CN107728122A - A kind of measure and device of more radar information amounts based on comentropy - Google Patents

A kind of measure and device of more radar information amounts based on comentropy Download PDF

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CN107728122A
CN107728122A CN201710807918.0A CN201710807918A CN107728122A CN 107728122 A CN107728122 A CN 107728122A CN 201710807918 A CN201710807918 A CN 201710807918A CN 107728122 A CN107728122 A CN 107728122A
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radar
fusion
observation
msup
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CN107728122B (en
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葛建军
李春霞
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CETC Information Science Research Institute
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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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/40—Means for monitoring or calibrating
    • G01S7/4052—Means for monitoring or calibrating by simulation of echoes
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A90/00—Technologies having an indirect contribution to adaptation to climate change
    • Y02A90/10—Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation

Abstract

The present embodiments relate to a kind of measure and device of more radar information amounts based on comentropy, this method includes：S1, for more radar target observation systems, establish unified more radar observation information fusion models；S2, according to the observation information Fusion Model, establish the fusion entropy model based on the multiple radar system fusion result of decision；S3, according to the fusion entropy model, the information content of more radar target observation systems is measured.The present invention proposes the measure and device of more radar information amounts based on comentropy, method is described using more radar information amounts based on comentropy, it can be used to the levels of precision of the fusion decision-making output information of the different fusion levels of the more radars of quantitative measurement, and its influence factor is analyzed, provide certain guidance for the dynamic organization of more radars.

Description

A kind of measure and device of more radar information amounts based on comentropy
Technical field
The present embodiments relate to technical field of data processing, more particularly to a kind of more radar information amounts based on comentropy Measure and device.
Background technology
In practice, battlefield surroundings and target are in constantly change, it is necessary to according to combat duty, and multiple radar system is provided Source, including Method in Positioning of Radar, radar parameter and fusion method etc., real-time dynamic organization is carried out to adapt to continually changing complex environment And target, so as to maximize acquisition target information, realize optimal target acquisition, tracking or identification etc..
In general, detection system obtains information with target environment interaction, to reduce the uncertainty of target environment. Each radar node wide area distribution of distributed multiple radar system, can be from different dimensions, including space-time-frequency-polarizing field Deng, detection target obtain multi-source observation information, can preferably detect target compared to single radar system.Currently for more radars not The information that same fusion level obtains, is assessed, such as detection probability, target location estimated accuracy side in different ways Formula, but do not provide the unified metric model and method of the fusion decision-making results of the different fusion levels of multiple radar system.
The content of the invention
The purpose of the embodiment of the present invention is to propose a kind of measure and device of more radar information amounts based on comentropy, The uncertainty degree for the information that more radar different levels fusion decision-makings obtain can be measured, it is determined that obtaining the accuracy of information.
To achieve the above object, in one aspect of the invention, there is provided a kind of more radar information amounts based on comentropy Measure, including：
S1, for more radar target observation systems, establish unified more radar observation information fusion models；
S2, according to the observation information Fusion Model, establish the fusion entropy model of multiple radar system；
S3, according to the fusion entropy model, the information content of more radar target observation systems is measured.
Wherein, the measurement fusion model is：
Ψ=g (z1,z2,…,zN)
Wherein, g is information fusion method, zn(n=1,2 ... N) for the multi-section radar of more radar target observation systems sight Measurement；Work as znFor echo sequence when, emerging system output Ψ be testing result, that is, judge target whether there is；Work as znTo be exported after detection Point mark, then fusion results Ψ is target locating result；As observed quantity znFor target feature vector when, fusion output Ψ be Recognition result.
Wherein, the fusion entropy model for establishing multiple radar system, is specifically included：
According to the definition of conditional information entropy and the measurement fusion model, multiple radar system is merged into the result of decision not Determine that degree is represented with conditional entropy, be defined as merging entropy, its specific formula is：
H(Ψ|z1:N)=- ∫ ∫ p (z1:N,Ψ)logp(Ψ|z1:N)dΨdz1:N
=-∫ ∫ p (z1:N)p(Ψ|z1:N)logp(Ψ|z1:N)dΨdz1:N
Wherein, observation collection z1:N={ z1,z2,...,zN, each measurement vector zn(n=1,2 ..., N) represent N portions radar Radar n is to the observation of same target, p (z in emerging system1:N) be the radar observation of N portions joint probability density function, H (Ψ | z1:N) be N portions radar system fusion entropy, represent input observe z1,z2,…,zNUnder conditions of, export the average uncertain of Ψ Degree.
