou beacon-based passive positioning method and system for underwater mobile node - Google Patents
Beidou beacon-based passive positioning method and system for underwater mobile node Download PDFInfo
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- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/18—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using ultrasonic, sonic, or infrasonic waves
- G01S5/28—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using ultrasonic, sonic, or infrasonic waves by co-ordinating position lines of different shape, e.g. hyperbolic, circular, elliptical or radial
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Abstract
A Beidou beacon-based passive positioning method for underwater mobile nodes comprises the following steps: step 1, a sea surface beacon node receives a positioning navigation signal broadcast by a Beidou satellite navigation system, updates the position of the sea surface beacon node in real time and keeps synchronous with a Beidou clock; combining the self position and the serial number of the 3 sea surface beacons positioned at the vertex of the triangular grid into a positioning message, and broadcasting the positioning message to the underwater mobile node according to a time sequence table of the positioning message sent by the positioning message; step 2, when the underwater mobile node receives the positioning message, calculating the position of the current time by using a filtering algorithm by using the arrival time and the message content of the 3 positioning messages; when the underwater mobile node does not receive the positioning message, the position of the underwater mobile node at the current moment can be estimated by utilizing a filtering algorithm. The invention also includes a system for carrying out the method of the invention.
Description
Technical Field
The invention relates to a passive positioning method and a passive positioning system for an underwater mobile node, in particular to a method and a system for realizing the passive positioning of an underwater mobile node by adopting a Beidou satellite positioning navigation system and realizing the positioning of sea surface beacon nodes based on a plurality of sea surface beacon node positioning signals.
Background
With the increasingly frequent development of marine activities such as marine resource exploration, disaster prevention warning, marine wars and the like by human beings, underwater unmanned equipment is widely applied. Therefore, positioning and navigation of underwater unmanned equipment are receiving wide attention. In an underwater environment, radio signals and optical signals are faded fast, so that long-distance propagation requirements cannot be met, and sound is transmitted in water in a transparent mode, so that sound waves are generally adopted for long-distance transmission, and underwater sound positioning becomes a common means for positioning underwater unmanned equipment. However, the underwater acoustic positioning method still faces many challenges. Firstly, the bandwidth of the sound wave in transmission is small, so that the transmission rate is far lower than that of a radio frequency signal; secondly, the propagation speed of the sound wave is about 1500m/s, so that large propagation delay exists, and the propagation speed of the underwater sound wave is not a constant due to the uneven medium, so that the propagation track is not a straight line; in addition, underwater time-varying channel conditions and multipath propagation phenomena lead to poor link transmission quality. Therefore, high precision underwater positioning is a difficult problem to solve.
Positioning and navigation of land and sea surface equipment have many mature technologies, such as satellite navigation (GPS, beidou, etc.). The positioning navigation systems adopt electromagnetic wave positioning, and due to the strong absorption of the electromagnetic wave by seawater, the land and sea positioning systems lose the due positioning effect underwater.
The currently widely used underwater sound positioning system can be divided into a long baseline, a short baseline and an ultra-short baseline according to the length of the baseline. The existing long baseline positioning system can be used for autonomous positioning of underwater unmanned equipment, a sensor array is arranged on the seabed, and a response mechanism is adopted for ranging, so that higher positioning accuracy is obtained, but an underwater acoustic response device is required to be deployed in a fixed water area, and the calibration difficulty of the node position of a responder is high, so that the practical cost is higher; the short-baseline underwater acoustic positioning system needs to arrange a sensor array on a carrier platform, and the underwater unmanned equipment is provided with a transponder, so that the underwater unmanned equipment can be positioned, but the autonomous positioning of the underwater unmanned equipment cannot be realized; the ultra-short baseline underwater acoustic positioning system needs to arrange an acoustic baseline array on a carrier platform, an underwater unmanned device is provided with a transponder, and the underwater unmanned device is positioned by adopting a response mechanism, but the autonomous positioning of the underwater unmanned device can not be realized. In addition, the baseline scale of the short baseline and ultrashort baseline underwater sound positioning systems is far smaller than that of the long baseline, the action range is limited, and the positioning requirements of large-area sea areas cannot be met.
Another implementation manner of positioning and navigating the underwater unmanned equipment is an inertial navigation system, but underwater positioning errors of the underwater unmanned equipment can be accumulated, a good elimination mechanism is not provided, and the underwater positioning errors can be gradually worsened along with the lapse of time, so that accurate positioning is difficult to realize; meanwhile, the high-precision inertial measurement unit is large in size and high in price. The inertial navigation system and the satellite positioning navigation system are combined for positioning, and the introduction of the satellite positioning navigation signal can realize position correction of underwater unmanned equipment floating out of the water surface, thereby realizing a better positioning effect. However, the floating and sinking processes of the device interrupt the task of the underwater unmanned device, so that the operation efficiency is reduced, and meanwhile, the energy is consumed, and the concealment of the underwater unmanned device is not facilitated.
At present, an underwater target positioning technology based on a sea surface beacon node is also proposed, namely, a satellite positioning navigation system is firstly utilized to realize the positioning of the sea surface beacon node, and then the positioning of an underwater mobile node is realized based on a plurality of sea surface beacon node positioning signals. In the existing positioning system based on the sea surface beacon node, through retrieval, the system and the method for underwater positioning disclosed by the U.S. patent No. US7512036B2 and the method for expanding the GPS underwater application disclosed by the U.S. patent No. US5119341 have the limitations that the time synchronization between the sea surface beacon node and an underwater target node is assumed, and meanwhile, the problem that the clock of the underwater node can generate offset is not considered, so that the positioning error is increased; the underwater GPS positioning and navigation system without high stable frequency standard and the underwater vehicle positioning method based on GNSS satellite and the system thereof disclosed by the invention of Chinese patent application No. CN200310118440 are limited in that the problem that the synchronization between the beacon node and the target node can not be kept all the time is solved by utilizing two-way ranging, namely the underwater node needs to send a positioning request signal to interact with a sea surface positioning beacon. However, the two-way ranging causes poor concealment of underwater targets, increases power consumption, and limits the number of underwater nodes for realizing positioning; chinese patent application No. 201410073253 discloses an underwater positioning navigation system and method based on DGPS buoy, and is limited in that the system defaults that a fixed time difference exists between a beacon node and a target node, and does not consider the frequency offset and phase offset which can occur to the clock of an underwater target. In addition, none of the above systems takes into account the problem of bending of the underwater acoustic propagation path.
The invention aims to solve the technical problem that the passive autonomous positioning of the underwater mobile node is realized under the condition that the clock synchronization of a sea surface beacon node and the underwater mobile node cannot be ensured and the distance measurement is not carried out by adopting a response mechanism.
Disclosure of Invention
The invention provides a Beidou sea surface beacon-based passive positioning method and system for an underwater mobile node, aiming at overcoming the technical defects in the prior art.
