CN105676181B - Underwater movement objective Extended Kalman filter tracking based on distributed sensor energy ratio - Google Patents
Underwater movement objective Extended Kalman filter tracking based on distributed sensor energy ratio Download PDFInfo
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- CN105676181B CN105676181B CN201610028570.0A CN201610028570A CN105676181B CN 105676181 B CN105676181 B CN 105676181B CN 201610028570 A CN201610028570 A CN 201610028570A CN 105676181 B CN105676181 B CN 105676181B
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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
- G01S5/22—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements
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Abstract
The present invention discloses a kind of underwater movement objective Extended Kalman filter tracking based on distributed sensor energy ratio, is firstly introduced into the logarithm of energy ratio between two two sensors as observation, obtains observation sequence at different moments；Then in conjunction with the motion state of target, nonlinear observational equation in error controlled range is turned into approximately linear observational equation, constructs linear state space model；Then the sequential iterative solution algorithm of Extended Kalman filter of state-space model is exported；Utilize linear least-squares (ER LS) location algorithm, to being positioned into the moving target in the range of underwater sensor network, the initial value as Extended Kalman filter；Finally, the submarine target movement locus of performance improvement is obtained by Sequential filter.
Description
Technical field
The invention belongs to the filter tracking technologies under underwater sensor network frame, and in particular to a kind of particular state-sky
Between Extended Kalman filter tracking under model.
Background technology
Ocean covers the area of the earth more than 70%, has contained huge physical resources.Due to the particularity of seawater, sea
Water is too fast to radio wave and visible absorption, and attenuation is rapid, so as to can not achieve the remote transmission of energy, constrains these
Application of the technology in terms of marine exploration and underwater target tracking.Sound wave is the load that uniquely can be remotely propagated under water
Body, different propagation distances have different application scenarios, as propagation distance can be high using sound wave progress for rice to hundred meter levels
Resolving power is imaged, and propagation distance can carry out target acquisition using sound wave to hundred kilometers of grades for kilometer and positioning, propagation distance are
Hundred kilometers to thousand kilometers grades can utilize sound wave to be transmitted into row information.Moreover, acoustic detection tracking technique visits latent, ocean in sonar
The military and civilians fields such as biology tracking have a wide range of applications.
Wireless sensor network is made of multiple sensor nodes by no cableless communication, in order to realize its low-power consumption, fast
Speed is laid, the advantage of self-organization and fault-tolerance, and node is usually made of single sensor, thus node can not carry out battle array letter
Number processing.Sensor network is divided into center type and distribution for the method for target following, and center type refers to all sensings
The observation of acquisition is sent to the unique center node processing specified by device, and this structure needs considerable broadband into line sensor
Information transmission between node, this can challenge to node battery life, the structure drawback of center type be its robustness and
Reliability.In order to reduce the communications burden of center type structure, distributed frame comes into being, and each node of distributed frame is advanced
Row signal processing, compresses the data volume of required transmission, then handling result is sent to central processing node.It usually chooses close to mesh
Node is handled centered on the mark i.e. node of signal-to-noise ratio, with the progress of tracking process, central processing node constantly changes, will
The node that each moment is used to collect sensor information is considered as a subset, while other nodes are arranged to energy-conserving sleep pattern,
Distributed frame is more preferable compared with center type structural robustness.
Classical acoustic target localization method mainly has three classes：(DOA) is positioned based on direction of arrival, based on time delay localization
(TDOA) and based on signal energy (RSSI) is positioned.RSSI is relatively low to transmission bandwidth and sensor accuracy requirement, is more suitable for nothing
Line sensor network.RSSI includes maximum likelihood positioning and least square positioning etc., maximum likelihood method precision is high, energy consumption is big,
Computationally intensive, since single sensor node is small, finite energy, energy saving is overriding concern factor.Introduce the general of energy ratio
It reads, individual node need to only run the energy detector of calculation amount very little, it is possible to the energy observation number after being effectively compressed
According to, thus calculation amount can be reduced effectively, can realize that target location is estimated using least square method.