Wherein, when the observation data are that polar coordinates observe data, the formula of the fusion entropy is：
Wherein, x and y is respectively the horizontally and vertically position of target in rectangular coordinate system, and [r a] observes for more radar targets The polar coordinates observation data of the N portions internal loopback radar composition of system, r=[rn]1×N, a=[an]1×N, rnAnd anRespectively n-th Portion's radar detection target range and azimuth, RN,xyUnder conditions of being observed in polar coordinates, target rectangular co-ordinate location estimation association Variance matrix, | | it is determinant of a matrix, H is the information of the target rectangular co-ordinate position obtained using the observation of more radar polar coordinates Amount.
Wherein, the relation of the covariance matrix and the carat Metro lower bound of parameter Estimation is：
Wherein, the IN(x, y | r, a) it is Fisher information square.
Wherein, the lower bound of the fusion entropy is：
Wherein, the Fisher information matrix IN(x, y | r, a) be specially：
Wherein, f (r, is a) joint probability density function of multiple radar system observation.
Wherein, the joint probability density function of N portions radar observation, it is specially：
Wherein, rn,0For n-th radar detection target actual distance, an,0For n-th radar detection target real angle, its InWithThe distance and bearing angle observation noise criteria of respectively n-th radar is poor.
Another aspect of the present invention, there is provided a kind of measurement apparatus of more radar information amounts based on comentropy, including：
Fusion Model establishes unit, for for more radar target observation systems, establishing unified more radar observation information and melting Matched moulds type；
Fusion entropy model establishes unit, for according to the observation information Fusion Model, establishing based on multiple radar system Merge entropy model；
Metric element, for according to the fusion entropy model, being carried out to the information content of more radar target observation systems Measurement.
Wherein, the measurement fusion model is：
Ψ=g (z1,z2,…,zN)
Wherein, g is information fusion method, zn(n=1,2 ... N) for the multi-section radar of more radar target observation systems sight Survey data；Work as znFor echo sequence when, emerging system output Ψ be testing result, that is, judge target whether there is；Work as znTo be defeated after detection The point mark gone out, then fusion results Ψ is target locating result；As observed quantity znFor target feature vector when, fusion output Ψ For recognition result.
Wherein, fusion entropy model establishes unit and establishes fusion entropy model, specifically includes：
According to the definition of conditional information entropy and the measurement fusion model, multiple radar system is merged into the result of decision not Determine that degree is represented with conditional entropy, be defined as merging entropy, its specific formula is：
H(Ψ|z1:N)=- ∫ ∫ p (z1:N,Ψ)logp(Ψ|z1:N)dΨdz1:N
=-∫ ∫ p (z1:N)p(Ψ|z1:N)logp(Ψ|z1:N)dΨdz1:N
Wherein, observation collection z1:N={ z1,z2,...,zN, each measurement vector zn(n=1,2 ..., N) represent N portions radar Radar n is to the observation of same target, p (z in emerging system1:N) be the radar observation of N portions joint probability density function, H (Ψ | z1:N) be N portions radar system fusion entropy, represent input observe z1,z2,…,zNUnder conditions of, export the average uncertain of Ψ Degree.
The measure and device of a kind of more radar information amounts based on comentropy proposed by the present invention, using based on information More radar information amounts of entropy describe method, can be used to the fusion decision-making output information of the different fusion levels of the more radars of quantitative measurement Levels of precision, and its influence factor is analyzed, provide certain guidance for the dynamic organization of more radars.
Brief description of the drawings
Technical scheme in order to illustrate the embodiments of the present invention more clearly, below will be to embodiment or description of the prior art In the required accompanying drawing used be briefly described, it should be apparent that, drawings in the following description be only the present invention some Embodiment, for those of ordinary skill in the art, without having to pay creative labor, can also be according to these Accompanying drawing obtains other accompanying drawings.
Fig. 1 shows the flow chart of the measure of the different fusion level information content based on comentropy of the present invention.
