CN108872971A - A kind of object localization method and device based on the single array of movement - Google Patents
A kind of object localization method and device based on the single array of movement Download PDFInfo
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Abstract
The present invention relates to a kind of based on the object localization method and device that move single array, the signal data of target radiation source at least two observation gap of acquisition, construction is included in the observation station receiving array data model for the array flow vector that the signal frequency that each observation gap receives and time delay and target radiation source generate in each observation gap；Then observation station receiving array data model and the signal data are utilized, construct the objective cost function of target emanation source position, target emanation source position is solved according to objective cost function, and the target emanation source position solved is accurate, positioning accuracy with higher especially remains to approach a carat Metro lower bound under the conditions of low signal-to-noise ratio, low sample data volume and small-bore.
Description
Technical field
The invention belongs to the direct field of locating technology in passive location, and in particular to a kind of based on the mesh for moving single array
Demarcate position method and apparatus.
Background technique
Directly positioning is an important method in passive location, and compared with two traditional step localization methods, this method is not required to
The parameters such as DOA, TDOA are pre-estimated, are directly carried out with initial data by position of the modes such as maximum likelihood to target non-linear
Estimation, reduces the loss of the target information in parameter estimation procedure, has higher positioning accuracy under low signal-to-noise ratio.
For example, the Chinese patent of application publication number CN105929389A proposes, " one kind is based on external sort algorithm time delay and more
Time domain data is converted to frequency by calculating the fourier coefficient of reception signal by the general direct localization method for strangling frequency ", this method
Then numeric field data constructs Gauss maximum likelihood estimator module to the reception data of conversion to frequency domain, then will extract target from data
The problem of location information, is converted into the problem of maximum eigenvalue for solving information matrix, searches for finally by geographic grid and obtains mesh
The estimation of cursor position.But this method can't resolve motion view survey station to the location estimation problem of target radiation source.
Summary of the invention
Single moving observer be located through an individual motion view survey station come the radiation information of target radiation source is intercepted and captured,
Measure and obtain the location information of target.Single moving observer positioning system does not need a large amount of compared with Multi-Station passive location system
Communication data transfer has many advantages, such as that structure is simple, equipment is flexible, therefore instead to navigation and aviation, satellite positioning early warning, guidance
Many civilian, military domains such as radiation weapon, electronic reconnaissance suffer from wide application prospect.
Therefore, the purpose of the present invention is to provide a kind of based on the object localization method and device that move single array, for solving
Certainly location estimation problem of the motion view survey station to target radiation source.
For single moving observer orientation problem, direct localization method, which is applied in single moving observer location model, effectively to be mentioned
The precision of height positioning.Since the array acceptor of more array elements composition has better directionality, can survey more accurately
The arrival bearing angle of echo signal is measured, while receiver can export the signal-to-noise ratio directly proportional to array number.It is fixed in single moving observer
In bit model, how to improve the precision that single moving observer directly positions with more array systems is the key that during single moving observer directly positions
Problem.
For this purpose, the present invention proposes a kind of object localization method based on the single array of movement, include the following steps：
1) signal data of target radiation source in gap is observed in acquisition at least two, and construction is included in each observation gap and connects
The signal frequency and time delay and target radiation source received is received in the observation station for the array flow vector that each observation gap generates
Array data model；
2) observation station receiving array data model and the signal data are utilized, the target generation of target emanation source position is constructed
Valence function solves target emanation source position according to the objective cost function.
The present invention obtains the signal data of target radiation source in observation gap using single array is moved, by constructing observation station
Receiving array data model solves target then using the objective cost function of data model building target emanation source position
Radiation source positions, and the target emanation source position solved is accurate, positioning accuracy with higher.
It is further limited as to array flow vector, step 1) further includes：According to the sight in each observation gap of acquisition
The time delay when signal of time and target radiation source arrives each array element with respect to reference array element is surveyed, the target radiation source is constructed
In the array flow vector that each observation gap generates, array flow vector is as follows：
In formula, ak(p) the array flow vector that gap generates, ω are observed at k-th for target radiation source0For the number of carrier wave
Angular frequency, τkMTime delay when projecting m-th array element for the signal of target radiation source relative to selected reference array element, T is each
Observe the observation time in gap.