The content of the invention
The purpose of the present invention is being directed to tracking problem of the underwater sensor network to moving target, a kind of specific line is proposed
Property sunspot and the Extended Kalman filter tracking adapted to therewith, can effectively pass through two two sensors
Between the obtained observation sequence of energy ratio, time update and measurement updaue are carried out to motion state, pass through obtaining property of Sequential filter
It can improved tracking result.
Due to the dynamic changeability of marine environment and the kinetic characteristic of target so that ocean acoustical signal is in practical applications
Often refer to non-linear, the sunspot of structure is typically nonlinear.And method proposed by the present invention is to all
The energy observation data of effective node ask ratio to remake logarithmic transformation two-by-two, and obtained energy difference can turn on a log scale
Approximately linear state equation, optimum solution of the sequential Bayesian filter under linear case are Extended Kalman filter (EKF), can
It well adapts in this non-linear not serious underwater movement objective positioning situation.
The specific technical solution of the present invention is as follows：
A kind of underwater movement objective Extended Kalman filter tracking based on distributed sensor energy ratio, including step
Suddenly：
1) network being made of M sensor node is laid under water, and each node is made of single sensor, receives mesh
The acoustical signal given off is marked, the acoustical signal of acquisition is sampled by certain frequency, it is sequential to calculate each node fixed time period
The energy of interior acoustical signal obtains energy measure；
2) motion state equation is established according to the underwater characteristics of motion of target；
3) according to the measured value that each sensor node obtains in step 1), original observational equation is built；It is moved and advised with target
It restrains, according to linearization process is done to original measurement equation, to obtain linear equivalent observation equation；
4) filtering iteration equation is configured, obtains the time update equation of state estimation and measurement updaue equation, evaluated error
The time update equation of covariance and measurement renewal equation；
5) after being filtered iteration according to step 4) filtering iteration equation, each moment optimum state is obtained.
Further, in step 1), what what in shallow sea area seabed to be measured, plane was laid be made of M sensor node
Network, each node individually receive the acoustical signal size that target emanation goes out, and appropriate coordinate system is chosen according to target state,
It is assumed that seabed is flat, the position of each sensor node is represented by two-dimensional Cartesian system：
(xi,yi), i=1,2 ..., M (1)
Wherein, xiAnd yiAbscissa and ordinate of i-th of sensor in two dimensional surface are represented respectively.
When moving target enters monitoring area, if node is all available, M reception signal can be obtained, to obtaining
Acoustical signal sampled by certain frequency, the sequential energy for calculating acoustical signal in each node fixed time period.
Each sensor node of distribution will receive the signal from moving target, the target that each sensor section obtains
The acoustic energy signal measured value given off is：
In formula, Ei(k) the energy size for the target emanation that i-th of sensor of kth moment receives is represented；γiIt represents i-th
The reception gain of sensor；S (k) represents the acoustic intensity obtained at sound source 1m；LT(k) and Li(k) it is 3 × 1 vectors, point
Not Biao Shi acoustic target and i-th of sensor position, | | LT(k)-Li(k) | | it is the Euclidean of acoustic target and i-th of sensor
Distance；A is decay factor, related with the influence of bottom and surface of sea reflection；ni(k) it is that variance is σi 2Zero mean Gaussian white noise,
ni(k)~N (0, σ2), σ2For noise variance.
Further, in step 2), the speed of underwater movement objective is generally all smaller, therefore between the shorter time
It every interior, refers in particular to herein in adjacent observation interval, the state parameters such as displacement and depth can be approximately that first-order linear becomes
Change additional second order disturbance term, therefore it is linear that the motion state equation of simple target, which can be approximately considered,.Assuming that moving target
Linear uniform motion is done in the two dimensional surface apart from depths such as sea level.If moving target sound source state vector X (k) writes：
X (k)=[xT(k) vx(k) yT(k) vy(k)]T (3)
Four components are the x-axis coordinate of moving target successively in formula (3), along x-axis velocity component, y-axis coordinate, along y-axis
Velocity component.The motion state equation writing of target：
X (k+1)=Φ X (k)+Г w (k) (4)
State-transition matrix：
T is adjacent observation interval.
