CN110501694B - Underwater node passive motion speed estimation method based on Doppler frequency shift estimation - Google Patents
Underwater node passive motion speed estimation method based on Doppler frequency shift estimation Download PDFInfo
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Abstract
The invention discloses a Doppler frequency shift estimation-based underwater node passive motion speed estimation method, which comprises the steps of setting up the current kth positioning, establishing a positioning model based on an arrival time difference TDOA, obtaining communication time information of an underwater sensing node and a reference buoy node in the kth positioning process, and calculating the positioning position of the sensing node in the kth positioning process; calculating a projection component of the actual motion speed vector of the sensing node on a connecting line between the position of the sensing node and the position of the reference buoy node in the k-1 positioning process according to the Doppler frequency shift measured value and the actual motion speed vector of the reference buoy node obtained in the k-1 positioning process; estimating an actual motion velocity vector of the sensing node from a kth-1 positioning process to a kth positioning process; and obtaining the actual motion speed vector predicted value of the sensing node during the kth positioning process to the kth+1th positioning process, and predicting the real-time position of the node.
Description
Technical Field
The invention belongs to the field of underwater sensing network positioning, and particularly relates to an underwater node passive motion speed vector estimation method based on Doppler frequency shift estimation.
Background
The ocean is a huge resource treasury on the earth, but the knowledge and investigation of human beings on the ocean is less than 10%, and the huge ocean waits for the cognition, development and utilization of the human beings. Marine environmental monitoring, marine resource development and marine rights and interests protection are important strategic demands in various countries. The underwater huge pressure and huge area range are not suitable for direct long-term operation of human beings, and along with the development of an embedded system, the underwater acoustic communication and signal processing technology is improved, and the underwater acoustic communication sensing network becomes an important means for realizing deep sea oil well exploration, seismic observation, hydrologic environment monitoring, underwater navigation, underwater rescue and other applications.
In the underwater acoustic communication sensing network, the positioning function is indispensable, on one hand, the control center needs to know the position information of the network nodes so as to recover and maintain, and on the other hand, the sensing data is provided with the position information, so that the method has practical significance. However, due to the mobility of the water body, the underwater nodes can passively move along with the water body, and the positioning process needs to be periodically performed to maintain the accuracy of the positioning position.
In order to predict the position of a node at any time between two adjacent positioning processes, the passive motion velocity vector of the node needs to be estimated. The traditional node motion speed vector prediction method mainly comprises two methods, wherein the first method is to obtain past node motion speed information according to past positioning position information of the node, and predict future node motion speed vectors by adopting a wiener filter. The accuracy of the node motion speed vector estimation by the method depends on the positioning accuracy, and if the distance measurement and positioning error of a positioning system is increased, the node motion speed vector estimation is greatly influenced. According to the second method, the motion speed of the target node is estimated in a weighted average mode according to the motion speed information of the neighbor nodes of the target node. This approach requires each node to additionally broadcast a data packet containing its own speed information at least once during the positioning phase, increasing the network communication burden and node energy overhead.
In the actual ocean or river water body, the flow rates of water bodies at different depths are different, so that relative motion exists between the nodes at different depths, in two adjacent positioning, the relative motion condition of the transmitting node and the receiving node can be estimated by utilizing signal Doppler frequency shift, and when the nodes obtain the relative motion information of a plurality of reference nodes, the real motion velocity vector can be further estimated. Patent CN201710657205 discloses a method for positioning underwater sensor nodes based on TOA ranging and doppler effect, wherein the node movement speed is obtained by sensor measurement, and the doppler shift measurement value is used as a positioning model parameter to improve positioning accuracy. The invention discloses a method for estimating a passive motion velocity vector of an underwater node based on Doppler frequency shift estimation, which is a novel node motion estimation method and is used for predicting the position of the node.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides an underwater node passive motion speed vector estimation method based on Doppler frequency shift estimation, and aims to solve the problem that positioning information is invalid due to passive motion of an underwater node caused by water flow influence.
The technical scheme of the invention provides an underwater node passive motion speed estimation method based on Doppler frequency shift estimation, which comprises the following steps:
step 1, setting up a current positioning for the kth time, establishing a positioning model based on an arrival time difference TDOA, obtaining communication time information of an underwater sensing node and a reference buoy node in the kth-1 positioning process, and calculating the positioning position of the sensing node in the kth-1 positioning process;
step 2, measuring Doppler frequency shift according to the communication time information of the sensing node and the reference buoy node obtained in the step 1 and the communication time information of the sensing node and the reference buoy node in the kth positioning process;
step 3, calculating projection components of the actual motion velocity vector of the sensing node on the connecting line of the sensing node position and the reference buoy node position in the k-1 positioning process according to the Doppler frequency shift measured value obtained in the step 2 and the actual motion velocity vector of the reference buoy node in the k-1 positioning process and the k positioning process;
step 4, estimating the actual motion velocity vector of the sensing node from the kth-1 positioning process to the kth positioning process according to the projection components of the actual motion velocity vector between the sensing node and each reference buoy node obtained in the step 3;
step 5, obtaining an actual motion speed vector predicted value of the sensing node during the kth positioning process to the (k+1) th positioning process according to the actual motion speed vector estimated value of the sensing node obtained in the step 4, and predicting the real-time position of the node until a new positioning process starts;
and step 6, circularly executing the steps 1-5, and continuously estimating the motion speed.