A Beidou beacon-based passive positioning method for underwater mobile nodes comprises the following steps:
1. the Beidou satellite receiver on the sea surface beacon node receives a positioning navigation signal broadcast by the Beidou satellite navigation system, analyzes the longitude, the latitude and the elevation of the position where the Beidou satellite antenna of the sea surface beacon is located in real time, transmits the longitude, the latitude and the elevation to a sea surface master control system of the sea surface beacon node, and calibrates the clock of the sea surface master control system and the Beidou reference time to keep synchronous, namely, all the sea surface beacons keep synchronous; the sea surface master control system of the sea surface beacon subtracts the altitude difference value of the acoustic transceiving system with the integrated positioning/communication function from the altitude information of the Beidou satellite receiver to be used as the altitude of the sea surface beacon node, and then combines the beacon sequence number, longitude, latitude and altitude information of the sea surface beacon into a positioning message. According to a time sequence table for sending positioning messages, the sea surface beacon nodes at the vertex of one triangular grid broadcast the positioning messages through respective acoustic systems;
2. the underwater acoustic receiving system with the integrated positioning/communication function of the underwater mobile node is in a monitoring state, once a positioning signal is received, the acoustic system completes multi-user signal receiving, records the arrival time of 3 positioning messages and sends the decoded positioning messages and the arrival time thereof to an underwater main control system; an underwater main control system of the underwater mobile node reads and locates the message content and transmits the longitude, latitude, elevation and corresponding message arrival time in the message to an underwater resolving module; meanwhile, an underwater main control system of the underwater mobile node reads depth information from the pressure sensor in real time and transmits the depth information to an underwater resolving module; when an underwater resolving module of the underwater mobile node receives message information from an underwater main control system, resolving the current position of the underwater mobile node by using a filtering algorithm; when the message information from the underwater main control system is not received, the position of the underwater main control system at the current moment can be estimated by utilizing a filtering algorithm;
in the step 1, the number of the sea surface beacon nodes is at least 3, and the sea surface beacon deployment topology of the underwater mobile node positioning system is that firstly, three sea surface beacon nodes form a regular triangle grid, and the beacon nodes are positioned at the vertexes of the triangle; the deployment topology of all sea surface beacon nodes adopts a regular triangular grid as a basic unit, and a target sea area is seamlessly covered;
in step 1, a positioning signal broadcasting time sequence of a sea surface beacon node: taking a regular triangular grid as a unit, namely, simultaneously broadcasting the positioning messages of 3 sea surface beacon nodes positioned on one triangular grid; when the sea surface beacon node on one triangular grid broadcasts a positioning message, after a fixed time interval, the sea surface beacon node on the next time sequence triangular grid broadcasts the positioning message; restarting the broadcasting time sequence of the next round of positioning messages until all the triangular grids broadcast the positioning messages;
in step 1, 3 sea surface beacon nodes broadcast positioning messages simultaneously, the sea surface beacon nodes broadcast positioning signals in a Code Division Multiple Access (CDMA) mode, specifically, for the positioning messages generated by coding, a multi-system convolutional Code is combined with M-system Code Shift Keying (CSK) and allocated to different pseudo-random sequences of the sea surface beacon nodes, so as to implement multi-user communication. 3 sea surface beacons on each regular triangular grid are distributed with 3 different pseudo-random sequences when broadcasting positioning messages; the same sea surface beacon node belonging to different regular triangular grids can be distributed with different pseudo-random sequences when different regular triangular grids broadcast positioning messages;
in step 2,3 beacon nodes on the regular triangular grids broadcast positioning messages simultaneously in a CDMA mode, and the underwater mobile node receives 3 signals simultaneously. Due to the quasi-orthogonal property of a spread spectrum sequence in a CDMA mode, multi-user Interference (MAI) caused by a near-far effect is restrained by utilizing a serial Multiple Access Interference cancellation technology, and expected positioning message information is recovered;
in step 2, the underwater mobile node position calculating method comprises the following steps:
a. when an underwater acoustic receiving system of an underwater mobile node receives 3 positioning messages:
(1) the underwater resolving module receives longitude, latitude, elevation and positioning message arrival time T from an underwater main control systemiI is 1,2,3, which refers to the beacon sequence number and the depth information of the underwater mobile node; by T1△ T is used as reference time to obtain the time difference of arrival of different positioning messages12＝T2-T1And △ T13＝T3-T1；
(2) The resolving module converts longitude and latitude in the message into a Gaussian plane coordinate system by using Gaussian forward calculation and combines elevation as a three-dimensional coordinate position (X) of the beacon nodei,Yi,Zi) I is 1,2,3 denotes the sea beacon sequence number; the underwater mobile node position is set as (X)t,Yt,Zt) And t is used to refer to an underwater mobile node, wherein ZtFor depth information, obtained by a pressure sensor as a known quantity; the distance between the sea surface beacon node i and the underwater mobile node is expressed as
(3) The sound velocity is not constant due to the medium nonuniformity, and the sound velocity profile is expressed as c (z) regardless of the transverse change of the sound velocity profile, and z represents a depth variable; by utilizing Snell law, establishing the relationship between the horizontal distance, the propagation delay and the propagation constant between the sea surface beacon node i and the underwater mobile node, and discretizing to obtain the following results:
where ρ isi、τiAnd niRepresenting the horizontal distance, the propagation delay and the propagation constant corresponding to the sea surface beacon node i and the underwater mobile node; n represents the number of samples at c (Z), at depth ZiAnd ZtAre sampled uniformly, j denotes samplingNumber of spots, zjRepresenting the depth at the sampling point, c (z)j) Representing depth zjThe corresponding speed of sound is the speed of sound,
the ratio of the straight-line distance between the sea surface beacon node i and the underwater mobile node to the propagation delay is expressed as follows:
due to each item
The variation amount is small, and the above formula can be simplified into:
according to the Taylor expansion, the above equation can be further simplified:
because the beacon nodes are all located on the sea surface, and the depth difference between the beacon nodes is small, the ratio of the straight-line distance and the propagation delay of the beacon nodes on different sea surfaces and the underwater mobile node is considered to be equal and is expressed as m, namely:
based on the above formula, after obtaining the difference between the propagation delays of the positioning messages of the different sea surface beacon nodes, the difference △ D between the distances between the different sea surface beacon nodes and the underwater mobile node can be obtained12And △ D13Taking the node 1 as a reference:
(4) based on the step (a3), the resolving module obtains difference values △ D12 and △ D13 of the distances between the beacon nodes on different sea surfaces and the underwater mobile node, and an observation equation and a state equation of the extended Kalman filtering are established:
θt,k＝θt,k-1+TkVk-1+wk(8)
wherein the subscripts k-1 and k denote the time scalar quantities introduced in the Kalman filtering, which are k-1 and k times, △ D12,k，△D13,kExpressing the observed quantity at the moment k, namely the difference value of the distances between the beacon nodes at different sea surfaces at the moment k and the underwater mobile node; thetat,kAnd thetat,k-1State vectors representing time k and time k-1, respectively, i.e. two-dimensional coordinates (X) of the underwater mobile nodet,k,Yt,k) And (X)t,k-1,Yt,k-1)；Zt,kDepth information of the underwater mobile node at the moment k is represented; s1,k,S2,k,S3,kThree-dimensional coordinates (X) of 3 sea surface beacon nodes at the time of ki,k,Yi,k,Zi,k)，i＝1,2,3；Vk-1Representing the two-dimensional moving speed of the underwater mobile node at the k-1 moment; t iskRepresenting the time interval of time k-1 and time k; deltakAnd wkObserving noise and process noise for time k;
