CN107390171B - Underwater sensor node positioning method based on TOA ranging and Doppler effect - Google Patents

Underwater sensor node positioning method based on TOA ranging and Doppler effect Download PDF

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CN107390171B
CN107390171B CN201710657205.0A CN201710657205A CN107390171B CN 107390171 B CN107390171 B CN 107390171B CN 201710657205 A CN201710657205 A CN 201710657205A CN 107390171 B CN107390171 B CN 107390171B
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CN107390171A (en
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孙海信
谢宇芳
齐洁
苗永春
许静萱
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Xiamen University
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    • G—PHYSICS
    • 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
    • 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
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/0257—Hybrid positioning
    • G01S5/0268—Hybrid positioning by deriving positions from different combinations of signals or of estimated positions in a single positioning system
    • G—PHYSICS
    • 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
    • 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
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/0278—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves involving statistical or probabilistic considerations
    • G—PHYSICS
    • 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
    • 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
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/14—Determining absolute distances from a plurality of spaced points of known location
    • G—PHYSICS
    • 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
    • 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
    • G01S5/16—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using electromagnetic waves other than radio waves
    • G—PHYSICS
    • 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
    • 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
    • G—PHYSICS
    • 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
    • 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
    • G01S5/30—Determining absolute distances from a plurality of spaced points of known location

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  • Radar, Positioning & Navigation (AREA)
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  • Electromagnetism (AREA)
  • Probability & Statistics with Applications (AREA)
  • Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)
  • Position Fixing By Use Of Radio Waves (AREA)

Abstract

An underwater sensor node positioning method based on TOA ranging and Doppler effect relates to an underwater sensor. In a positioning period, a node to be positioned receives positioning beacons transmitted by N anchor nodes, and the positioning beacons measure corresponding inter-node distance and Doppler frequency shift information. In addition, in the positioning period, the node to be positioned can obtain multiple groups of self speed measurement through the IMU sensor. On the basis that various measurement information is known, the node to be positioned firstly uses the speed of the node to correlate the actual information at different measurement moments with the position of the node to be positioned at the initial moment of the positioning period, then uses a relation obtained by information preprocessing and the measurement information to construct a maximum likelihood function, and finally estimates the motion track of the node to be positioned in the positioning period.