Fig. 2 shows the radar polar coordinates and rectangular co-ordinate corresponding relation schematic diagram of embodiments of the invention.
Fig. 3 shows the structured flowchart of the measurement apparatus of the different fusion level information content based on comentropy of the present invention.
Embodiment
Below by drawings and examples, technical scheme is described in further detail.
For more radar observation decision systems, it is desirable to which the target information of acquisition is more accurate better, i.e., system is not true It is the smaller the better to determine degree.Measure of the comentropy as stochastic variable uncertainty, entropy is smaller, and stochastic variable is not known Degree is smaller.Therefore, the degree of uncertainty that use information entropy of the present invention exports to more radar observation decision-makings is measured, i.e., it is more The fusion entropy of radar.
In information theory, entropy is a particularly important concept, and for the system of a broad sense, entropy can be used as system The confusion of state or the measurement of randomness.In general entropy is smaller, and the degree of systematic uncertainty is just smaller, namely system The information content contained is more.Similarly, comentropy is the measurement of stochastic variable uncertainty, and it is also to be described at random on average The measurement of information content needed for variable, a comentropy with the random variable of continuous type W that f (w) is density function are defined as
H (W)=- ∫ f (w) lnf (w) dw (1)
Wherein, H (W) is stochastic variable W comentropy, and f (w) is stochastic variable W probability density function.
If stochastic variable W and S joint probability density function f (w, s), defining conditional information entropy is
H (W | S)=- ∫ f (w, s) lnf (w | s) dwds (2)
Wherein, H (W | S) is the comentropy of the stochastic variable W under the conditions of S, and the joint that f (w, s) is stochastic variable W and S is general Rate density function, f (w | s) for the stochastic variable W under the conditions of S probability density function.
In an embodiment of the present invention, without loss of generality, the observation system for having N portions radar internal loopback, gained knot are considered By the multiple radar system for being equally applicable to MIMO, therefore, the different fusion level information content of the invention based on comentropy Measure, as shown in figure 1, specifically including：
S1, for more radar target observation systems, establish unified more radar observation information fusion models；
S2, according to the observation information Fusion Model, establish the fusion entropy model of multiple radar system；
S3, according to the fusion entropy model, the information content of more radar target observation systems is measured.
In a further embodiment, in the above method, measurement fusion model is：
Ψ=g (z1,z2,…,zN) (3)
Wherein, g is information fusion method, zn(n=1,2 ... N) for the multi-section radar of more radar target observation systems sight Measurement；According to the level of fusion, zn(n=1,2 ... N) can be echo sequence, observation arrow of the N portions radar to same target Amount or the characteristic vector of extraction.Work as znFor echo sequence when, emerging system output Ψ be testing result, that is, judge target whether there is； Work as znFor the point mark exported after detection, then fusion results Ψ is target locating result；As observed quantity znFor target feature vector When, fusion output Ψ is recognition result.
Further, in step s 2, seen according to the definition of information theory conditional entropy, and more radars that step S1 is established Measurement information Fusion Model, the uncertainty degree (namely accuracy of fusion results) that multiple radar system is merged to the result of decision use bar Part entropy represents, is defined as merging entropy, is formula (4)
Wherein, observation collection z1:N={ z1,z2,...,zN, each measurement vector zn(n=1,2 ..., N) represent N portions radar Radar n is to the observation of same target, p (z in emerging system1:N) be the radar observation of N portions joint probability density function, by believing Breath understands by principle, and the fusion entropy H of more radars defined in above formula (4) (Ψ | z1:N), represent to observe z in input1,z2,…,zN Under conditions of, after the method for amalgamation processing g in step S00, export Ψ average uncertainty.
The measure of the embodiment of the present invention, by the formula (4) in the formula (3) and step S2 in step S1, The fusion entropy of more radars is relevant with radar observation and fusion method, and radar observation and radar station location and relating to parameters, thus It is relevant with Method in Positioning of Radar position, parameter and information fusion method to merge entropy, radar resource can be wrapped by optimizing fusion entropy Include radar site, parameter and fusion method etc. adaptively to be adjusted, when target and environment constantly change, realize that more radars move State tissue.
Below based on fusion entropy defined above, to the fusion entropy of more radar observations fusion decision-making containing different observed quantities Analyzed, theoretically illustrate that more radars have more advantage compared to single radar-probing system.