observation equation h (theta)t,k,Zt,k,S1,k,Si,k) And l is 2,3 denotes the beacon number 2,3, denoted as:
firstly, based on the estimated value theta of the position of the underwater mobile node at the moment of k-1t,k-1|k-1And an estimate of the speed of movement
And predicting the position of the underwater mobile node at the moment k:
wherein theta ist,k|k-1＝[Xt,k|k-1Yt,k|k-1]TRepresenting the predicted value of the underwater mobile node at the moment k;
calculating its covariance Pk|k-1：
Wherein, Pk|k-1Covariance matrix, P, representing predicted values of underwater mobile nodes at time kk-1|k-1Covariance matrix, Q, representing the estimate of the position of an underwater mobile node at time k-1k-1|k-1Representing a covariance of the estimate of the velocity of movement of the underwater mobile node;
kalman gain KkExpressed as:
wherein R iskA covariance representing the observation error; hkFor observing the matrix, because of the nonlinear equation of the observation equation, the first-order Taylor expansion is carried out, and the approximation linearization is carried out:
wherein the content of the first and second substances,
expressed as:
therefore, the position estimation value of the underwater mobile node at the time k is as follows:
converting the two-dimensional coordinate position into longitude and latitude by inverse Gaussian calculation; and updating the covariance of the position of the underwater mobile node at the moment k for calculation at the next moment:
Pk|k＝Pk|k-1-KkHkPk|k-1(15)
estimating moving speed of underwater mobile node at k moment
And calculates its covariance Qk|kFor the next time calculation:
b. when the acoustic receiving system of the underwater mobile node does not receive 3 positioning messages:
the resolving module of the underwater mobile node can not receive the message information submitted from the main control system and the arrival time of the message, and only receives the depth information of the underwater mobile node, namely, the depth information is between the time k-1 and the time k. Estimating the position and the moving speed of the underwater mobile node based on the moment k-1, and estimating the position theta of the underwater mobile node at the current moment't,k|kI.e. by
Wherein, T'kA time interval representing the distance k-1 from the current time;
and converting the two-dimensional space coordinate position into longitude and latitude by using inverse Gaussian calculation.
The system for implementing the Beidou sea surface beacon-based passive positioning method of the underwater mobile node comprises at least 3 sea surface beacon nodes, the underwater mobile node, a shore-based data control center and a ship-based control center. In addition, the system of the invention needs to realize the positioning of the sea surface beacon by means of a Beidou satellite navigation system.
The sea surface beacon node comprises a Beidou satellite receiver, a sea surface master control system, a sea surface acoustic transceiver system with a comprehensive positioning/communication function and the like. The underwater mobile node can complete position calculation only by receiving the positioning signals of 3 positioning beacons, and the topological structure of the regular triangular grid formed by the beacon nodes can maximally cover the sea area. Therefore, the deployment topology of the sea surface beacon nodes adopts a regular triangle as a grid, 3 sea surface beacons are positioned at the vertex of the regular triangle, and the deployment topology of all the sea surface beacon nodes is formed on the basis of the regular triangle grid, so that a target sea area is covered, and underwater mobile nodes covering any position below the sea area can receive positioning signals sent by the 3 sea surface beacons at the vertex of the regular triangle grid.
The underwater mobile node has a certain moving speed and comprises a propeller, a pressure sensor and an underwater positioning receiver; the underwater positioning receiver comprises an underwater main control system, an underwater acoustic receiving system with a comprehensive positioning/communication function, an underwater resolving module and an underwater short message processing module;
the ship-based control center is a positioning auxiliary system, is deployed in a sea surface beacon node coverage sea area, carries a ship-based positioning receiver, comprises a ship-based acoustic receiving system with a comprehensive positioning/communication function, a ship-based resolving module and a ship-based short message processing module, and is used for monitoring the working condition of the sea surface beacon node; and the ship-based control center monitors the message sent by the specific sea surface beacon node through the ship-based acoustic receiving system in the sea area covered by the sea surface beacon node, and judges the working state of the sea surface beacon node according to the time sequence and the content of the received message. In addition, the ship-based control center can monitor the working conditions of all the sea surface beacon nodes intermittently by moving, so that the running condition of the positioning system is monitored;
and the shore-based data control center is used for controlling the underwater mobile node. The shore-based data control center can issue instructions to the sea surface beacon nodes through the Beidou satellite navigation system, and the sea surface beacon nodes broadcast the instructions to the corresponding underwater mobile nodes in a short data message mode.
The deployment topology of the sea surface beacon nodes is formed by taking a regular triangle grid as a basis:
the underwater mobile node can complete position calculation only by receiving at least 3 positioning signals, and the beacon nodes form a topological structure of a regular triangular grid, so that the sea area can be covered to the maximum extent; therefore, the deployment topology of the sea surface beacon nodes adopts a regular triangle as a grid, 3 sea surface beacons are positioned at the vertex of the regular triangle, and the deployment topology of all the sea surface beacon nodes is formed on the basis of the regular triangle grid, so that a target sea area is covered, and the underwater mobile nodes covering any position below the sea area can receive positioning signals sent by the 3 sea surface beacons at the vertex of the regular triangle grid;
the broadcast timing of the sea surface beacon node is: taking a regular triangular grid as a unit, namely, simultaneously broadcasting the positioning messages of 3 sea surface beacon nodes positioned on one triangular grid; when the sea surface beacon node on one triangular grid broadcasts a positioning message, after a fixed time interval, the sea surface beacon node on the next time sequence triangular grid broadcasts the positioning message; restarting the broadcasting time sequence of the next round of positioning messages until all the triangular grids broadcast the positioning messages;
the sea surface beacon node broadcasts a positioning message to the underwater in a CDMA spread spectrum mode: 3 sea surface beacons on a triangular grid need to broadcast positioning messages at the same time, so that a CDMA mode is adopted; for the generated positioning message, combining a multi-system convolutional Code with an M-system Code element Shift Keying (CSK) and distributing the multi-system convolutional Code to different pseudo-random sequences of a sea surface beacon node to realize multi-user communication;
the underwater mobile node utilizes a serial multiple access interference cancellation technology to inhibit multi-user interference caused by a near-far effect and recover expected positioning message information;
the positioning calculation process of the underwater mobile node is as follows:
a. when an acoustic receiving system of the underwater mobile node receives 3 positioning messages:
the underwater mobile node calculates the arrival time difference of different positioning messages according to the arrival time of the 3 positioning messages, and compensates the sound ray bending based on the Snell law to obtain the distance difference between the beacon nodes on different sea surfaces and the underwater mobile node;
based on an extended Kalman filtering method, taking the difference value of the distances between different sea surface beacon nodes and the underwater mobile node as an observed value, and resolving the position and the moving speed of the underwater mobile node at the current moment according to the position and the moving speed information at the previous moment;
b. when the underwater acoustic receiving system of the underwater mobile node does not receive 3 positioning messages:
when the underwater mobile node does not receive the positioning message, based on an extended Kalman filtering method; and estimating the position of the underwater mobile node at the current moment by using the position and the moving speed calculated at the last moment.