In the step 1, the positioning model consists of underwater sensing nodes and water surface reference buoy nodes, wherein the water surface buoy nodes serve as positioning reference nodes to assist in positioning the underwater sensing nodes; the sensing node adopts an active positioning mode, and realizes positioning by a distance measurement mode based on arrival time.
Moreover, the positioning of the sensing node is realized by adopting a ranging mode based on the arrival time as follows,
let p=1, 2..p is the sensing node number, b n A reference buoy node is a one-hop neighbor in the communication range of the sensing node p, n=1, 2.
In the k-1 positioning process, the moment when the sensing node p sends the positioning request information isThe position to be positioned isReference buoy node b n The time for receiving the positioning request information is +.>The reference position isN is the total number of reference nodes which receive the positioning request information of the sensing node p; reference buoy node b n The time for transmitting the positioning response information is +.>The sensing node p receives the reference buoy node b n The positioning response information time of (a) is
According to the solid geometry relation, the sensing node p and the reference buoy node b n Distance ofExpressed as:
distance ofCan be expressed as:
where c is the speed of sound, the formula (1) expands to:
wherein the method comprises the steps ofFor the sensing node p and the reference buoy node b n A related constant term;
when n=1 and n+.1, the sensing node p and the reference buoy node b are based on the TDOA positioning principle 1 、b n Distance difference betweenThe method comprises the following steps:
another expression of formula (4) is:
wherein the method comprises the steps ofn is not equal to 1 and is the k-1 positioning process sensing node p and the reference buoy node b n Distance between->n is not equal to 1 and is the reference buoy node b in the kth-1 positioning process 1 、b n Distance difference between>Sensing node p and reference buoy node b for the kth-1 positioning process 1 The distance between them, formula (3) brings into formula (5) where:
in the formula (6)The term is written in the form of formula (3), and formula (6) is rewritten as:
wherein the method comprises the steps ofIs the sensing node p and the reference buoy node b in the k-1 positioning process 1 The relative terms of the constants are used,is the reference buoy node b 1 X, y coordinate values of (c);
in the k-1 positioning process, the sensor node p and the reference buoy node b are based 1 、b n N=2, 3..n distance information is written in matrix form, expressed as:
H＝GΨ+W (8)
in the formula (8), W is a gaussian noise matrix:
wherein the method comprises the steps ofIndicating node b with reference buoy in the k-1 positioning process 1 And b n N=2,.. N-dependent Gaussian noise term, N (0, σ) 2 ) Representing the mean value of the Gaussian noise as 0 and the variance as sigma 2 ；
In the formula (8), H and G are known constant matrices, and are expressed as follows:
in the formula (8), ψ is a parameter to be solved, and the parameter includes the horizontal position information of the sensing node p, and is expressed as:
the least squares solution of equation (8) is:
Ψ＝(G T G) -1 G T H (12)
wherein G is T Transposed matrix of G () -1 The inverse of the matrix is represented;
solving the formula (12) by adopting a Chan algorithm and a Taylor series expansion algorithm to obtain a positioning position estimation value of the sensing node p in the (k-1) th positioning process
Furthermore, the step 2 is implemented as follows,
in the kth positioning process, the moment when the sensing node p sends the positioning request information is set asThe position to be positioned isReference buoy node b n The time for receiving the positioning request information is +.>The reference position is +.>Reference buoy node b n The time for transmitting the positioning response information is +.>The sensing node p receives the reference buoy node b n The location response information time of (2) is +.>
Obtaining the positioning position estimated value of the sensing node p in the kth positioning process according to the step 1In the kth positioning process and the kth-1 positioning process, the time difference of sending the positioning request information by the sensing node p is thatThe frequency of the positioning request information is +.>Reference buoy node b n The time difference for receiving the positioning request information is +.>The frequency of receiving positioning request information is +.>Sensing node p and reference buoy node b n The doppler shift associated with the location request information is between,
wherein,,indicating that the nodes are close to each other, +.>Indicating that the nodes are relatively far apart.