According to the defined formula (4) of fusion entropy, the fusion entropy containing N number of observation and the N-1 relation for merging entropy observed For formula (5)
As available from the above equation, fusion entropy meets following recurrence formula
H(Ψ|z1:N)≤H(Ψ|z1:N-1)≤…≤H(Ψ|z1) (6)
So as to which the fusion entropy after N portions radar observation fusion is not more than the fusion entropy of N-1 portions radar, that is, increases radar number Mesh, the fusion outputs for observing decision system can obtain smaller uncertainty, more information content more.
Describe the measurement of the different fusion level information content based on comentropy of the present invention in detail below by way of specific implementation Method.
The present embodiment is directed to the fusion tracking level in more radars, gives straight by more radar polar coordinates observation acquisition target The fusion entropy of Angle Position.The radar polar coordinates of embodiments of the invention and rectangular co-ordinate corresponding relation schematic diagram as shown in Figure 2.
Step S11：Observed for N portions two-dimensional radar, establish N portions radar observation Fusion Model, be formula (7)
Ψ=g (z1,z2,…,zN) (7)
Wherein, g is more radar polar coordinates measurement fusion methods, and output Ψ is the position coordinates Ψ of target in rectangular coordinate system =(x, y), x and y are respectively the horizontally and vertically position of target.Input zn=[rn an], n=1 ..., N is n-th radar Measure vector, rnAnd anRespectively n-th radar detection target range and azimuth.More radars of N portions internal loopback radar composition The measurement vector z=[r a] of system, wherein r=[rn]1×N, a=[an]1×N, each observed quantity is formula
Wherein, rn,0For n-th radar detection target actual distance, an,0For n-th radar detection target real angle, mesh Subject distance observation noise isAzimuth observation noise is WithRespectively Distance and bearing angle observation noise criteria for n-th radar is poor.
Step S12：According to information theory principle, and more radar observation Fusion Models that step S00 is established, and combine fusion The defined formula (4) of entropy, it is formula (10) through being derived by the fusion entropy of more radar polar coordinates measurement fusions
Wherein, RN,xyUnder conditions of multiple radar system polar coordinates to be formed in N portions radar are observed, target rectangular co-ordinate position Put estimate covariance matrix.| | the determinant of representing matrix.Above formula (10) represents the mesh obtained using the observation of more radar polar coordinates Mark the information content of rectangular co-ordinate position.
It can be seen from parameter estimation theories, the covariance matrix that the target location obtained is estimated is observed by more radar polar coordinates Relation with the carat Metro lower bound (CRLB) of parameter estimating error is formula (11)
Wherein, IN(x, y | r, a) it is Fisher information square, its specific solution is introduced below.
From formula (10) and formula (11), the lower bound for merging entropy for obtaining target location is observed by more radar polar coordinates For formula (12)
According to parameter estimation theories, the Fisher information matrix I of target location estimationN(x, y | r, a) it is formula (13)
Wherein, f (r, is a) joint probability density function of multiple radar system observation.Assuming that each detection target observation value Connection that is independent uncorrelated, being observed according to measurement formula (8) and formula (9), the multiple radar system being made up of N portions internal loopback radar Conjunction probability density function is formula (14)
From formula (12), formula (13) and formula (14), the comentropy lower bound that decision-makings are merged in more radar observations is influenceed Factor include each radar station and target range, azimuth, and the range accuracy and angle measurement accuracy of each radar station.
In yet another embodiment of the present invention, there is provided a kind of measurement apparatus of more radar information amounts based on comentropy, Including：
Fusion Model establishes unit 10, for for more radar target observation systems, establishing unified more radar observation information Fusion Model；
Fusion entropy model establishes unit 20, for according to the observation information Fusion Model, establishing melting for multiple radar system Close entropy model；
Metric element 30, for according to the fusion entropy model, entering to the information content of more radar target observation systems Row measurement.
Wherein, the measurement fusion model is：
Ψ=g (z1,z2,…,zN)
Wherein, g is information fusion method, zn(n=1,2 ... N) for the multi-section radar of more radar target observation systems sight Survey data；Work as znFor echo sequence when, emerging system output Ψ be testing result, that is, judge target whether there is；Work as znTo be defeated after detection The point mark gone out, then fusion results Ψ is target locating result；As observed quantity znFor target feature vector when, fusion output Ψ For recognition result.