The underwater mobile node and the sea surface beacon node do not need to keep synchronous and do not need to send out any signal.
The positioning message need not contain a transmission timestamp.
The invention also comprises an auxiliary communication function:
and the shore-based data control center is used for controlling the underwater mobile node. When a shore-based data control center needs to send a control instruction to a certain underwater mobile node, the control instruction is firstly sent to a sea surface beacon node by means of a Beidou satellite navigation system. In the interval of broadcasting the positioning message by the sea surface beacon nodes, one sea surface beacon node on each triangular grid encodes a control instruction from the shore-based data control center into a short message, and broadcasts the short message to the underwater mobile node so as to ensure that the underwater mobile node covering the sea area by the sea surface beacon nodes receives the short message at least once; when the comprehensive positioning/communication acoustic receiving system of the underwater mobile node receives the short message, submitting the short message to a main control system; the main control system of the underwater mobile node transmits the message to a short message processing module of the underwater mobile node according to the type of the message; the short message processing module analyzes the destination address of the message, when the destination address matches the underwater mobile node, the instruction content in the message is analyzed, the underwater mobile node is instructed to carry out corresponding operation, and if the addresses do not match, the corresponding short message is discarded.
The invention has the advantages that: the passive positioning of the underwater mobile node is realized under the condition that the underwater mobile node and the sea surface beacon node are asynchronous. The problem of propagation path bending is considered, and positioning errors are reduced. The sea surface beacon nodes realize maximized sea area coverage in a deployment mode with regular triangular grids as units, and can provide node positioning in a large area; the calculation method of the sequential filtering is realized, and the position of the self-body can be estimated when the positioning message is not obtained; the CDMA mode of the comprehensive positioning/communication acoustic system combines M-system CSK high-order modulation, and compared with the traditional direct sequence spread spectrum mode, the positioning receiver eliminates MAI (maximum amplitude interference) caused by near-far effect by using the zero setting serial multiple access interference cancellation technology, and improves the communication rate; on the other hand, the auxiliary communication function is added, and the function diversification of the system is realized.
Description of the drawings:
FIG. 1 is a general configuration diagram of a system for carrying out the method of the present invention;
FIG. 2 is a diagram of a topology of a sea-surface beacon node according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of the operation of a sea beacon node and an underwater mobile node of the system of the present invention;
fig. 4 is a timing diagram illustrating arrival of a grid positioning message at a sea surface beacon node according to an embodiment of the present invention.
The specific implementation mode is as follows:
for a more detailed explanation of the invention, reference is made to the accompanying drawings, which are to be considered illustrative, and not restrictive, in which structures are omitted or scaled differently than actual dimensions, for further illustration.
A Beidou beacon-based passive positioning method for underwater mobile nodes comprises the following steps:
1. the Beidou satellite receiver on the sea surface beacon node receives a positioning navigation signal broadcast by the Beidou satellite navigation system, analyzes the longitude, the latitude and the elevation of the position where the Beidou satellite antenna of the sea surface beacon is located in real time, transmits the longitude, the latitude and the elevation to a sea surface master control system of the sea surface beacon node, and calibrates the clock of the sea surface master control system and the Beidou reference time to keep synchronous, namely, all the sea surface beacons keep synchronous; the sea surface master control system of the sea surface beacon subtracts the altitude difference value of the acoustic transceiving system with the integrated positioning/communication function from the altitude information of the Beidou satellite receiver to be used as the altitude of the sea surface beacon node, and then combines the beacon sequence number, longitude, latitude and altitude information of the sea surface beacon into a positioning message. According to a time sequence table for sending positioning messages, the sea surface beacon nodes at the vertex of one triangular grid broadcast the positioning messages through respective acoustic systems;
2. the acoustic receiving system with the integrated positioning/communication function of the underwater mobile node is in a monitoring state, and once a positioning signal is received, the acoustic system completes multi-user signal receiving, records the arrival time of 3 positioning messages and sends the decoded positioning messages and the arrival time thereof to a main control system; an underwater main control system of the underwater mobile node reads and locates the content of the message and transmits the longitude, the latitude, the elevation and the corresponding arrival time of the message to a resolving module; meanwhile, an underwater main control system of the underwater mobile node reads depth information from the pressure sensor in real time and transmits the depth information to the resolving module; when an underwater resolving module of the underwater mobile node receives message information from an underwater main control system, resolving the current position of the underwater mobile node by using a filtering algorithm; when the message information from the underwater main control system is not received, the position of the underwater main control system at the current moment can be estimated by using a filtering algorithm.