It is further limited as to observation station receiving array data model, the observation station receiving array data model is such as
Under：
rk(t)=bkak(p)sk(t-τk)ej2πft+nk(t)
In formula, rkIt (t) is k-th of received array data in observation gap observation station of t moment, bkFor the letter of target radiation source
Number k-th observe gap reach observation station propagation coefficient, ak(p) observe what gap generated at k-th for target radiation source
Array flow vector, nkIt (t) is the Gaussian noise in k-th of t moment observation gap, τkFor radiation source signal in k-th of observation gap
The time delay of observation station is reached, f is the signal frequency that observation station receives in k-th of observation gap, sk(t-τk) it is (t- τk) moment
The signal that k-th of observation gap target radiation source issues.
It is further limited as to signal frequency, it is as follows in the signal frequency that each observation gap receives：
F=fc·(1+μk(p))
In formula, f is the signal frequency received in each observation gap, fcFor the signal carrier frequency of target radiation source, μk(p)
The Doppler effect generated for observation station and target radiation source relative motion, c are electromagnetic wave propagation speed, pkFor observation station
In the position that k-th is observed in gap, vkFor observation station k-th observe gap in speed,For vkTransposition, p is target
The position of radiation source.
It is further limited as to objective cost function, objective cost function described in step 2) is that observation station is received
The least mean-square error of array data, calculating formula are as follows：
In formula, Q (p) is the objective cost function, rkFor k-th observe gap target radiation source signal data to
Amount, bkThe propagation coefficient that gap reaches observation station, a are observed at k-th for the signal of target radiation sourcek(p) exist for target radiation source
The array flow vector that k-th of observation gap generates,fc
For the signal carrier frequency of target radiation source,μk(p) it is generated more for observation station and target radiation source relative motion
General Le effect, TsFor sampling time interval in k-th of observation gap, τkFor radiation source signal in k-th of observation gap to taking things philosophically
The time delay of survey station, skThe signal vector that gap target radiation source issues is observed for k-th.
Further, in the solution procedure of the objective cost function, the objective cost function is converted to so that comprising
It is as follows to maximize cost function for the maximum maximization cost function of the characteristic value of the conjugate matrices of radiation source positions information：
Wherein
In formula,To maximize cost function, VkFor the conjugate matrices comprising radiation source positions information, λmaxFor conjugation
The maximum eigenvalue of matrix, vkFor intermediate variable, ak(p) the array stray arrow that gap generates is observed at k-th for target radiation source
Amount,fcFor the signal carrier frequency of target radiation source, μk(p) it is produced for observation station and target radiation source relative motion
Raw Doppler effect, TsFor sampling time interval in k-th of observation gap, τkFor radiation source signal in k-th of observation gap
Reach the time delay of observation station, skThe signal vector issued for target radiation source.
Further, make coordinate value corresponding to the characteristic value maximum of conjugate matrices using two-dimentional geographical grid search, as
The position coordinates of target radiation source.
In order to solve the above technical problems, the present invention also proposes a kind of target locating set based on the single array of movement, including
Observation station receiving array data model structural unit and computing unit, wherein：
Observation station receiving array data model structural unit is used for：Target radiation source at least two observation gap of acquisition
Signal data, construction are included in the signal frequency that each observation gap receives and time delay and target radiation source in each sight
Survey the observation station receiving array data model for the array flow vector that gap generates；
Computing unit is used for：Using observation station receiving array data model and the signal data, target radiation source is constructed
The objective cost function of position solves target emanation source position according to the objective cost function.
It is further limited as to observation station receiving array data model structural unit, the observation station receiving array number
It is also used to according to Construction of A Model unit：It is arrived according to the observation time in each observation gap of acquisition and the signal of target radiation source
With respect to the time delay of reference array element when each array element, the array stray arrow that the target radiation source generates in each observation gap is constructed
Amount, array flow vector are as follows：
In formula, ak(p) the array flow vector that gap generates, ω are observed at k-th for target radiation source0For the number of carrier wave
Angular frequency, τkMTime delay when projecting m-th array element for the signal of target radiation source relative to selected reference array element, T is each
Observe the observation time in gap.
It is further limited as to observation station receiving array data model, the observation station receiving array data model is such as
Under：
rk(t)=bkak(p)sk(t-τk)ej2πft+nk(t)
In formula, rkIt (t) is k-th of received array data in observation gap observation station of t moment, bkFor the letter of target radiation source
Number k-th observe gap reach observation station propagation coefficient, ak(p) observe what gap generated at k-th for target radiation source
Array flow vector, nkIt (t) is the Gaussian noise in k-th of t moment observation gap, τkFor radiation source signal in k-th of observation gap
The time delay of observation station is reached, f is the signal frequency that observation station receives in k-th of observation gap, sk(t-τk) it is (t- τk) moment
The signal that k-th of observation gap target radiation source issues.