Process noise matrix：
W (k) is the zero mean Gaussian white noise that probability distribution is N (0, Q (k)),
The covariance matrix of process noise：
Q is process noise intensity, and T is the time interval between neighbouring sample point.
Further, in step 3), observation vector is
Zi(k)=log { Ei(k)/Em(k)} (5)
Em(k) all E in kth time interval are representedi(k) maximum in represents m-th of sensing in kth time interval
It is maximum that device receives energy；Zi(k) represent that the energy ratio of i-th of sensor and m-th of sensor in kth time interval is taken the logarithm；Z
(k) kth moment each observation vector Z is representedi(k) column vector formed.
Because target uniform motion, then equivalent observation equation simplification be bidimensional, observation vector using the target characteristics of motion as
According to linearization process is done to original measurement equation, obtaining linear equivalent observation equation can write
Δ Z (k)=Hx·ΔxT(k)+Hy·ΔyT(k)+v(k) (7)
Wherein, Δ Z (k) is observation vector increment in kth time interval：ΔZi(k)=Zi(k)-Zi(k-1) it is one
Scalar；Zi(k-1) represent that the energy ratio of i-th of sensor and m-th of sensor in -1 time interval of kth is taken the logarithm；HxAnd HyPoint
It Biao Shi not x-axis and the relevant observing matrix of y-axis；ΔxT(k) and Δ yT(k) represent respectively in kth time interval in x-axis and y-axis
Displacement；ν (k) is zero mean Gaussian white noise, meets Gaussian probability density distribution N (0, R (k))；R (k) is observation noise
Covariance matrix；
Further, in step 3), observation model x-axis and the relevant observing matrix H of y-axisx, HyIn corresponding element make
Initial estimate is generated by the least square location algorithm based on energy ratio.Least square positioning based on energy ratio is calculated
Method essence is to solve for a matrix equation.
Further, in step 4), target movement only does linear uniform motion, y-axis displacement component and speed in x-axis
Component is all zero, and state vector and state motion equation are as follows,
X (k)=[xT(k) vx(k) yT(k) vy(k)]T (8)
X (k-1)=[xT(k-1) vx(k-1) yT(k-1) vy(k-1)]T (9)
Δ X (k)=[Δ xT(k) 0 0 0]T (10)
The time update equation of state estimation：
ΔxT(k+1 | k)=Δ xT(k|k) (11)
The measurement updaue equation of state estimation：
ΔxT(k+1 | k+1)=Δ xT(k+1|k)+K(k+1)·[ΔZ(k+1)-Hx·ΔxT(k+1|k)] (12)
The time update equation of error covariance：
Δ P (k+1 | k)=Δ P (k | k) (13)
The measurement updaue equation of error covariance：
Kalman gain：
K (k+1)=Δ P (k+1 | k) Hx T·[Hx·ΔP(k+1|k)·Hx+R]-1 (15)
R represents process noise；Δ P represents Δ xT(k) error co-variance matrix.
The beneficial effects of the invention are as follows：The present invention be suitable for target it is adjacent observation the moment in displacement be far smaller than target with
The tracking scene of sensor node distance constructs linear condition-spatial model according to motion state, phase is obtained by Sequential filter
The Extended Kalman filter tracking based on energy ratio under the underwater sensor network frame improved to precision.It if will be non-
Linear equation must ask Jacobian matrix and its power as observational equation, computationally intensive, and can only be light in nonlinear degree
It is used when micro-.The present invention is more advantageous in calculation amount than traditional Extended Kalman filter for seeking Jacobian matrix.Due to this
The application for inventing the sunspot of construction is restricted, it is necessary to assume that in each adjacent time inter, moving target moves
The absolute value of dynamic distance is far smaller than it and participates in the distance between sensor node of tracking, therefore limited to tracking scene
System, once breaking through this limitation, the advantages of Extended Kalman filter, can not highlight.