In the step 1, the number of the sea surface beacon nodes is at least 3, and the sea surface beacon deployment topology of the underwater mobile node positioning system is that firstly, three sea surface beacon nodes form a regular triangle grid, and the beacon nodes are positioned at the vertexes of the triangle; the deployment topology of all sea surface beacon nodes adopts a regular triangular grid as a basic unit, and a target sea area is seamlessly covered;
in step 1, a positioning signal broadcasting time sequence of a sea surface beacon node: taking a regular triangular grid as a unit, namely, simultaneously broadcasting the positioning messages of 3 sea surface beacon nodes positioned on one triangular grid; when the sea surface beacon node on one triangular grid broadcasts a positioning message, after a fixed time interval, the sea surface beacon node on the next time sequence triangular grid broadcasts the positioning message; restarting the broadcasting time sequence of the next round of positioning messages until all the triangular grids broadcast the positioning messages;
in step 1, 3 sea surface beacon nodes broadcast positioning messages simultaneously, the sea surface beacon nodes broadcast positioning signals in a Code Division Multiple Access (CDMA) mode, specifically, for the positioning messages generated by coding, a multi-system convolutional Code is combined with M-system Code Shift Keying (CSK) and allocated to different pseudo-random sequences of the sea surface beacon nodes, so as to implement multi-user communication. 3 sea surface beacons on each regular triangular grid are distributed with 3 different pseudo-random sequences when broadcasting positioning messages; the same sea surface beacon node belonging to different regular triangular grids can be distributed with different pseudo-random sequences when different regular triangular grids broadcast positioning messages;
in step 2,3 beacon nodes on the regular triangular grids broadcast positioning messages simultaneously in a CDMA mode, and the underwater mobile node receives 3 signals simultaneously. Due to the quasi-orthogonal property of a spread spectrum sequence in a CDMA mode, multi-user Interference (MAI) caused by a near-far effect is restrained by utilizing a serial Multiple Access Interference cancellation technology, and expected positioning message information is recovered;
in step 2, the underwater mobile node position calculating method comprises the following steps:
c. when an underwater acoustic receiving system of an underwater mobile node receives 3 positioning messages:
(1) the underwater resolving module receives longitude, latitude, elevation and positioning message arrival time T from an underwater main control systemiI is 1,2,3, which refers to the beacon sequence number and the depth information of the underwater mobile node; by T1△ T is used as reference time to obtain the time difference of arrival of different positioning messages12＝T2-T1And △ T13＝T3-T1；
(2) The resolving module converts longitude and latitude in the message into a Gaussian plane coordinate system by using Gaussian forward calculation and combines elevation as a three-dimensional coordinate position (X) of the beacon nodei,Yi,Zi) I is 1,2,3 denotes the sea beacon sequence number; the underwater mobile node position is set as (X)t,YtZt), t is used to refer to an underwater mobile node, where ZtFor depth information, obtained by a pressure sensor as a known quantity; the distance between the sea surface beacon node i and the underwater mobile node is expressed as
(3) The sound velocity is not constant due to the medium nonuniformity, and the sound velocity profile is expressed as c (z) regardless of the transverse change of the sound velocity profile, and z represents a depth variable; by utilizing Snell law, establishing the relationship between the horizontal distance, the propagation delay and the propagation constant between the sea surface beacon node i and the underwater mobile node, and discretizing to obtain the following results:
where ρ isi、τiAnd niRepresenting the horizontal distance, the propagation delay and the propagation constant corresponding to the sea surface beacon node i and the underwater mobile node; n represents the number of samples at c (Z), at depth ZiAnd ZtIs uniformly sampled, j represents the serial number of the sampling point, zjRepresenting the depth at the sampling point, c (z)j) Representing depth zjThe corresponding speed of sound is the speed of sound,
the ratio of the straight-line distance between the sea surface beacon node i and the underwater mobile node to the propagation delay is expressed as follows:
due to each item
The variation amount is small, and the above formula can be simplified into:
according to the Taylor expansion, the above equation can be further simplified:
because the beacon nodes are all located on the sea surface, and the depth difference between the beacon nodes is small, the ratio of the straight-line distance and the propagation delay of the beacon nodes on different sea surfaces and the underwater mobile node is considered to be equal and is expressed as m, namely:
based on the above formula, after obtaining the difference between the propagation delays of the positioning messages of the different sea surface beacon nodes, the difference △ D between the distances between the different sea surface beacon nodes and the underwater mobile node can be obtained12And △ D13(with node 1 as a reference) that is:
(4) based on the step (a3), the resolving module obtains difference values △ D12 and △ D13 of the distances between the beacon nodes on different sea surfaces and the underwater mobile node, and an observation equation and a state equation of the extended Kalman filtering are established:
θt,k＝θt,k-1+TkVk-1+wk(8)
wherein the subscripts k-1 and k denote the moments introduced in the Kalman filteringScalar quantities, at time k-1 and k, △ D12,k，△D13,kExpressing the observed quantity at the moment k, namely the difference value of the distances between the beacon nodes at different sea surfaces at the moment k and the underwater mobile node; thetat,kAnd thetat,k-1State vectors representing time k and time k-1, respectively, i.e. two-dimensional coordinates (X) of the underwater mobile nodet,k,Yt,k) And (X)t,k-1,Yt,k-1)；Zt,kDepth information of the underwater mobile node at the moment k is represented; s1,k,S2,k,S3,kThree-dimensional coordinates (X) of 3 sea surface beacon nodes at the time of ki,k,Yi,k,Zi,k)，i＝1,2,3；Vk-1Representing the two-dimensional moving speed of the underwater mobile node at the k-1 moment; t iskRepresenting the time interval of time k-1 and time k; deltakAnd wkObserving noise and process noise for time k;
observation equation h (theta)t,k,Zt,k,S1,k,Si,k) Where l ═ 2,3 denotes the beacon number 2,3, denoted as:
firstly, based on the estimated value theta of the position of the underwater mobile node at the moment of k-1t,k-1|k-1And an estimate of the speed of movement
And predicting the position of the underwater mobile node at the moment k:
wherein theta ist,k|k-1＝[Xt,k|k-1Yt,k|k-1]TRepresenting the predicted value of the underwater mobile node at the moment k;
calculating its covariance Pk|k-1：
Wherein, Pk|k-1Covariance matrix, P, representing predicted values of underwater mobile nodes at time kk-1|k-1Covariance matrix, Q, representing the estimate of the position of an underwater mobile node at time k-1k-1|k-1Representing a covariance of the estimate of the velocity of movement of the underwater mobile node;
kalman gain KkExpressed as:
wherein R iskA covariance representing the observation error; hkFor observing the matrix, because of the nonlinear equation of the observation equation, the first-order Taylor expansion is carried out, and the approximation linearization is carried out:
wherein the content of the first and second substances,
where l ═ 2,3 denotes the beacon number 2,3 denotes:
therefore, the position estimation value of the underwater mobile node at the time k is as follows:
converting the two-dimensional coordinate position into longitude and latitude by inverse Gaussian calculation; and updating the covariance of the position of the underwater mobile node at the moment k for calculation at the next moment:
Pk|k＝Pk|k-1-KkHkPk|k-1(15)
estimating water at time kLower mobile node moving speed
And calculates its covariance Qk|kFor the next time calculation:
d. when the underwater acoustic receiving system of the underwater mobile node does not receive 3 positioning messages:
the underwater resolving module of the underwater mobile node does not receive the message information submitted from the main control system and the arrival time of the message, and only receives the depth information of the underwater mobile node, namely, the depth information is between the time k-1 and the time k. Estimating the position and the moving speed of the underwater mobile node based on the moment k-1, and estimating the position theta of the underwater mobile node at the current moment't,k|kI.e. by
Wherein, T'kA time interval representing the distance k-1 from the current time;
and converting the two-dimensional space coordinate position into longitude and latitude by using inverse Gaussian calculation.
The invention relates to an example of an underwater mobile node positioning system based on Beidou beacons, which consists of a shore-based data center 12, 10 wave gliders 13-1 and 2 … 10, a ship-based control center 14, and 2 underwater gliders 15-1 and 2 containing positioning receivers; the system also realizes the positioning and synchronization of the sea surface beacon nodes by means of the Beidou satellite navigation system 11. Wherein the wave glider acts as a sea beacon node, and the underwater glider acts as an underwater mobile node. As shown in fig. 1.