Furthermore, the step 3 is implemented as follows,
during the kth positioning process and the kth-1 positioning process, reference is made to the buoy node b n Actual motion velocity vectorThe method comprises the following steps:
reference buoy node b n Estimating position of sensing node p during kth-1 positioningAnd reference buoy node b n Reference position +.>Projection on a wire->The method comprises the following steps:
wherein the method comprises the steps ofEstimating the position for the sensing node p>And reference buoy node b n Reference positionThe included angle between the connecting line and the horizontal plane,
in the kth positioning process and the kth-1 positioning process, the passive movement speed of the sensing node and the reference buoy node along with water flow is slower, and the positioning method is characterized in thatIn time, the passive movement distance is far smaller than the distance between the sensing node and the reference buoy node, a far-field condition is formed, and the propagation track of the positioning request information is approximately parallel;
position request information propagation path differenceThe method comprises the following steps:
wherein the method comprises the steps ofFor the estimated position of the sensing node p in the k-1 positioning processAnd reference buoy node b n Reference position +.>Projection components on the connection;
phase difference of propagation of positioning request informationThe method comprises the following steps:
wherein the method comprises the steps ofFor the communication carrier wavelength, c is the speed of sound, and f is the carrier frequency. The second expression of the Doppler shift of equation (13) is:
combining (17) (18) (19) to obtain the estimated position of the sensing node p in the k-1 positioning process of the actual motion speed vector of the sensing node pAnd reference buoy node b n Reference position +.>Projection component on the connection +.>Is a calculated expression of (a):
furthermore, the step 4 is implemented as follows,
projecting component of actual motion velocity vector of sensing node p in step 3Written in vector form:
wherein the method comprises the steps ofIs->Absolute value of>For the estimated position of the sensing node p in the k-1 positioning processAnd reference buoy node b n Reference position +.>The unit direction vector on the connecting line has the following value:
wherein the method comprises the steps ofThe unit vectors are respectively in the directions of coordinate axes x, y and z;
through the position of the sensing node pAnd projection component of the actual motion velocity vector with the sense node p +.>The general expression for the vertical plane equation is:
wherein the method comprises the steps ofIs plane equation parameterThe numbers, x, y, z represent coordinate axes, normal vector of plane equationCan be expressed as:
projection component of actual motion velocity vector of sensing node pA set of normal vectors substantially satisfying the plane of formula (23), let
Plane equation parametersThe method comprises the following steps:
general expression (23) of plane equation passes through projection component of actual motion velocity vector of sensing node pEnd point of->Expressed in vector form as:
endpoint vectorsCoordinates of the representation +.>Substituting the general expression (23) of the plane equation to obtain the plane equation parameter +.>
When n=1, 2,..n, a plurality of sets of plane equations are expressed in matrix form:
wherein the method comprises the steps ofIs a plane equation parameter matrix +.>Is the intersection point of plane equation, which is the position of the sensing node pThe actual motion velocity vector as starting point +.>End point of->Expressed as:
the involved nodes need to satisfy node location constraints: at least 3 reference buoy nodes are not located on the same straight line; to be used forSolving (29) by least square method to obtain the position of the sensing node pActual motion speed vector estimate as starting point +.>Endpoint coordinates +.>
Actual motion velocity vector estimation of the sensor node p during the kth-1 positioning and kth positioningThe method comprises the following steps:
furthermore, the step 5 is implemented as follows,
actual motion velocity vector predictors for sense node p during kth position fix and kth+1th position fixThe method comprises the following steps:
during the kth position fix and the kth+1th position fix, the position fix prediction value of the sensor node pThe method comprises the following steps:
wherein the method comprises the steps ofPositioning estimation value for kth positioning sensing node p +.>For the sensing node p at the moment it sends the location request information +.>Time after passing, when->Satisfy->When (I)>Representing any time between the (k+1) th positioning and the kth positioning of the sensing node p.
Aiming at the problem that the positioning position of the underwater node is invalid due to the fact that the underwater node is influenced by water flow, the invention provides the underwater node passive motion speed vector estimation method based on Doppler frequency shift estimation, the method does not need speed vector information of neighbor nodes, network communication overhead is reduced, and node energy is saved; the underwater node passive motion velocity vector obtained by the method is only related to the first positioning position in the adjacent two positioning processes, reduces the influence of positioning errors on the velocity vector estimated value, is beneficial to improving the accuracy of node positioning prediction, and is an underwater node passive motion velocity vector estimation method with good application prospect.
Drawings
Fig. 1 is a schematic diagram of a positioning scenario according to an embodiment of the present invention.
FIG. 2 is a schematic diagram of single positioning process node data interaction in accordance with an embodiment of the present invention.
FIG. 3 is a schematic diagram of node location constraints according to an embodiment of the present invention.
Fig. 4 is a schematic view of passive motion velocity vector estimation of an underwater node according to an embodiment of the present invention.