It is further limited as to signal frequency, it is as follows in the signal frequency that each observation gap receives：
F=fc·(1+μk(p))
In formula, f is the signal frequency received in each observation gap, fcFor the signal carrier frequency of target radiation source, μk(p)
The Doppler effect generated for observation station and target radiation source relative motion, c are electromagnetic wave propagation speed, pkFor observation station
In the position that k-th is observed in gap, vkFor observation station k-th observe gap in speed,For vkTransposition, p is target
The position of radiation source.
It is further limited as to objective cost function, the objective cost function is the received array data in observation station
Least mean-square error, calculating formula is as follows：
In formula, Q (p) is the objective cost function, rkFor k-th observe gap target radiation source signal data to
Amount, bkThe propagation coefficient that gap reaches observation station, a are observed at k-th for the signal of target radiation sourcek(p) exist for target radiation source
The array flow vector that k-th of observation gap generates,fcFor
The signal carrier frequency of target radiation source,μk(p) it how general is generated for observation station and target radiation source relative motion
Strangle effect, TsFor sampling time interval in k-th of observation gap, τkObservation is reached in k-th of observation gap for the signal of radiation source
The time delay stood, skThe signal vector that gap target radiation source issues is observed for k-th.
Further, in the solution procedure of the objective cost function, the objective cost function is converted to so that comprising
It is as follows to maximize cost function for the maximum maximization cost function of the characteristic value of the conjugate matrices of radiation source positions information：
Wherein
In formula,To maximize cost function, VkFor the conjugate matrices comprising radiation source positions information, λmaxFor conjugation
The maximum eigenvalue of matrix, vkFor intermediate variable, ak(p) the array stray arrow that gap generates is observed at k-th for target radiation source
Amount,fcFor the signal carrier frequency of target radiation source, μk(p) it is produced for observation station and target radiation source relative motion
Raw Doppler effect, TsFor sampling time interval in k-th of observation gap, τkFor radiation source signal in k-th of observation gap
Reach the time delay of observation station, skThe signal vector issued for target radiation source.
Further, make coordinate value corresponding to the characteristic value maximum of conjugate matrices using two-dimentional geographical grid search, as
The position coordinates of target radiation source.
Detailed description of the invention
Fig. 1 is the flow diagram of the direct localization method of the single array of movement of the invention；
Fig. 2 is single moving observer positioning schematic diagram of the present invention；
Fig. 3 is the geographical location relation schematic diagram between target radiation source and observation station；
Fig. 4 is the position error curve comparison schematic diagram of method and two step localization methods of the invention under different signal-to-noise ratio；
Fig. 5 is that method of the invention under different sample points is illustrated compared with the position error curve of two step localization methods
Figure；
Fig. 6 is in position error curve of the different round battle array radius wavelength than lower method of the invention and two step localization methods
Comparison schematic diagram.
Specific embodiment
A specific embodiment of the invention is further described with reference to the accompanying drawing.
A kind of embodiment based on the object localization method for moving single array of the invention, including the following contents：
1) signal data of target radiation source in gap is observed in acquisition at least two, and construction is included in each observation gap and connects
The signal frequency and time delay and target radiation source received is received in the observation station for the array flow vector that each observation gap generates
Array data model.