The sea surface acoustic transceiver system is characterized in that 10 wave gliders serve as sea surface beacon nodes, the upper half portion of each wave glider is located on the sea surface, the lower half portion of each wave glider is located below the sea surface, and each wave glider is provided with a Beidou satellite receiver, a sea surface master control system, a sea surface acoustic transceiver system with a comprehensive positioning/communication function and the like; the Beidou satellite receiver is positioned on the sea surface part of the wave glider, and the sea surface acoustic transceiver system is positioned on the underwater part of the wave glider; the wave gliders update the self positions in real time by receiving navigation signals of the Beidou satellite navigation system and keep synchronous with the Beidou satellite reference clock, namely all the wave gliders keep time synchronization; each wave glider encodes the self position information and the serial number into a positioning message according to the self time sequence table and broadcasts the positioning message to the underwater glider;
2 underwater gliders serve as underwater mobile nodes and are provided with underwater positioning receivers, wherein each underwater positioning receiver comprises an underwater main control system, an underwater acoustic receiving system with a comprehensive positioning/communication function, an underwater resolving module, an underwater short message processing module, a pressure sensor and the like; when the underwater glider receives the positioning signal, the position of the underwater glider is calculated by using a sequential algorithm; when the positioning signal is not received, the self position can be estimated by utilizing a sequential algorithm;
and the shore-based data control center is positioned on the seashore and is used for controlling the underwater glider. The shore-based data control center issues instructions to the wave glider through the Beidou satellite navigation system, and the wave glider broadcasts the instructions to the corresponding underwater glider in a short data message mode.
The ship-based control center is provided with a positioning receiver, comprises a ship-based acoustic receiving system with a comprehensive positioning/communication function, a ship-based resolving module and a ship-based short message processing module and is used for monitoring the working condition of the wave glider. The ship-based control center is positioned in a wave glider covered sea area, monitors messages sent by a specific wave glider through a ship-based acoustic receiving system, and judges the working state of the wave glider according to the time sequence and the content of the received messages. In addition, the ship-based control center can monitor the working conditions of all the wave gliders discontinuously by moving, so that the running condition of the positioning system is monitored;
the 10 wave gliders are intended to adopt the topology shown in fig. 2, where 21,22 … 210 represent the 10 wave gliders, respectively. Firstly, 3 wave gliders form a regular triangle grid, the side length of the triangle grid is 4.5 kilometers, and the wave gliders are positioned at the vertexes of the triangle; 10 wave gliders form 10 regular triangular grids 1 and 2 … 10 to seamlessly cover a target sea area; the sea area coverage of more than 100 square kilometers can be realized.
Firstly, 3 wave gliders on a grid 1 broadcast positioning messages at the same time, after a fixed time interval, 3 wave gliders on a grid 2 broadcast positioning messages at the same time until 3 wave gliders on a grid 10 broadcast the positioning messages, and then the next round of broadcasting time sequence is started.
When 3 wave gliders on a grid broadcast positioning messages simultaneously in a CDMA mode, 3 different pseudo-random sequences are distributed, for example, when the grid 1 broadcasts the positioning messages, the wave gliders 21, 23 and 24 are distributed with 3 different pseudo-random sequences; the same wave glider belonging to different regular triangular grids can be assigned with different pseudo-random sequences when the positioning messages are broadcast by different regular triangular grids, for example, the wave glider 24 belongs to grids 1 and 2, when the positioning messages are broadcast on the grid 1 or the grid 2, the assigned pseudo-random sequences are different when the wave glider 24 broadcasts the positioning messages twice;
when the shore-based data control center needs to control the underwater gliders, the underwater gliders can be issued to the two wave gliders 21 and 22 through satellite communication, and the wave gliders 21 and 22 encode control commands and destination addresses into short message messages; and broadcasting the positioning message interval on two grids with adjacent serial numbers, and broadcasting a short message to the underwater glider.
When 3 wave gliders on a grid broadcast their positioning messages simultaneously, the underwater glider realizes multi-user reception. Specifically, as shown in fig. 3.
3 wave gliders on one grid, wherein each wave-gliding Beidou satellite receiver 31 analyzes the longitude, the latitude and the elevation of the antenna to transmit to a sea surface main control system by receiving satellite signals from a Beidou satellite navigation system, and realizes the synchronization of the sea surface main control system 32 and a Beidou reference clock; the sea surface master control system subtracts the height difference between the satellite antenna and the acoustic receiving and transmitting system 33 from the height of the satellite antenna to be used as the height of the wave glider, the sea surface master control system encodes longitude, latitude, height and self serial number into positioning messages, and 3 wave gliders broadcast the positioning messages through the underwater acoustic receiving systems 33 with respective comprehensive positioning/communication functions according to self time sequence tables;
the underwater acoustic receiving system 34 with the integrated positioning/communication function of the underwater glider is in a monitoring state, completes multi-user signal receiving once receiving the positioning signal, records the arrival time of 3 positioning messages, and sends the decoded positioning messages and the arrival time thereof to the underwater main control system 35; the underwater main control system of the underwater glider reads and positions the message content, and transmits the longitude, latitude, elevation and the corresponding message arrival time in the message to the underwater resolving module 38; meanwhile, an underwater main control system of the underwater glider reads depth information from the pressure sensor 36 in real time and transmits the depth information to the underwater resolving module; when an underwater resolving module of the underwater glider receives message information from an underwater main control system, resolving the current position of the underwater glider by using a filtering algorithm; when the message information from the underwater main control system is not received, the position of the underwater main control system at the current moment can be estimated by using a filtering algorithm.
When the wave glider receives the short message, the sea surface master control system judges the destination address in the message, and when the destination address is matched, the sea surface master control system submits the message to the short message processing module 37 to make a corresponding response, otherwise, the short message is discarded.
Referring to fig. 4, after the underwater glider realizes multi-user reception, the resolving module obtains the arrival time T1，T2，T3Let the propagation delay of the positioning signal for the wave gliders 1,2,3 on a triangular grid be △ T1，△T2，△T3Since 3 wave gliders broadcast their positioning signals at the same time, △ T can be known2-△T1＝T2-T1＝△T12,△T3-△T1＝T3-T1＝△T13. Therefore, based on the arrival time obtained at the receiving end, the difference value of the propagation delay of different positioning signals can be obtained; according to the bending of sound rayAnd (4) correcting and resolving the difference value of the linear distance between the gliders with different waves and the gliders under water. In addition, the resolving module also needs to perform Gaussian forward calculation on longitude, latitude and elevation to obtain a three-dimensional coordinate corresponding to the wave glider; after the three-dimensional coordinates of the underwater glider are obtained, the corresponding longitude and latitude and elevation also need to be obtained through inverse Gaussian calculation.
The above is an example of the present invention, in which the sea surface beacon node may be replaced by a buoy, etc., to realize the positioning of other underwater targets; the ship-based control center can be replaced by other carriers or a plurality of carriers as an auxiliary system to realize the monitoring function of the positioning system; the shore-based data center can be built in other places besides the coast, and needs to realize satellite communication;
in addition, instead of using the beidou satellite navigation system, other global navigation systems may be used, such as GPS, GLONASS, GALILEO, etc. When the underwater mobile node can provide a speed vector, the positioning precision can be improved; when the underwater mobile node does not provide depth information, the regular triangle grating is only required to be changed into other shapes such as quadrangle, and the underwater mobile node can be ensured to receive more than 4 positioning messages at one time.
The embodiments described in this specification are merely illustrative of implementations of the inventive concept and the scope of the present invention should not be considered limited to the specific forms set forth in the embodiments but rather by the equivalents thereof as may occur to those skilled in the art upon consideration of the present inventive concept.