Detailed Description
The technical scheme of the present invention is described in detail below with reference to the accompanying drawings and examples.
Examples of the embodiments are shown in the drawings, and the embodiments described below by referring to the drawings are exemplary only for explaining the present invention and not to be construed as limiting the present invention.
The embodiment of the invention provides an underwater node passive motion speed vector estimation method based on Doppler frequency shift estimation, which comprises the following steps of:
step 1: setting the current positioning for the kth time, establishing a positioning model based on the arrival time difference (different time of arrival, TDOA), obtaining the communication time information of the sensing node and the reference buoy node in the positioning process for the kth time and calculating the positioning position of the sensing node in the positioning process for the kth time-1;
preferably, in the step 1, the positioning model is composed of underwater sensing nodes and water surface buoy nodes, and all the nodes are provided with pressure sensors, so that node depth information can be obtained, and the depth is kept unchanged; the water surface buoy node obtains a real-time position through a global positioning system and is used as a positioning reference node to assist in positioning the underwater sensing node, namely a reference buoy node; the underwater sensing node adopts an active positioning mode, and realizes positioning by a distance measurement method based on arrival time. Establishing a rectangular coordinate system in a positioning area, wherein coordinate axes are represented by x, y and z, and in the embodiment, x is a horizontal coordinate and represents the east-west direction and the forward direction; y is a horizontal coordinate, and represents the north-south direction and the forward direction; z is a vertical coordinate representing depth, forward vertically downward. k=2, 3..k is the positioning procedure number, representing the kth positioning; p=1, 2..p is the sensing node number; b n For one-hop neighbor reference buoy nodes within communication range of the sensing node p, n=1, 2.
Let k-1 timesIn the positioning process, the moment when the sensing node p sends the positioning request information isThe position to be positioned is Coordinate values in x, y and z directions of a sensing node p are respectively shown, p represents a sensing node number, and k-1 represents a positioning process number; reference buoy node b n The time for receiving the positioning request information is +.>The reference position is Respectively reference buoy node b n The coordinate values in the x, y and z directions of the sensor node p are represented by N, wherein N represents the number of the buoy node, the value of n=1, 2, N and N are the total number of reference nodes which receive the positioning request information of the sensor node p, and the node is required to be satisfied that N is more than or equal to 3 when successfully positioned; reference buoy node b n The time for transmitting the positioning response information is +.>The sensing node p receives the reference buoy node b n The location response information time of (2) is +.>
According to the solid geometry relation, the sensing node p and the reference buoy node b n Distance ofExpressed as:
distance ofIt can also be expressed as:
where c is the speed of sound. The expansion of formula (1) can be obtained:
wherein the method comprises the steps ofFor the sensing node p and the reference buoy node b n Related constant terms. When n=1 and n+.1, the sensing node p and the reference buoy node b are based on the TDOA positioning principle 1 、b n Distance difference between>The method comprises the following steps:
another expression of formula (4) is:
wherein the method comprises the steps ofn is not equal to 1 and is the k-1 positioning process sensing node p and the reference buoy node b n Distance between->n is not equal to 1 and is the reference buoy node b in the kth-1 positioning process 1 、b n Distance difference between>Sensing node p and reference buoy node b for the kth-1 positioning process 1 The distance between them, formula (3) brings into formula (5) where:
in the formula (6)The term is written in the form of formula (3), and formula (6) is rewritable as follows:
wherein the method comprises the steps ofIs the sensing node p and the reference buoy node b in the k-1 positioning process 1 The relative terms of the constants are used,is the reference buoy node b 1 X, y coordinate values of (c).
In the k-1 positioning process, the sensor node p and the reference buoy node b are based 1 、b n N=2, 3..n distance information is written in matrix form as:
H＝GΨ+W (8)
in the formula (8), W is a gaussian noise matrix:
wherein the method comprises the steps ofIndicating node b with reference buoy in the k-1 positioning process 1 And b n N=2,.. N-dependent Gaussian noise term, N (0, σ) 2 ) Representing the mean value of the Gaussian noise as 0 and the variance as sigma 2 ；
In the formula (8), H and G are known constant matrices, and are expressed as follows:
in the formula (8), ψ is a parameter to be solved, and the parameter includes the horizontal position information of the sensing node p, and is expressed as:
the least squares solution of equation (8) is:
Ψ＝(G T G) -1 G T H (12)
wherein G is T Transposed matrix of G () -1 Representing the matrix inverse.
Solving the formula (12) by adopting a Chan algorithm and a Taylor series expansion algorithm to obtain a positioning position estimation value of the sensing node p in the (k-1) th positioning process X, y, z coordinate values, respectively.