Specifically, existing consider the positioning scene to target as illustrated in fig. 2, it is assumed that there are a static target spokes to be positioned
Source, position vector p are penetrated, transmitting signal s (t) bandwidth is W, carrier frequency fc.Certain M array-element antenna array is mounted on a motion view
On survey station, the data of radiation source are sampled in K observation gap, the observation time in each observation gap is T, uses pkWith
vk(k=1 ..., K) indicate the Position And Velocity that observation station is observed in gap at k-th.Then observation station is received in t moment
Data model is：
rk(t)=bkak(p)sk(t-τk)ej2πft+nk(t)
In formula：bkIndicate that signal observes the propagation coefficient that gap reaches observation station at k-th；ak(p) indicate radiation source the
Array manifold vector caused by k observation gap, is represented by：
Wherein, τkMTime delay when projecting m-th array element for emitter Signals, relative to selected reference array element.nk(t) table
Show that mean value is 0, variance σ2Gaussian noise, ω0For the digital angular frequency of carrier wave；τkIndicate that emitter Signals are observed at k-th
The time delay of gap arrival observation station；F indicates that the signal frequency that gap receives is observed at k-th in observation station, can be expressed as：
F=fc·(1+μk(p))
In formula, μk(p) Doppler effect for indicating target radiation source and observation station relative motion and generating, is represented by：
In formula, c indicates electromagnetic wave propagation speed, vkFor observation station k-th observe gap in speed,For vk's
Transposition, p are the position of target radiation source.Due to fcFor known quantity, then the signal frequency obtained after being handled by Digital Down Convert
For：
Can directly to be positioned to target radiation source, need to make following two points hypothesis herein：
(1) time delay of signal is short enough in each observation gap, i.e. τk< < T, so that the instantaneous position p of observation stationk, speed
Spend vkAnd signal transmission delay τkIt may be considered in observation time constant；
(2) target radiation source is narrow band signal, meets condition W < < fc。
Signal can be used following complex envelope form to indicate：
U (t) is the amplitude for receiving signal in formula,It is the phase for receiving signal.For the narrow band signal of far field,
U (t) of the synchronization space source signal at each array element andIt remains unchanged, only because space source signal reaches each array element
Progressive error caused by phase change.
If d is array element interval, λ is signal wavelength, for narrow band signal, is represented by d/ λ < < fc/W。
As it can be seen that the hypothesis of narrowband depends not only on the relative bandwidth of signal, but also related with wavelength ratio with array element interval.
According to above it is assumed that following equation available for narrow band signal：
It can obtain：
Assuming that observation station sampling time interval in k-th of observation gap is Ts, sampling snap number is Ns, above formula is used
Vector form indicates：
rk=bkak(p)FkDksk+nk
In above formula：
2) observation station receiving array data model is utilized, objective cost function, the i.e. received array data in observation station are constructed
Least mean-square error, objective cost function is converted to so that the characteristic value of the conjugate matrices comprising radiation source positions information most
Big maximization cost function.
Specifically, the estimation under the observation station receiving array data model that single moving observer directly positions, to target position
It can be considered as and utilize reception data rkEstimate radiation source positions coordinate p.The problem of positioning to radiation source, which is converted into, passes through structure
Cost function solution is made, then the Minimum Mean Squared Error estimation of target position is the minimum value of following cost function：
Make the smallest b of above formulakEstimation can be obtained by following formula：
bk=[(ak(p)FkDksk)H(ak(p)FkDksk)]-1×(ak(p)FkDksk)Hrk
=(ak(p)FkDksk)Hrk
Without loss of generality, to arbitrary k, it is assumed that：
||sk||2=1, | | ak(p)||2=1
Therefore cost function can be expressed as：
Due to | | rk||2Unrelated with parameter, then the minimum of Q (p) can pass through maximizationTo realize：
In formula：
Maximize cost functionIt is converted into selection and skCorresponding VkMaximum eigenvalue, therefore, maximize cost
Function is as follows：
3) by the geographical grid search of two dimension, making coordinate value corresponding to the characteristic value maximum of conjugate matrices is radiation source
Position coordinates.
By carrying out two-dimentional grid spatial index, finding out makesCoordinate value corresponding to maximum is the position of radiation source
Coordinate is set, that is, is had：
Detailed process is as follows：
(1) it is first depending on known conditions grid division, according to the wide scope x ∈ [x of scenemin,xmax], y ∈ [ymin,
ymax] it is divided into uniform M equal portions, amount to M2A mesh point；
(2) in each mesh point (xm,yn) at, wherein m, n≤M, calculate the delay parameter τ needed for each pointkWith
Doppler frequency difference parameter fk；
(3) the maximization cost function of mesh point is constructed according to observation station receiving array data model, and will be calculated
Delay parameter τkWith Doppler frequency difference parameter fkIt substitutes into and maximizes cost function, calculate the maximum eigenvalue of the mesh point；
(4) by x, the search of two dimensions of y acquires the maximum eigenvalue of cost function, corresponding to coordinate value (x,
Y) be target position coordinates.