Description of the drawings
Fig. 1 is underwater distributed sensor networks trace model；
Fig. 2 is based on energy ratio least square location algorithm result and actual road for M=20 node underwater sensor network
The comparison in footpath；
Fig. 3 is M=20 mean square error of the node underwater sensor network based on energy ratio least square location algorithm result
Difference；
Fig. 4 is M=20 node underwater sensor network application extension Kalman filter tracking arithmetic result and actual road
The comparison in footpath；
Fig. 5 is the mean square error of M=20 node underwater sensor network application extension Kalman filter tracking arithmetic result
Difference.
Specific embodiment
The present invention will be further described with specific example below in conjunction with the accompanying drawings, to verify effectiveness of the invention.Fig. 1
For underwater distributed sensor networks trace model, it is made of, is calculating moving target, head node, activation node and sleeping nodes
In each locating periodically of method, a certain range of a certain number of sensor nodes are adaptively activated, by multiple activation
Sensor synergism cooperation carry out locating and tracking moving target.Specific implementation process is as follows：
Step 1：Set target state model, observation model and ocean environment parameter.Extra large is uniformly deeply 28m, used
Ocean sound velocity gradient be Zhoushan shallow sea experiment obtained by, sensor network has M=20 node, at depth 28m seabeds
It is laid at random in the range of 6000*6000.Moving target sound source does linear uniform motion at depth 15m, and target velocity 1m/s is false
If the sound-source signal that moving target is sent is the broadband signal of a below 1000Hz, amplitude average energy value is 5000, and variance can
The signal of tune.It is the standardized normal distribution that 1 average is 0 that the ambient noise of all the sensors node, which is set to variance,.Because target exists
The horizontal in-plane movings of depth of water 15m can represent its position with two-dimensional Cartesian coordinate system, and target initial position is (0,0), each time
Time of measuring interval T is 1sec, and moving target by initial position along x-axis uniform motion.Arrangement above can be seen that satisfaction and exist
In each adjacent time inter, moving target movement distance absolute value be far smaller than it and participate in tracking sensor it
Between apart from this condition, meet the application conditions of the sunspot described in patent.
Original state
X (0)=[0 10 0]T
Initial estimated state
Original state error co-variance matrix
Measurement noise covariance matrix
Process noise covariance matrix
Step 2：Using Distributed localization tracking, totally 20 sensor nodes, with the least square based on energy ratio
Location algorithm generates initial estimate.In each locating periodically of algorithm, an a certain range of fixed number is adaptively activated
The sensor of amount carrys out locating and tracking moving target by the sensor synergism cooperation of multiple activation.Due to the overall process in tracking
In, the node that each tracking moment is not involved in tracking is counted as sleeping nodes, therefore the mistake of pseudoinverse is often sought in formula (30)
Journey.Fig. 2 show least square location algorithm as a result, there is part moment single moment position error to reach more than 2 meters, due to it is each when
Individually estimate at quarter, so countershaft seems unsmooth to positioning result on time, without continuity.Fig. 3 shows that least square is determined
The target trajectory mean square error at position algorithm part moment is maximum up to more than 5 meters.
Step 3：The motion state time updates and measurement updaue.According to state-transition matrix and state-noise to initial estimation
Carry out time update.Original state variable is updated according to the brand-new measured value at each moment of each node acquisition of sensor network
Estimate, observing matrix and observation noise in observational equation, process noise in state equation calculate Kalman
Thus gain updates initial error covariance matrix value.Observing matrix is in target linear uniform motion proximal line
Property, the initial estimate that each constant uses in matrix is generated by the least square location algorithm based on energy ratio.Fig. 4 provides expansion
The target trajectory curve that exhibition kalman filter method obtains.Due to using Sequential filter, the evolution knowledge that target make use of to move,
It is smooth curve because obtained from.Fig. 5 is the tracking error of Extended Kalman filter method, and the tracking error at each moment is all small
In 1, have than least-squares estimation result and significantly improve.As it can be seen that on the basis of having used the linear condition-spatial model constructed
Extended Kalman filter, tracking result have obtained smoothly, and tracking accuracy is improved.