Step 2: measuring Doppler frequency shift according to the communication time information of the sensing node and the reference buoy node obtained in the step 1 and the communication time information of the sensing node and the reference buoy node in the kth positioning process;
in the kth positioning process, the moment when the sensing node p sends the positioning request information is thatThe position to be positioned isReference buoy node b n The time for receiving the positioning request information is +.>The reference position is +.> Respectively x, y and z coordinate values, wherein N represents the number of the buoy node, the value n=1, 2, N and N are the total number of reference nodes which receive the positioning request information of the sensing node p, and the node is required to meet that N is more than or equal to 3 when successfully positioned; reference buoy node b n The time for transmitting the positioning response information is +.>The sensing node p receives the reference buoy node b n The location response information time of (2) is +.>According to the positioning method of step 1, the positioning position estimation value of the sensor node p is +.> X, y, z coordinate values, respectively.
In the kth positioning process and the kth-1 positioning process, the time difference of sending the positioning request information by the sensing node p is thatThe frequency of the positioning request information is +.>Reference buoy node b n The time difference for receiving the positioning request information is +.>The frequency of receiving positioning request information is +.>Sensing node p and reference buoy node b n The Doppler shift associated with the location request information is:
indicating that the relative positions of the nodes are close;Indicating that the nodes are relatively far apart.
Step 3: calculating projection components of the actual motion speed vector of the sensing node on a connecting line between the position of the sensing node and the position of the reference buoy node in the k-1 positioning process according to the Doppler frequency shift measured value obtained in the step 2 and the actual motion speed vector of the reference buoy node in the k-1 positioning process and the k positioning process;
in an embodiment, the buoy node b is referenced during the kth positioning process and the kth-1 positioning process n Actual motion velocity vectorThe method comprises the following steps:
reference buoy node b n Positioning at the k-1 st timeIn-process sensing node p estimates positionAnd reference buoy node b n Reference position +.>Projection on a wire->The method comprises the following steps:
wherein the method comprises the steps ofEstimating the position for the sensing node p>And reference buoy node b n Reference position->The included angle between the connecting line and the horizontal plane is as follows:
in the kth positioning process and the kth-1 positioning process, the passive movement speed of the sensing node and the reference buoy node along with water flow is slower, and the positioning method is characterized in thatIn the time, the passive movement distance is far smaller than the distance between the sensing node and the reference buoy node, a far-field condition is formed, the propagation tracks of the positioning request information are approximately parallel, and the propagation path difference of the positioning request information is +.>The method comprises the following steps:
wherein the method comprises the steps ofFor the estimated position of the sensing node p in the k-1 positioning processAnd reference buoy node b n Reference position +.>Projection components on the connection.
Phase difference of propagation of positioning request informationThe method comprises the following steps:
wherein the method comprises the steps ofFor the communication carrier wavelength, c is the speed of sound, and f is the carrier frequency. The second expression of the Doppler shift of equation (13) is:
combining (17) (18) (19) to obtain the estimated position of the sensing node p in the k-1 positioning process of the actual motion speed vector of the sensing node pAnd reference buoy node b n Reference position +.>Projection component on the connection +.>Is a calculated expression of (a):
step 4: according to the sensing node p obtained in the step 3 and each reference buoy node b n The projection component of the actual motion velocity vector between the two positioning processes is used for estimating the actual motion velocity vector of the sensing node from the kth-1 positioning process to the kth positioning process;
in an embodiment, the projected component of the actual motion velocity vector of the sensing node p in step 3Written in vector form:
wherein the method comprises the steps ofIs->Absolute value of>For the estimated position of the sensing node p in the k-1 positioning processAnd reference buoy node b n Reference position +.>The unit direction vector on the connecting line has the following value: />
Wherein the method comprises the steps ofThe unit vectors are in the directions of coordinate axes x, y and z respectively. Through the position of the sensing node pAnd projection component of the actual motion velocity vector with the sense node p +.>The general expression for the vertical plane equation is:
wherein the method comprises the steps ofIs a plane equation parameter, x, y and z represent coordinate axes, and a plane equation normal vectorCan be expressed as:
projection component of actual motion velocity vector of sensing node pA set of normal vectors substantially satisfying the plane of formula (23), let
Plane equation parametersThe method comprises the following steps:
general expression (23) of plane equation passes through projection component of actual motion velocity vector of sensing node pEnd point of->Expressed in vector form as:
endpoint vectorsCoordinates of the representation +.>Substituting the general expression (23) of the plane equation to obtain the plane equation parameter +.>
When n=1, 2,..n, a plurality of sets of plane equations are expressed in matrix form:
wherein the method comprises the steps ofIs a plane equation parameter matrix +.>For plane equation intersection, it is the sense node p at position +.>The actual motion velocity vector as starting point +.>End point of->Expressed as:
the involved nodes need to satisfy node location constraints: at least 3 reference buoy nodes are not located on the same line. Solving (29) by least square method to obtain the position of the sensing node pActual motion speed vector estimate as starting point +.>Endpoint coordinates +.>
In the k-1Actual motion velocity vector estimation values of the sensing node p during the next and kth positioningThe method comprises the following steps:
step 5: obtaining an actual motion speed vector predicted value of the sensing node during the kth positioning process to the kth+1th positioning process according to the actual motion speed vector estimated value of the sensing node obtained in the step 4, and predicting the real-time position of the node until a new positioning process starts;
in an embodiment, the actual motion velocity vector predictor of the sensing node p during the kth position fix and the kth+1th position fixThe method comprises the following steps:
during the kth position fix and the kth+1th position fix, the position fix prediction value of the sensor node pThe method comprises the following steps:
wherein the method comprises the steps ofPositioning estimation value for kth positioning sensing node p +.>For the sensing node p at the moment it sends the location request information +.>Time after passing, when->Satisfy->When (I)>Representing any time between the (k+1) th positioning and the kth positioning of the sensing node p.