Description

Underwater sensor node positioning method based on TOA ranging and Doppler effect
Technical Field
The invention relates to an underwater sensor, in particular to an underwater sensor node positioning method based on TOA ranging and Doppler effects.
Background
With the increasing shortage of land resources, the coastal countries pay more and more attention to the development and utilization of oceans, and the ocean equity is more and more fierce. The underwater sensor network has wide application prospect in the aspects of ocean development and national defense safety, and becomes a hot topic of common attention of all countries in the world at present. For an underwater sensor network, the position information of the underwater sensor nodes is crucial and is a prerequisite for realizing applications such as battlefield reconnaissance, environment monitoring, underwater navigation, target identification and the like. In an actual marine environment, the underwater sensor nodes are not usually static, which results in that positioning beacons of different anchor nodes cannot synchronously reach a node to be positioned. Therefore, the traditional node positioning method based on synchronous measurement cannot be used in the underwater sensor network.
Disclosure of Invention
Aiming at the defects of the traditional node positioning method based on synchronous measurement, the invention provides an underwater sensor node positioning method based on TOA ranging and Doppler effect.
The invention comprises the following steps:
1) information preprocessing step;
2) and (5) a maximum likelihood positioning step.
In the step 1), the information preprocessing refers to that the actual information at different measurement moments is associated with the position of the node to be positioned at the initial moment of the positioning cycle by using the speed of the node to be positioned; the velocity of the node to be positioned can be measured by an IMU sensor, and the time interval of velocity measurement needs to be small enough; positioning beacons of different anchor nodes cannot synchronously reach the node to be positioned, namely the time of measuring information is asynchronous; the measurement information of the same anchor node is two types of inter-node distance and Doppler frequency shift.
In step 2), the maximum likelihood positioning refers to constructing a maximum likelihood function by using a relation obtained by information preprocessing and measured information, then calculating the position of the node to be positioned at the initial moment of the positioning period according to the maximum likelihood function, and finally estimating the motion trajectory of the node to be positioned in the positioning period by combining the speed of the node to be positioned.
According to the method, the actual information at different measurement moments is associated with the position of the node to be positioned at the initial moment of the positioning period by using the speed of the node to be positioned, then a maximum likelihood function is constructed by using a relational expression obtained by information preprocessing and the measurement information, and finally the motion track of the node to be positioned in the positioning period is estimated.
The invention has the following advantages:
(1) in the positioning process, the positioning beacons of different anchor nodes are not assumed to synchronously reach the node to be positioned, the actual information at different measurement moments is associated with the position of the node to be positioned at the initial moment of the positioning period according to the speed of the node to be positioned, and then the maximum likelihood function is constructed by using the relation obtained by information preprocessing and the measurement information, so that the method can be suitable for positioning the moving node of the underwater sensor at any speed (even static).
(2) The invention adopts the distance between the nodes and the Doppler frequency shift information to estimate the position of the node to be positioned, and is more accurate and efficient than a node positioning method which independently adopts the distance between the nodes.
Drawings
Fig. 1 is a schematic diagram of an underwater sensor network model according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of a position relationship between a node to be positioned and an anchor node at a certain measurement time according to an embodiment of the present invention. In fig. 2, reference ● is an anchor node and ■ is a pending node.
FIG. 3 is a schematic diagram of a test scenario in accordance with an embodiment of the present invention.
Fig. 4 is a performance comparison diagram of different node location methods according to an embodiment of the present invention.
Detailed Description
In order that the objects, aspects and advantages of the present invention will become more apparent, the invention is further described with reference to the following detailed description and the accompanying drawings.
The invention comprises the following steps:
1) information preprocessing step; the information preprocessing refers to that the actual information at different measurement moments is associated with the position of the node to be positioned at the initial moment of the positioning period by utilizing the speed of the node to be positioned; the velocity of the node to be positioned can be measured by an IMU sensor, and the time interval of velocity measurement needs to be small enough; positioning beacons of different anchor nodes cannot synchronously reach the node to be positioned, namely the time of measuring information is asynchronous; the measurement information of the same anchor node is two types of inter-node distance and Doppler frequency shift.
2) And a maximum likelihood positioning step, wherein the maximum likelihood positioning refers to constructing a maximum likelihood function by using a relation obtained by information preprocessing and measured information, then calculating the position of the node to be positioned at the initial moment of a positioning period according to the maximum likelihood function, and finally estimating the motion track of the node to be positioned in the positioning period by combining the speed of the node to be positioned.
Specific examples are given below.
Suppose there is N in an underwater sensor networksAn anchor node and a node to be positioned, as shown in fig. 1. In a positioning period, a node to be positioned can receive N (N is more than or equal to 2 and less than or equal to N)s) And the positioning beacon is transmitted by each anchor node, and the positioning beacon measures the corresponding inter-node distance and Doppler frequency shift information. Following the positioning period (t)0,t0+ T) is an example to describe the measurement values that the node to be located can obtain during this period. Assume that the position of the N-th (N-1, 2, …, N) anchor node is Sn(sn,x,sn,y,sn,z) The time of arrival of the positioning beacon at the node to be positioned is tn(t0≤tn≤t0+ T). At tnAt the moment, the measured inter-node distance and the Doppler shift are respectively
Figure BDA0001369603180000031
And
Figure BDA0001369603180000032
the position of the node to be positioned is
Figure BDA0001369603180000033
As shown in particular in fig. 2. In addition, in the positioning period, the node to be positioned can obtain M groups of speed measurement through the IMU sensor, the time interval of the measurement is delta t, and the moment when the mth group of speed measurement occurs is t0+ m.DELTA.t, denoted by vm. Since Δ t is small, t is considered to benThe velocity of the node to be positioned at the moment is
Figure BDA0001369603180000034
LnIs (t)n-t0) Integer part of/[ delta ] t.
It is important to note that the above measurements all contain measurement errors. The measurement error is generally considered to follow a gaussian distribution with known parameters, and therefore:
Figure BDA0001369603180000035
in the formula,
Figure BDA0001369603180000036
respectively the actual inter-node distance, the Doppler shift, nd,n、nf,nRespectively obey a mean value of 0 and a variance of
Figure BDA0001369603180000037
A gaussian distribution of (a).
For ease of writing, equation (1) is written as a vector expression:
Figure BDA0001369603180000038
wherein,
Figure BDA0001369603180000039
because the node to be positioned is moving, the time for the positioning beacon of each anchor node to reach the node to be positioned is inconsistent. Therefore, information preprocessing is required before maximum likelihood positioning, that is, the node to be positioned associates actual information at different measurement times with the position of the node at the initial time of the positioning cycle by using the speed of the node to be positioned. With tnPosition at time of day
Figure BDA00013696031800000310
For example, if (t) is known0,t0+ T) all velocity measurements of the node to be positioned within the time interval, then
Figure BDA00013696031800000311
And
Figure BDA00013696031800000312
have the following relationship between:
Figure BDA00013696031800000313
at tnNode to be positioned at moment and anchor node Sn(sn,x,sn,y,sn,z) Relative position therebetween
Figure BDA00013696031800000314
Comprises the following steps:
Figure BDA0001369603180000041
in the above formula except
Figure BDA0001369603180000042
Other parameters are known, except that they are unknown, so there are:
Figure BDA0001369603180000043
therefore, the node to be positioned can be estimated in the positioning period (t)0,t0+ T) to estimate the node to be located at T0The position at the moment. Then, when known (t)0,t0+ T) time interval, the node to be positioned is determined at T0The position at a time is converted to a position at any one time.
It is assumed that different information measurements of the same anchor node are independent of each other and that the same information measurements between different anchor nodes are also independent of each other. Due to the fact that
Figure BDA0001369603180000044
And
Figure BDA0001369603180000045
the measured error difference of the information is subject to the mean value of 0 and the variance of
Figure BDA0001369603180000046
Is the unknown position P (P) of the node to be positionedx,py,pz) With all measurements taken during the positioning period
Figure BDA0001369603180000047