4) simulated experiment emulation is carried out to method of the invention.Defining root-mean-square error is：
Simulation parameter setting：Assuming that there are a static emission source, transmitting carrier frequency fc=0.5GHz, bandwidth are 300kHz's
Gaussian signal, spread speed c are the light velocity.Observation station and target position be distributed as shown in figure 3, radiation source positions be (5500m,
2500m), observation station is moved along y=500m to positive direction of the x-axis, speed 300m/s, observation array circle battle array radius and wavelength ratio
It is 1, observation interval 3.33s, and observation frequency is set as 10 times.The method of the present invention and two step of Taylor series iteration are positioned
Method is (two step localization method of Taylor series iteration according to the delay parameter and Doppler parameter of acquisition, using Taylor series
Method carries out positioning calculation) carry out simulation comparison.Fig. 4 is the position error curve under different signal-to-noise ratio of the invention with other methods
Compare；Fig. 5 be under sample points of the invention different compared with the position error curve of above-mentioned two steps localization method；Fig. 6 is this hair
Bright different circle battle array radius wavelength are than lower compared with the position error curve of two step localization methods；Emulation experiment shows the method for the present invention
Positioning performance to be substantially better than two step localization methods, can preferably approach CRLB (carat Metro lower bound)；With signal-to-noise ratio,
The raising of sample data volume and circle battle array aperture, the RMSE (root-mean-square error) of distinct methods decrease, and with CRLB's
Downward trend is consistent.Compared to two step localization methods, under the conditions of low signal-to-noise ratio, low sample data volume and small-bore, the present invention
Method have higher positioning accuracy.
Direct localization method is introduced into single moving observer positioning system by the present invention, compared with traditional single moving observer positioning side
Method can preferably inhibit the influence of noise, positioning accuracy be improved, especially in low signal-to-noise ratio, low sample data volume and small-bore
Under the conditions of remain to approach a carat Metro lower bound.
The present invention proposes also to propose a kind of based on the target locating set for moving single array, including observation station receiving array number
According to Construction of A Model unit and computing unit, wherein：
Observation station receiving array data model structural unit is used for：Target radiation source at least two observation gap of acquisition
Signal data, construction are included in the signal frequency that each observation gap receives and time delay and target radiation source in each sight
Survey the observation station receiving array data model for the array flow vector that gap generates.
Computing unit is used for：Using observation station receiving array data model and signal data, target emanation source position is constructed
Objective cost function, according to objective cost function solve target emanation source position.
The above description is only a preferred embodiment of the present invention, is not intended to restrict the invention, for those skilled in the art
For member, the invention may be variously modified and varied.All within the spirits and principles of the present invention, it is made it is any modification,
Equivalent replacement, improvement etc., should be included within scope of the presently claimed invention.
Claims (10)
1. a kind of based on the object localization method for moving single array, which is characterized in that include the following steps：
1) signal data of target radiation source in gap is observed in acquisition at least two, and construction is included in each observation gap and receives
Signal frequency and the observation station receiving array of array flow vector that is generated in each observation gap of time delay and target radiation source
Data model；
2) observation station receiving array data model and the signal data are utilized, the target cost letter of target emanation source position is constructed
Number solves target emanation source position according to the objective cost function.
2. according to claim 1 based on the object localization method for moving single array, which is characterized in that step 1) is also wrapped
It includes：It is opposite when according to the observation time in each observation gap of acquisition and the signal of target radiation source to each array element to refer to
The time delay of array element, constructs the array flow vector that the target radiation source generates in each observation gap, and array flow vector is as follows：
In formula, ak(p) the array flow vector that gap generates, ω are observed at k-th for target radiation source0For the digital angular frequency of carrier wave
Rate, τkMTime delay when projecting m-th array element for the signal of target radiation source relative to selected reference array element, T are each observation
The observation time in gap.
3. according to claim 1 based on the object localization method for moving single array, which is characterized in that the observation station connects
It is as follows to receive array data model：
rk(t)=bkak(p)sk(t-τk)ej2πft+nk(t)
In formula, rkIt (t) is k-th of received array data in observation gap observation station of t moment, bkExist for the signal of target radiation source
K-th of observation gap reaches the propagation coefficient of observation station, ak(p) array that gap generates is observed at k-th for target radiation source
Flow vector, nkIt (t) is the Gaussian noise in k-th of t moment observation gap, τkIt is reached for the signal of radiation source in k-th of observation gap
The time delay of observation station, f are the signal frequency that observation station receives in k-th of observation gap, sk(t-τk) it is (t- τk) moment kth
The signal that a observation gap target radiation source issues.