The foregoing is merely the preferable implementation examples of the present invention, are not intended to limit the invention, it is all in spirit of the invention and
Within principle, any modifications, equivalent replacements and improvements are made should all be included in the protection scope of the present invention.
Claims (7)
1. a kind of underwater movement objective Extended Kalman filter tracking based on distributed sensor energy ratio, feature exist
In including step：
1) network being made of M sensor node is laid under water, each sensor node is receiving the sound that target emanation goes out
Signal, and the acoustical signal of acquisition is sampled by frequency, then the sequential each sensor node of calculating corresponds to sound in the period
The energy measure of signal；
2) motion state equation is established according to the underwater characteristics of motion of target；
The motion state equation writing of target：
X (k+1)=Φ X (k)+Γ w (k)
State-transition matrix：
Process noise matrix：
W (k) is the zero mean Gaussian white noise that probability distribution is N (0, Q (k)),
The covariance matrix of process noise：
Q is process noise intensity, and T is the time interval between neighbouring sample point；
3) according to the energy measure that each sensor node obtains in step 1), each two node in M sensor node is calculated
Between acoustic energy ratio and take the logarithm, as observed quantity, build original observational equation；Using the target characteristics of motion as according to original sight
It surveys equation and does linearization process, obtain linear equivalent observation equation；
4) filtering iteration equation is configured, obtains the time update equation of state estimation and measurement updaue equation, evaluated error association side
The time update equation of difference and measurement updaue equation；
5) after being filtered iteration according to step 4) filtering iteration equation, each moment optimum state is obtained.
2. it is according to claim 1 based on the underwater movement objective Extended Kalman filter of distributed sensor energy ratio with
Track method, which is characterized in that in the step 1), the acoustical signal that the target emanation of each sensor node acquisition goes out is：
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In formula, Ei(k) the energy size for the target emanation that i-th of sensor of kth moment receives is represented；γiRepresent i-th of sensing
The reception gain of device；S (k) represents the acoustic intensity obtained at sound source 1m；LT(k) and Li(k) it is 3 × 1 vectorial, difference table
Show the position of acoustic target and i-th of sensor, | | LT(k)-Li(k) | | be acoustic target and i-th of sensor Euclidean away from
From；α is decay factor, related with the influence of bottom and surface of sea reflection；ni(k) it is that variance is σi 2Zero mean Gaussian white noise, ni
(k)~N (0, σ2), σ2For noise variance.
3. it is according to claim 1 based on the underwater movement objective Extended Kalman filter of distributed sensor energy ratio with
Track method, which is characterized in that in the step 2), the motion state of target is linear uniform motion.
4. it is according to claim 1 based on the underwater movement objective Extended Kalman filter of distributed sensor energy ratio with
Track method, which is characterized in that in the step 3), target uniform motion, then equivalent observation equation simplification is bidimensional, is represented
For：
Δ Z (k)=Hx·ΔxT(k)+Hy·ΔyT(k)+v(k)
Wherein
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Zi(k) it is energy ratio measured value, is the observed quantity in step 3), represents the energy of i-th of sensor in kth time interval
Measure Ei(k) with the ENERGY E of m-th sensorm(k) ratio is taken the logarithm：
Zi(k)=log { Ei(k)/Em(k)}
In formula, Zi(k-1) represent that the energy ratio of i-th of sensor and m-th of sensor in -1 time interval of kth is taken the logarithm；ΔZi
(k)=Zi(k)-Zi(k-1) Z is representedi(k) and Zi(k-1) difference is a scalar；Δ Z (k) is represented in kth time interval
The respective Δ Z of all the sensors nodei(k) vector formed；HxAnd HyX-axis and the relevant observing matrix of y-axis are represented respectively；ΔxT
(k) and Δ yT(k) displacement in kth time interval in target two-dimensional coordinate in x-axis and y-axis is represented respectively；ν (k) is zero equal
It is worth white Gaussian noise, meets Gaussian probability density distribution N (0, R (k)), R (k) is covariance matrix.