The joint likelihood function of (a) may be expressed as:
Figure BDA0001369603180000048
in the formula,
Figure BDA0001369603180000049
is that
Figure BDA00013696031800000410
The covariance matrix of the measurement errors.
To simplify the calculation, the logarithm is generally taken from both ends of the above formula to obtain a log-likelihood function
Figure BDA00013696031800000411
As shown in the following formula:
Figure BDA00013696031800000412
the maximum value of equation (8) is obtained as
Figure BDA00013696031800000413
So the objective function of the node location method is:
Figure BDA00013696031800000414
and deducing the Crame-Rao lower bound of the node positioning method. Order to
Figure BDA00013696031800000415
Due to the fact that
Figure BDA00013696031800000416
The maximum likelihood estimation of (2) is an unbiased estimation, so there are:
Figure BDA00013696031800000417
performing a derivation operation on equation (10)
Figure BDA00013696031800000418
) Then, there are:
Figure BDA0001369603180000051
because of the fact that
Figure BDA0001369603180000052
Therefore, it can be obtained from formula (11):
Figure BDA0001369603180000053
due to the fact that
Figure BDA0001369603180000054
Equation (12) can be rewritten as follows:
Figure BDA0001369603180000055
according to the Schwarz inequality:
Figure BDA0001369603180000056
equation (14) can be rewritten as follows:
Figure BDA0001369603180000057
namely:
Figure BDA0001369603180000058
therefore, the Crame-Rao lower bound C of the node positioning method-1The specific expression of (A) is as follows:
Figure BDA0001369603180000059
will be provided with
Figure BDA00013696031800000510
The substitution formula (17) includes:
Figure BDA00013696031800000511
in the formula (18), C is called Fisher information matrix, and the corresponding Crame-Rao lower bound can be obtained by carrying out inversion operation on the Fisher information matrix. Due to the fact that
Figure BDA00013696031800000512
Equation (18) can be expanded as:
Figure BDA0001369603180000061
in the formula,
Figure BDA0001369603180000062
in order to verify the performance of the above node positioning method, a simulation experiment will be performed by MATLAB. The deployment of each anchor node and the initial position of a node to be positioned in the simulation experiment are shown in fig. 3, the position of an anchor node 1 is (-1000,0,0), the position of an anchor node 2 is (0,0,1000), the position of an anchor node 3 is (1000,0,0), and the initial position of the node to be positioned is (0, -4000, 0). Assuming that a node to be positioned does uniform linear motion with the speed of 2m/s along the positive direction of the Y axis; the positioning period T is 3 s; the positioning beacons of all anchor nodes reach the nodes to be positioned in the sequence of anchor node 1, anchor node 2 and anchor node 3, and the time interval is 1 s; positioning beacon of anchor node 1-3The frequencies are known, 10kHz, 12kHz, 14kHz respectively; the standard deviation of the error of the measurement of the distance between the nodes is (sigma)d,1,σd,2,σd,3) The standard deviation of the doppler shift measurement error is (σ) at (0.8,0.8,0.8)f,1,σf,2,σf,3) (1,1, 1); the number of independent experiments was 100. Under the above experimental conditions, a graph comparing the performance of different node positioning methods is shown in fig. 4. In fig. 4, an iml (improved Maximum likelihood) positioning method represents the node positioning method disclosed in the present invention; IML-CRLB represents the Crame-Rao lower bound of the node positioning method disclosed by the invention; the tml (traditional Maximum likelihood) positioning method represents a conventional Maximum likelihood positioning method.
The method for positioning the nodes of the underwater sensor based on the TOA ranging and the Doppler effect comprises the following steps:
in a positioning period, a node to be positioned receives positioning beacons transmitted by N anchor nodes, and the positioning beacons measure corresponding inter-node distance and Doppler frequency shift information. In addition, in the positioning period, the node to be positioned can obtain multiple groups of self speed measurement through the IMU sensor. On the basis that various measurement information is known, the node to be positioned firstly uses the speed of the node to correlate the actual information at different measurement moments with the position of the node to be positioned at the initial moment of the positioning period, then uses a relation obtained by information preprocessing and the measurement information to construct a maximum likelihood function, and finally estimates the motion track of the node to be positioned in the positioning period.
The positioning method of the underwater sensor network mobile node based on the TOA ranging and the Doppler effect can be suitable for positioning the underwater sensor mobile node at any speed (even at a standstill). In addition, the position of the node to be positioned is estimated by adopting the distance between the nodes and the Doppler frequency shift information, so that the method is more accurate and efficient than a node positioning method which singly adopts the distance between the nodes.