Step 6: returning to the step 1, circularly executing the step 1-5 to perform next positioning, and continuously performing motion speed estimation.
In an embodiment, for k=2, 3..k, let k=k+1, step 1 to step 5 are repeatedly performed. In particular implementations, execution may continue until the system stops.
In specific implementation, the method provided by the invention can realize automatic operation flow based on software technology, and the corresponding device for executing the flow is also in the protection scope of the invention.
Fig. 1 is a schematic diagram of a positioning scenario according to an embodiment of the present invention. The positioning system consists of reference buoy nodes and sensing nodes, wherein the nodes move passively along with water flow, the reference buoy nodes position themselves through a global positioning system of a satellite, and the real-time positions of the reference buoy nodes are known and serve as positioning reference nodes; the sensing node actively transmits positioning request information, positioning is carried out according to positioning reply information returned by the reference buoy node, and the successful positioning of the sensing node requires that at least 3 or more than 3 reference buoy nodes which are not in the same straight line are received.
FIG. 2 is a schematic diagram of data interaction according to an embodiment of the present invention. In the kth positioning process, the sensing node p is positioned atTransmitting positioning request information at the moment and respectively at +.>n=1, 2..n, n.gtoreq.3 moment arrives at reference buoy node b 1 ,b 2 ,...,b n N=1, 2,.. 1 ,b 2 ,...,b n N=1, 2,..n=1, 2..n, N is not less than 3 times of return positioning reply information and reach the sensing node p, the arrival times are respectively +.>n＝1,2,...,N,N≥3。
Fig. 3 is a schematic diagram of a relationship between a real motion vector and a projected motion vector of a sensing node according to an embodiment of the present invention, and illustrates 3 reference buoy nodes as an example. The positioning process of the (k-1) th time, the positioning position of the sensing node p is as followsThe sensor node p is located +_ during the positioning process from the (k-1) th to the (k) th positioning process>The end point of the true motion velocity vector, which is the start point, isIn the k-1 positioning process, the reference buoy node position is +>Connecting line of true motion speed vector of sensing node p between sensing node and reference buoy node position +.>Is a directed line segment, denoted +.>Wherein the method comprises the steps ofA, B, C are projection points respectively. The sense node p is located +.>The end point of the true motion velocity vector as the start point is +.>Respectively pass through projection points A, B and C, and respectively and +.>A common intersection of the perpendicular three planes.
Fig. 4 is a schematic view of passive motion velocity vector estimation of an underwater node according to an embodiment of the present invention. In the k-1, k, k+1 positioning process, the moments when the sensor node p sends the positioning request information are respectively as followsThe estimated positions obtained by the positioning algorithm are +.>Reference buoy node b n The time for receiving the positioning request information is +.>The positions of the positioning request information are respectively +.>Reference buoy node b during the kth-1 positioning process to the kth positioning process n Is +.>The actual motion speed vector predicted value of the sensing node p obtained by the method of the embodiment of the invention is +.>The estimated value is +.>Reference buoy node b during the kth positioning process to the kth+1th positioning process n Is +.>The actual motion speed vector predicted value of the sensing node p obtained by the method of the embodiment of the invention is +.>The estimated value is +.>During the (k+1) th positioning process to the (k+2) th positioning process, the actual motion velocity vector predicted value of the sensing node p obtained by the method according to the embodiment of the invention is +.>The relation between the actual motion velocity vector predicted value and the estimated value of the sensing node p is satisfied +.>
It should be understood that parts of the specification not specifically set forth herein are all prior art.
It should be understood that the foregoing description of the preferred embodiments is not intended to limit the scope of the invention, but rather to limit the scope of the claims, and that those skilled in the art can make substitutions or modifications without departing from the scope of the invention as set forth in the appended claims.