4. according to claim 1 based on the object localization method for moving single array, which is characterized in that between each observation
The signal frequency that gap receives is as follows：
F=fc·(1+μk(p))
In formula, f is the signal frequency received in each observation gap, fcFor the signal carrier frequency of target radiation source, μkIt (p) is sight
Survey station and target radiation source relative motion and the Doppler effect generated, c are electromagnetic wave propagation speed, pkIt is observation station
Position in k observation gap, vkFor observation station k-th observe gap in speed,For vkTransposition, p is target emanation
The position in source.
5. according to claim 1 based on the object localization method for moving single array, which is characterized in that described in step 2)
Objective cost function is the least mean-square error of the received array data in observation station, and calculating formula is as follows：
In formula, Q (p) is the objective cost function, rkThe signal data vector of gap target radiation source, b are observed for k-thkFor
The signal of target radiation source observes the propagation coefficient that gap reaches observation station, a at k-thkIt (p) is target radiation source at k-th
The array flow vector that gap generates is observed,
fcFor the signal carrier frequency of target radiation source,μk(p) it is generated for observation station and target radiation source relative motion
Doppler effect, TsFor sampling time interval in k-th of observation gap, τkIt is reached for the signal of radiation source in k-th of observation gap
The time delay of observation station, skThe signal vector that gap target radiation source issues is observed for k-th.
6. according to claim 5 based on the object localization method for moving single array, which is characterized in that the target cost
In the solution procedure of function, the objective cost function is converted to the spy so that the conjugate matrices comprising radiation source positions information
It is as follows to maximize cost function for the maximum maximization cost function of value indicative：
Wherein
In formula,To maximize cost function, VkFor the conjugate matrices comprising radiation source positions information, λmaxFor conjugate matrices
Maximum eigenvalue, vkFor intermediate variable, ak(p) the array flow vector that gap generates is observed at k-th for target radiation source,fcFor the signal carrier frequency of target radiation source, μk(p) it is generated for observation station and target radiation source relative motion
Doppler effect, TsFor sampling time interval in k-th of observation gap, τkIt is reached for the signal of radiation source in k-th of observation gap
The time delay of observation station, skThe signal vector issued for target radiation source.
7. according to claim 6 based on the object localization method for moving single array, which is characterized in that geographical using two dimension
Grid search is sought making coordinate value corresponding to the characteristic value maximum of conjugate matrices, the position coordinates as target radiation source.
8. a kind of based on the target locating set for moving single array, which is characterized in that including observation station receiving array data model
Structural unit and computing unit, wherein：
Observation station receiving array data model structural unit is used for：The signal of target radiation source at least two observation gap of acquisition
Data, construction are included in each observation gap signal frequency received and time delay and target radiation source between each observation
The observation station receiving array data model for the array flow vector that gap generates；
Computing unit is used for：Using observation station receiving array data model and the signal data, target emanation source position is constructed
Objective cost function, according to the objective cost function solve target emanation source position.
9. according to claim 8 based on the target locating set for moving single array, which is characterized in that the observation station connects
Array data Construction of A Model unit is received to be also used to：According to the observation time and target radiation source in each observation gap of acquisition
Signal to each array element when opposite reference array element time delay, construct the battle array that the target radiation source generates in each observation gap
Column flow vector, array flow vector are as follows：
In formula, ak(p) the array flow vector that gap generates, ω are observed at k-th for target radiation source0For the digital angular frequency of carrier wave
Rate, τkMTime delay when projecting m-th array element for the signal of target radiation source relative to selected reference array element, T are each observation
The observation time in gap.
10. according to claim 8 based on the target locating set for moving single array, which is characterized in that the observation station
Receiving array data model is as follows：
rk(t)=bkak(p)sk(t-τk)ej2πft+nk(t)
In formula, rkIt (t) is k-th of received array data in observation gap observation station of t moment, bkExist for the signal of target radiation source
K-th of observation gap reaches the propagation coefficient of observation station, ak(p) array that gap generates is observed at k-th for target radiation source
Flow vector, nkIt (t) is the Gaussian noise in k-th of t moment observation gap, τkIt is reached for the signal of radiation source in k-th of observation gap
The time delay of observation station, f are the signal frequency that observation station receives in k-th of observation gap, sk(t-τk) it is (t- τk) moment kth
The signal that a observation gap target radiation source issues.
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