5. it is according to claim 4 based on the underwater movement objective Extended Kalman filter of distributed sensor energy ratio with
Track method, which is characterized in that the initial estimate used in the observing matrix is positioned by the least square based on energy ratio and calculated
Method generates.
6. it is according to claim 4 based on the underwater movement objective Extended Kalman filter of distributed sensor energy ratio with
Track method, which is characterized in that in the step 3), to meet the condition of observational equation linearisation is：In the target unit time
Displacement is far smaller than the distance of sensor distance target,
xT(k)=xT(k-1)+ΔxT(k),yT(k)=yT(k-1)+ΔyT(k)
ΔxT(k)≈0,ΔyT(k)≈0
In formula, xT(k) and yT(k) kth moment target position is represented respectively.
7. it is according to claim 4 based on the underwater movement objective Extended Kalman filter of distributed sensor energy ratio with
Track method, which is characterized in that in the step 4), establish coordinate system, making target movement, only there are displacement, y-axis in x-axis
Displacement component is zero, then the time update equation of state estimation：
ΔxT(k+1 | k)=Δ xT(k|k)
The measurement updaue equation of state estimation：
ΔxT(k+1 | k+1)=Δ xT(k+1|k)+K(k+1)·[ΔZ(k+1)-Hx·ΔxT(k+1|k)]
The time update equation of error covariance：
Δ P (k+1 | k)=Δ P (k | k)
The measurement updaue equation of error covariance：
Δ P (k+1 | k+1)=[I-K (k+1) Hx]·ΔP(k+1|k)
·[I-K(k+1)·Hx]T+K(k+1)·R·K(k+1)T
Kalman gain：
K (k+1)=Δ P (k+1 | k) Hx T·[Hx·ΔP(k+1|k)·Hx+R]-1
I represents unit matrix；
R represents process noise；
Δ P represents Δ xT(k) error co-variance matrix.
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| CN108931806B (en) * | 2017-05-25 | 2024-04-12 | 中国辐射防护研究院 | Positioning coordinate algorithm for wireless positioning personal radiation dosimeter |
| CN108444478B (en) * | 2018-03-13 | 2021-08-10 | 西北工业大学 | Moving target visual pose estimation method for underwater vehicle |
| CN109246637B (en) * | 2018-08-20 | 2020-11-06 | 上海交通大学 | Distributed sensor network collaborative registration method and system |
| CN109239647B (en) * | 2018-09-04 | 2020-11-13 | 电子科技大学 | Multi-target tracking method based on multi-dimensional fitting |
| CN110167124B (en) * | 2019-05-21 | 2020-07-07 | 浙江大学 | Target tracking method of underwater wireless sensor network with self-adaptive transmission power |
| CN110749891B (en) * | 2019-10-21 | 2021-08-24 | 哈尔滨工程大学 | Self-adaptive underwater single beacon positioning method capable of estimating unknown effective sound velocity |
| CN110764053B (en) * | 2019-10-22 | 2021-08-17 | 浙江大学 | Multi-target passive positioning method based on underwater sensor network |
| CN110895332B (en) * | 2019-12-03 | 2023-05-23 | 电子科技大学 | Distributed tracking method for extended target |
| CN111781556B (en) * | 2020-05-18 | 2023-08-18 | 中国民用航空总局第二研究所 | Distributed time difference positioning method and device based on target signal TDOA filtering |
| CN114994601A (en) * | 2022-06-02 | 2022-09-02 | 合肥联睿微电子科技有限公司 | Generalized Kalman filtering positioning method and system based on distance measurement |
| CN115379560B (en) * | 2022-08-22 | 2024-03-08 | 昆明理工大学 | Target positioning and tracking method in wireless sensor network under condition of only distance measurement information |
| CN115201799A (en) * | 2022-09-09 | 2022-10-18 | 昆明理工大学 | Time-varying Kalman filtering tracking method for sonar |
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