Claims (3)
1. The method for estimating the passive motion speed of the underwater node based on Doppler frequency shift estimation is characterized by comprising the following steps of:
step 1, setting up a current positioning for the kth time, establishing a positioning model based on an arrival time difference TDOA, obtaining communication time information of an underwater sensing node and a reference buoy node in the kth-1 positioning process, and calculating the positioning position of the sensing node in the kth-1 positioning process;
step 2, measuring Doppler frequency shift according to the communication time information of the sensing node and the reference buoy node obtained in the step 1 and the communication time information of the sensing node and the reference buoy node in the kth positioning process;
the step 2 is implemented as follows,
in the kth positioning process, the moment when the sensing node p sends the positioning request information is set asThe position to be positioned isReference buoy node b n The time for receiving the positioning request information is +.>The reference position is +.>Reference buoy node b n The time for transmitting the positioning response information is +.>The sensing node p receives the reference buoy node b n The location response information time of (2) is +.>
Obtaining the positioning position estimated value of the sensing node p in the kth positioning process according to the step 1During the kth positioning process and the kth-1 positioning process, the sensor nodeThe time difference of sending the positioning request information by the point p is +.>The frequency of sending the positioning request information is +.>Reference buoy node b n The time difference of receiving the positioning request information is thatThe frequency of receiving positioning request information is +.>Sensing node p and reference buoy node b n The doppler shift associated with the location request information is between,
wherein,,indicating that the nodes are close to each other, +.>Indicating that the relative positions of the nodes are far away;
step 3, calculating projection components of the actual motion velocity vector of the sensing node on the connecting line of the sensing node position and the reference buoy node position in the k-1 positioning process according to the Doppler frequency shift measured value obtained in the step 2 and the actual motion velocity vector of the reference buoy node in the k-1 positioning process and the k positioning process;
the implementation of step 3 is as follows,
during the kth positioning process and the kth-1 positioning process, reference is made to the buoy node b n Actual motion velocity vectorThe method comprises the following steps:
reference buoy node b n The actual motion speed vector estimates the position of the sensing node p in the k-1 positioning processAnd reference buoy node b n Reference position +.>Projection on a wire->The method comprises the following steps:
wherein the method comprises the steps ofEstimating the position for the sensing node p>And reference buoy node b n Reference positionThe included angle between the connecting line and the horizontal plane,
in the kth positioning procedureIn the process of positioning the sensor node and the reference buoy node along with water flow, the passive movement speed is slower in the (k-1) th positioning processIn time, the passive movement distance is far smaller than the distance between the sensing node and the reference buoy node, a far-field condition is formed, and the propagation track of the positioning request information is approximately parallel;
position request information propagation path differenceThe method comprises the following steps:
wherein the method comprises the steps ofEstimated position of the sensor node p during the kth-1 positioning for the actual motion velocity vector of the sensor node p>And reference buoy node b n Reference position +.>Projection components on the connection;
phase difference of propagation of positioning request informationThe method comprises the following steps:
wherein the method comprises the steps ofFor the communication carrier wavelength, c is the speed of sound, f is the carrier frequency, and the second of the Doppler shifts of equation (13) is expressed as:
combining (17) (18) (19) to obtain the estimated position of the sensing node p in the k-1 positioning process of the actual motion speed vector of the sensing node pAnd reference buoy node b n Reference position +.>Projection component on the connection +.>Is a calculated expression of (a):
step 4, estimating the actual motion velocity vector of the sensing node from the kth-1 positioning process to the kth positioning process according to the projection components of the actual motion velocity vector between the sensing node and each reference buoy node obtained in the step 3;
the step 4 is implemented as follows,
projecting component of actual motion velocity vector of sensing node p in step 3Written in vector form:
wherein the method comprises the steps ofIs->Absolute value of>For the estimated position of the sensing node p in the k-1 positioning processAnd reference buoy node b n Reference position +.>The unit direction vector on the connecting line has the following value:
wherein the method comprises the steps ofThe unit vectors are respectively in the directions of coordinate axes x, y and z;
through the position of the sensing node pAnd projection component of the actual motion velocity vector with the sense node p +.>The general expression for the vertical plane equation is:
wherein the method comprises the steps ofIs a plane equation parameter, x, y and z represent coordinate axes, and a plane equation normal vector +.>Can be expressed as:
projection component of actual motion velocity vector of sensing node pA set of normal vectors substantially satisfying the plane of formula (23), let
Plane equation parametersThe method comprises the following steps:
general expression (23) of plane equation passes through projection component of actual motion velocity vector of sensing node pEnd point of (c)Expressed in vector form as:
endpoint vectorsCoordinates of the representation +.>Substituting the general expression (23) of the plane equation to obtain the plane equation parameter +.>
When n=1, 2,..n, a plurality of sets of plane equations are expressed in matrix form:
wherein the method comprises the steps ofIs a plane equation parameter matrix +.>For plane equation intersection, it is the sense node p at position +.>The actual motion velocity vector as starting point +.>End point of->Expressed as:
the involved nodes need to satisfy node location constraints: at least 3 reference buoy nodes are not located on the same straight line; solving (29) by least square method to obtain the position of the sensing node pActual motion speed vector estimate as starting point +.>Endpoint coordinates +.>
Wherein, ψ is a parameter to be solved and comprises the horizontal position information of the sensing node p;
actual motion velocity vector estimation of the sensor node p during the kth-1 positioning and kth positioningThe method comprises the following steps:
step 5, obtaining an actual motion speed vector predicted value of the sensing node during the kth positioning process to the (k+1) th positioning process according to the actual motion speed vector estimated value of the sensing node obtained in the step 4, and predicting the real-time position of the node until a new positioning process starts;
the step 5 is implemented as follows,
actual motion velocity vector predictors for sense node p during kth position fix and kth+1th position fixThe method comprises the following steps:
during the kth position fix and the kth+1th position fix, the position fix prediction value of the sensor node pThe method comprises the following steps:
wherein the method comprises the steps ofPositioning estimation value for kth positioning sensing node p +.>For the sensing node p at the moment it sends the location request information +.>Time after passing, when->Satisfy->When (I)>Representing any time between the (k+1) th positioning and the kth positioning of the sensing node p;
and 6, returning to the step 1, and circularly executing the step 1-5 to perform next positioning and continuously performing motion speed estimation.
2. The method for estimating the passive motion speed of the underwater node based on Doppler shift estimation according to claim 1, wherein: in the step 1, the positioning model consists of underwater sensing nodes and water surface reference buoy nodes, wherein the water surface reference buoy nodes serve as positioning reference nodes to assist in positioning the underwater sensing nodes; the sensing node adopts an active positioning mode, and realizes positioning by a distance measurement mode based on arrival time.
3. The method for estimating the passive motion speed of the underwater node based on Doppler shift estimation according to claim 2, wherein: the positioning of the sensing node is realized by adopting a ranging mode based on arrival time as follows,
let p=1, 2..p is the sensing node number, b n A reference buoy node is a one-hop neighbor in the communication range of the sensing node p, n=1, 2.
In the k-1 positioning process, the moment when the sensing node p sends the positioning request information isThe position to be positioned isReference buoy node b n The time for receiving the positioning request information is +.>The reference position isN is the total number of reference nodes which receive the positioning request information of the sensing node p; reference buoy node b n The time for transmitting the positioning response information is +.>The sensing node p receives the reference buoy node b n The positioning response information time of (a) is
According to the solid geometry relation, the sensing node p and the reference buoy node b n Distance ofExpressed as:
distance ofCan be expressed as:
where c is the speed of sound, the formula (1) expands to:
wherein the method comprises the steps ofFor the sensing node p and the reference buoy node b n A related constant term;
when n=1 and n+.1, the sensing node p and the reference buoy node b are based on the TDOA positioning principle 1 、b n Distance difference betweenThe method comprises the following steps:
another expression of formula (4) is:
wherein the method comprises the steps ofSensing node p and reference buoy node b for the kth-1 positioning process n Distance between->Reference buoy node b for the kth-1 positioning process 1 、b n Distance difference between>Sensing node p and reference buoy node b for the kth-1 positioning process 1 The distance between them, formula (3) brings into formula (5) where:
in the formula (6)The term is written in the form of formula (3), and formula (6) is rewritten as:
wherein the method comprises the steps ofIs the sensing node p and the reference buoy node b in the k-1 positioning process 1 Related constant term, < ->Is the reference buoy node b 1 X, y coordinate values of (c);
in the k-1 positioning process, the sensor node p and the reference buoy node b are based 1 、b n N=2, 3..n distance information is written in matrix form, expressed as:
H＝GΨ+W (8)
in the formula (8), W is a gaussian noise matrix:
wherein the method comprises the steps ofIndicating node b with reference buoy in the k-1 positioning process 1 And b n N=2,.. N-dependent Gaussian noise term, N (0, σ) 2 ) Representing the mean value of the Gaussian noise as 0 and the variance as sigma 2 ；
In the formula (8), H and G are known constant matrices, and are expressed as follows:
in the formula (8), ψ is a parameter to be solved, and the parameter includes the horizontal position information of the sensing node p, and is expressed as:
the least squares solution of equation (8) is:
Ψ＝(G T G) -1 G T H (12)
wherein G is T Transposed matrix of G () -1 The inverse of the matrix is represented;
solving the (12) by adopting a Chan algorithm and a Taylor series expansion algorithm to obtain the positioning position estimated value of the sensing node p in the k-1 positioning process
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