Claims (1)

1. The method for positioning the node of the underwater sensor based on the TOA ranging and the Doppler effect is characterized by comprising the following steps of:
1) the method comprises the steps of information preprocessing, wherein the information preprocessing refers to the fact that a node to be positioned associates actual information on different measurement moments with positions of the node to be positioned on the initial moment of a positioning cycle by utilizing the speed of the node to be positioned; the speed of the node to be positioned is measured by an IMU sensor, and the time interval of the speed measurement needs to be small enough; positioning beacons of different anchor nodes cannot synchronously reach the node to be positioned, namely the time of measuring information is asynchronous; the measurement information of the same anchor node is two types of inter-node distance and Doppler frequency shift;
the information preprocessing comprises the following steps:
step 1: assuming that Ns anchor nodes and a node to be positioned are arranged in the underwater sensor network, in a positioning period, the node to be positioned receives positioning beacons transmitted by the N anchor nodes, and the positioning beacons measure the distance between the node to be positioned and the anchor nodes and Doppler frequency shift information, wherein N is more than or equal to 2 and is less than or equal to Ns, and the positioning period is (t)0,t0+ T), assuming the location of the nth anchor node as Sn(sn,x,sn,y,sn,z) N is 1,2, …, N, and the time when the positioning beacon reaches the node to be positioned is tn，t0≤tn≤t0+ T, at TnAt the time, the measured inter-node distance and the Doppler shift are respectively
Figure FDA0002540280920000011
And
Figure FDA0002540280920000012
the position of the node to be positioned is
Figure FDA0002540280920000013
Further, in the (t)0,t0+ T) positioning period, the node to be positioned obtains M sets of speed measurement through the IMU sensor, the time interval of the measurement is delta T, and the moment when the mth set of speed measurement occurs is T0+ m.DELTA.t, denoted by vmSince Δ t is small, t is considered to benThe moment is to be positionedThe velocity of the node is
Figure FDA0002540280920000014
LnIs (t)n-t0) The integer part of/Δ t;
since the above-mentioned measurement values all contain measurement errors, which are generally considered to follow a gaussian distribution with known parameters, there are:
Figure FDA0002540280920000015
in the formula,
Figure FDA0002540280920000016
respectively the actual inter-node distance, the Doppler shift, nd,n、nf,nRespectively obey a mean value of 0 and a variance of
Figure FDA0002540280920000017
The measurement error of the gaussian distribution of (a);
for ease of writing, equation (1) is written as a vector expression:
Figure FDA0002540280920000018
wherein,
Figure FDA0002540280920000019
step 2: knowing said (t)0,t0+ T) all velocity measurements of the node to be positioned within the positioning period, then
Figure FDA0002540280920000021
And
Figure FDA0002540280920000022
have the following relationship between:
Figure FDA0002540280920000023
at tnNode to be positioned at moment and anchor node Sn(sn,x,sn,y,sn,z) Relative position therebetween
Figure FDA0002540280920000024
Comprises the following steps:
Figure FDA0002540280920000025
in the above formula except
Figure FDA0002540280920000026
Other parameters are known, except that they are unknown, so there are:
Figure FDA0002540280920000027
therefore, the above procedure will estimate that the node to be positioned is at the (t)0,t0+ T) motion trajectory problem in the positioning period is converted into an estimation of the node to be positioned at T0Position in time, then, knowing said (t)0,t0+ T) positioning period, on the basis of all velocity measurements of the node to be positioned, the node to be positioned is positioned at T0Converting the position at the moment into a position at any moment;
2) the maximum likelihood positioning step, wherein the maximum likelihood positioning refers to constructing a maximum likelihood function by using a relational expression obtained by information preprocessing and measurement information, then calculating the position of a node to be positioned at the initial moment of a positioning period according to the maximum likelihood function, and finally estimating the motion track of the node to be positioned in the positioning period by combining the speed of the node to be positioned;
the maximum likelihood function is constructed in the following way:
assuming that different information measurements of the same anchor node are faciesIndependent of each other, and the same information measurement between different anchor nodes is also independent of each other because
Figure FDA0002540280920000028
And
Figure FDA0002540280920000029
the measured error difference of the information is subject to the mean value of 0 and the variance of
Figure FDA00025402809200000210
Is calculated, the unknown position P (P) of the node to be positioned is calculatedx,py,pz) And all the measured values obtained in the positioning period
Figure FDA00025402809200000211
The joint likelihood function of (a) is expressed as:
Figure FDA00025402809200000212
in the formula,
Figure FDA00025402809200000213
is that
Figure FDA00025402809200000214
The covariance matrix of the measurement errors.
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