Claims (2)
1. The Beidou beacon-based passive positioning method for the underwater mobile node comprises the following steps:
step 1, a Beidou satellite receiver on a sea surface beacon node receives a positioning navigation signal broadcast by a Beidou satellite navigation system, analyzes the longitude, the latitude and the elevation of the position of a Beidou satellite antenna of the sea surface beacon in real time, transmits the longitude, the latitude and the elevation to a sea surface master control system of the sea surface beacon node, and calibrates the clock of the sea surface master control system and keeps synchronous with the Beidou reference time, namely all the sea surface beacons keep synchronous; the sea surface master control system of the sea surface beacon subtracts the altitude difference value of the acoustic transceiving system with the integrated positioning/communication function from the altitude information of the Beidou satellite receiver to be used as the altitude of the sea surface beacon node, and then combines the beacon sequence number, longitude, latitude and altitude information of the sea surface beacon into a positioning message; according to a time sequence table for sending positioning messages, the sea surface beacon nodes at the top points of a triangular grid broadcast the positioning messages through respective acoustic transceiving systems;
the number of the sea surface beacon nodes is at least 3, and the sea surface beacon deployment topology of the underwater mobile node positioning system is that firstly, three sea surface beacon nodes form a regular triangle grid, and the beacon nodes are positioned at the vertexes of the triangle; the deployment topology of all sea surface beacon nodes adopts a regular triangular grid as a basic unit, and a target sea area is seamlessly covered;
positioning signal broadcasting time sequence of sea surface beacon nodes: taking a regular triangular grid as a unit, namely, simultaneously broadcasting the positioning messages of 3 sea surface beacon nodes positioned on one triangular grid; when the sea surface beacon node on one triangular grid broadcasts a positioning message, after a fixed time interval, the sea surface beacon node on the next time sequence triangular grid broadcasts the positioning message; restarting the broadcasting time sequence of the next round of positioning messages until all the triangular grids broadcast the positioning messages;
the method comprises the following steps that 3 sea surface beacon nodes broadcast positioning messages simultaneously, the sea surface beacon nodes broadcast positioning signals in a code division multiple access CDMA mode, specifically, for the positioning messages generated by coding, multi-system convolutional codes and M-system code element shift keying (CSK) are combined and distributed to different pseudo-random sequences of the sea surface beacon nodes, and multi-user communication is achieved; 3 sea surface beacons on each regular triangular grid are distributed with 3 different pseudo-random sequences when broadcasting positioning messages; the same sea surface beacon node belonging to different regular triangular grids can be distributed with different pseudo-random sequences when different regular triangular grids broadcast positioning messages;
step 2, the acoustic receiving system of the integrated positioning/communication function of the underwater mobile node is in a monitoring state, and once receiving the positioning signal, the acoustic receiving system completes multi-user signal reception, records the arrival time of 3 positioning messages, and sends the decoded positioning message and the arrival time thereof to the underwater main control system; an underwater main control system of the underwater mobile node reads and locates the message content and transmits the longitude, latitude, elevation and corresponding message arrival time in the message to an underwater resolving module; meanwhile, an underwater main control system of the underwater mobile node reads depth information from the pressure sensor in real time and transmits the depth information to an underwater resolving module; when an underwater resolving module of the underwater mobile node receives message information from an underwater main control system, resolving the current position of the underwater mobile node by using a filtering algorithm; when the message information from the underwater main control system is not received, the position of the underwater main control system at the current moment can be estimated by utilizing a filtering algorithm;
because 3 beacon nodes on the regular triangular grids broadcast positioning messages simultaneously in a CDMA mode, the underwater mobile node receives 3 signals simultaneously; due to the quasi-orthogonal property of a spread spectrum sequence in a CDMA mode, multi-user interference MAI caused by a near-far effect is restrained by utilizing a serial multiple access interference cancellation technology, and expected positioning message information is recovered;
the underwater mobile node position calculating method comprises the following steps:
a. when an underwater acoustic receiving system of an underwater mobile node receives 3 positioning messages:
(1) the underwater resolving module receives longitude, latitude, elevation and positioning message arrival time T from an underwater main control systemiI is 1,2,3, which refers to the beacon sequence number and the depth information of the underwater mobile node; by T1△ T is used as reference time to obtain the time difference of arrival of different positioning messages12＝T2-T1And △ T13＝T3-T1；
(2) The resolving module converts longitude and latitude in the message into a Gaussian plane coordinate system by using Gaussian forward calculation and combines elevation as a three-dimensional coordinate position (X) of the beacon nodei,Yi,Zi) I is 1,2,3 denotes the sea beacon sequence number; the underwater mobile node position is set as (X)t,Yt,Zt) And t denotes an underwater mobile node, wherein ZtFor depth information, byThe pressure sensor acquires as a known quantity; the distance between the sea surface beacon node i and the underwater mobile node is expressed as
(3) The sound velocity is not constant due to the medium nonuniformity, and the sound velocity profile is expressed as c (z) regardless of the transverse change of the sound velocity profile, and z represents a depth variable; by utilizing Snell law, establishing the relationship between the horizontal distance, the propagation delay and the propagation constant between the sea surface beacon node i and the underwater mobile node, and discretizing to obtain the following results:
where ρ isi、τiAnd niRepresenting the horizontal distance, the propagation delay and the propagation constant corresponding to the sea surface beacon node i and the underwater mobile node; n represents the number of samples at c (Z), at depth ZiAnd ZtIs uniformly sampled, j represents the serial number of the sampling point, zjRepresenting the depth at the sampling point, c (z)j) Representing depth zjThe corresponding speed of sound is the speed of sound,
the ratio of the straight-line distance between the sea surface beacon node i and the underwater mobile node to the propagation delay is expressed as follows:
due to each item
The variation amount is small, and the above formula can be simplified into:
according to the Taylor expansion, the above equation can be further simplified:
because the beacon nodes are all located on the sea surface, and the depth difference between the beacon nodes is small, the ratio of the straight-line distance and the propagation delay of the beacon nodes on different sea surfaces and the underwater mobile node is considered to be equal and is expressed as m, namely:
based on the above formula, after obtaining the difference between the propagation delays of the positioning messages of the different sea surface beacon nodes, the difference △ D between the distances between the different sea surface beacon nodes and the underwater mobile node can be obtained12And △ D13With node 1 as a reference, that is:
(4) based on the step (3), the calculation module obtains the difference values △ D12 and △ D13 of the distances between the beacon nodes on different sea surfaces and the underwater mobile node, and an observation equation and a state equation of the extended Kalman filtering are established:
θt,k＝θt,k-1+TkVk-1+wk(8)
wherein the subscripts k-1 and k denote the time scalar quantities introduced in the Kalman filtering, which are k-1 and k times, △ D12,k，△D13,kExpressing the observed quantity at the moment k, namely the difference value of the distances between the beacon nodes at different sea surfaces at the moment k and the underwater mobile node; thetat,kAnd thetat,k-1State vectors representing time k and time k-1, respectively, i.e. two-dimensional coordinates (X) of the underwater mobile nodet,k,Yt,k) And (X)t,k-1,Yt,k-1)；Zt,kDepth information of the underwater mobile node at the moment k is represented; s1,k,S2,k,S3,kThree-dimensional coordinates (X) of 3 sea surface beacon nodes at the time of ki,k,Yi,k,Zi,k)，i＝1,2,3；Vk-1Representing the two-dimensional moving speed of the underwater mobile node at the k-1 moment; t iskRepresenting the time interval of time k-1 and time k; deltakAnd wkObserving noise and process noise for time k;
observation equation h (theta)t,k,Zt,k,S1,k,Si,k) Expressed as equation (9), where l ═ 2,3 denotes the beacon number 2, 3:
firstly, based on the estimated value theta of the position of the underwater mobile node at the moment of k-1t,k-1|k-1And an estimate of the speed of movement
And predicting the position of the underwater mobile node at the moment k:
wherein theta ist,k|k-1＝[Xt,k|k-1Yt，k|k-1]TRepresenting the predicted value of the underwater mobile node at the moment k;
calculating its covariance Pk|k-1：
Wherein, Pk|k-1Covariance matrix, P, representing predicted values of underwater mobile nodes at time kk-1|k-1Covariance matrix, Q, representing the estimate of the position of an underwater mobile node at time k-1k-1|k-1Representing a covariance of the estimate of the velocity of movement of the underwater mobile node;
kalman gain KkExpressed as:
wherein R iskA covariance representing the observation error; hkFor observing the matrix, because of the nonlinear equation of the observation equation, the first-order Taylor expansion is carried out, and the approximation linearization is carried out:
wherein the content of the first and second substances,
expressed as:
therefore, the position estimation value of the underwater mobile node at the time k is as follows:
converting the two-dimensional coordinate position into longitude and latitude by inverse Gaussian calculation; and updating the covariance of the position of the underwater mobile node at the moment k for calculation at the next moment:
Pk|k＝Pk|k-1-KkHkPk|k-1(15)
estimating moving speed of underwater mobile node at k moment
And calculates its covariance Qk|kFor the next time calculation:
b. when the underwater acoustic receiving system of the underwater mobile node does not receive 3 positioning messages:
the underwater resolving module of the underwater mobile node does not receive message information submitted by an underwater main control system and the arrival time of the message, and only receives the depth information of the underwater mobile node, namely the depth information is between the time k-1 and the time k; estimating the position and the moving speed of the underwater mobile node based on the moment k-1, and estimating the position theta of the underwater mobile node at the current moment't,k|kI.e. by
Wherein, Tk' represents the time interval from the current time to the time k-1;
and converting the two-dimensional space coordinate position into longitude and latitude by using inverse Gaussian calculation.
2. The system for implementing the Beidou beacon based passive positioning method for underwater mobile nodes as claimed in claim 1, wherein: the system consists of at least 3 sea surface beacon nodes, underwater mobile nodes, a shore-based data control center and a ship-based control center;
the sea surface beacon node comprises a Beidou satellite receiver, a sea surface master control system and a sea surface acoustic transceiver system with a comprehensive positioning/communication function;
the underwater mobile node comprises a propeller, an underwater positioning receiver and a pressure sensor; the underwater positioning receiver comprises an underwater main control system, an underwater acoustic receiving system with a comprehensive positioning/communication function, an underwater resolving module and an underwater short message processing module;
the ship-based control center is a positioning auxiliary system, is deployed in a sea surface beacon node coverage sea area, carries a ship-based positioning receiver and is used for monitoring the working condition of the sea surface beacon node, and the ship-based positioning receiver comprises a ship-based acoustic receiving system with a comprehensive positioning/communication function, a ship-based resolving module and a ship-based short message processing module; the ship-based control center monitors messages sent by specific sea surface beacon nodes in the sea area covered by the sea surface beacon nodes through a ship-based acoustic receiving system, and judges the working states of the sea surface beacon nodes according to the time sequence and the content of the received messages; in addition, the ship-based control center monitors the working conditions of all sea surface beacon nodes discontinuously by moving, so as to monitor the running condition of the positioning system;
the shore-based data control center is used for controlling the underwater mobile node; the shore-based data control center issues instructions to the sea surface beacon nodes through the Beidou satellite navigation system, and the sea surface beacon nodes broadcast the instructions to the corresponding underwater mobile nodes in a short data message mode;
the deployment topology of the sea surface beacon nodes is formed by taking a regular triangle grid as a basis:
the underwater mobile node can complete position calculation only by receiving at least 3 positioning signals, and the beacon nodes form a topological structure of a regular triangular grid, so that the sea area can be covered to the maximum extent; therefore, the deployment topology of the sea surface beacon nodes adopts a regular triangle as a grid, 3 sea surface beacons are positioned at the vertex of the regular triangle, and the deployment topology of all the sea surface beacon nodes is formed on the basis of the regular triangle grid, so that a target sea area is covered, and the underwater mobile nodes covering any position below the sea area can receive positioning signals sent by the 3 sea surface beacons at the vertex of the regular triangle grid;
the broadcast timing of the sea surface beacon node is: taking a regular triangular grid as a unit, namely, simultaneously broadcasting the positioning messages of 3 sea surface beacon nodes positioned on one triangular grid; when the sea surface beacon node on one triangular grid broadcasts a positioning message, after a fixed time interval, the sea surface beacon node on the next time sequence triangular grid broadcasts the positioning message; restarting the broadcasting time sequence of the next round of positioning messages until all the triangular grids broadcast the positioning messages;
the sea surface beacon node broadcasts a positioning message to the underwater in a CDMA spread spectrum mode:
3 sea surface beacons on a triangular grid need to broadcast positioning messages at the same time, so that a CDMA mode is adopted; for the generated positioning message, combining a multi-system convolutional Code with an M-system Code element Shift Keying (CSK) and distributing the multi-system convolutional Code to different pseudo-random sequences of a sea surface beacon node to realize multi-user communication;
the underwater mobile node utilizes a serial multiple access interference cancellation technology to inhibit multi-user interference caused by a near-far effect and recover expected positioning message information;
the positioning calculation process of the underwater mobile node is as follows:
c. when an acoustic receiving system of the underwater mobile node receives 3 positioning messages:
the underwater mobile node calculates the arrival time difference of different positioning messages according to the arrival time of the 3 positioning messages, and compensates the sound ray bending based on the Snell law to obtain the distance difference between the beacon nodes on different sea surfaces and the underwater mobile node;
based on an extended Kalman filtering method, taking the difference value of the distances between different sea surface beacon nodes and the underwater mobile node as an observed value, and resolving the position and the moving speed of the underwater mobile node at the current moment according to the position and the moving speed information at the previous moment;
d. when the acoustic receiving system of the underwater mobile node does not receive 3 positioning messages:
and when the underwater mobile node does not receive the positioning message, estimating the position of the underwater mobile node at the current moment by using the position and the moving speed calculated at the previous moment based on an extended Kalman filtering method.
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