Wherein, fusion entropy model establishes unit and establishes fusion entropy model, specifically includes：
According to the definition of conditional information entropy and the measurement fusion model, multiple radar system is merged into the result of decision not Determine that degree is represented with conditional entropy, be defined as merging entropy, its specific formula is：
H(Ψ|z1:N)=- ∫ ∫ p (z1:N,Ψ)logp(Ψ|z1:N)dΨdz1:N
=-∫ ∫ p (z1:N)p(Ψ|z1:N)logp(Ψ|z1:N)dΨdz1:N
Wherein, observation collection z1:N={ z1,z2,...,zN, each measurement vector zn(n=1,2 ..., N) represent N portions radar Radar n is to the observation of same target, p (z in emerging system1:N) be the radar observation of N portions joint probability density function, H (Ψ | z1:N) be N portions radar system fusion entropy, represent input observe z1,z2,…,zNUnder conditions of, export the average uncertain of Ψ Degree.
The measure and device of a kind of more radar information amounts based on comentropy proposed by the present invention, using based on information More radar information amounts of entropy describe method, can be used to the fusion decision-making output information of the different fusion levels of the more radars of quantitative measurement Levels of precision, and its influence factor is analyzed, provide certain guidance for the dynamic organization of more radars.
Furthermore, it is necessary to explanation, apparatus of the present invention embodiment have with embodiment of the method identical technique effect, no longer Repeat.
Through the above description of the embodiments, it is apparent to those skilled in the art that the present invention can borrow Software is helped to add the mode of required general hardware platform to realize, naturally it is also possible to which by hardware, but the former is in many cases More preferably embodiment.Based on such understanding, technical scheme substantially contributes to prior art in other words Part can be embodied in the form of software product, the computer software product is stored in a storage medium, including Some instructions are causing a computer equipment (can be personal computer, server, or network equipment etc.) to perform sheet Invent the method described in each embodiment.
Above-described embodiment, the purpose of the present invention, technical scheme and beneficial effect are carried out further Describe in detail, should be understood that the embodiment that the foregoing is only the present invention, be not intended to limit the present invention Protection domain, within the spirit and principles of the invention, any modification, equivalent substitution and improvements done etc., all should include Within protection scope of the present invention.

Claims (11)

  1. A kind of 1. measure of more radar information amounts based on comentropy, it is characterised in that including：
    S1, for more radar target observation systems, establish unified more radar observation information fusion models；
    S2, according to the observation information Fusion Model, establish the fusion entropy model of multiple radar system；
    S3, according to the fusion entropy model, the information content of more radar target observation systems is measured.
  2. 2. measure according to claim 1, it is characterised in that the measurement fusion model is：
    Ψ=g (z1,z2,…,zN)
    Wherein, g is information fusion method, zn(n=1,2 ... N) for the multi-section radar of more radar target observation systems observation number According to；Work as znFor echo sequence when, emerging system output Ψ be testing result, that is, judge target whether there is；Work as znFor what is exported after detection Point mark, then fusion results Ψ is target locating result；As observed quantity znFor target feature vector when, fusion output Ψ for know Other result.
  3. 3. measure according to claim 1, it is characterised in that described to establish based on multiple radar system fusion decision-making knot The fusion entropy model of fruit, is specifically included：
    According to the definition of conditional information entropy and the measurement fusion model, multiple radar system is merged into the uncertain of the result of decision Degree is represented with conditional entropy, is defined as merging entropy, its specific formula is：
    H(Ψ|z1:N)=- ∫ ∫ p (z1:N,Ψ)log p(Ψ|z1:N)dydz1:N
    =-∫ ∫ p (z1:N)p(Ψ|z1:N)log p(Ψ|z1:N)dΨdz1:N
    Wherein, observation collection z1:N={ z1,z2,...,zN, each measurement vector zn(n=1,2 ..., N) represent N portions radar fusion Radar n is to the observation of same target, p (z in system1:N) be the radar observation of N portions joint probability density function, H (Ψ | z1:N) For the fusion entropy of N portions radar system, represent to observe z in input1,z2,…,zNUnder conditions of, export Ψ average uncertainty.
  4. 4. measure according to claim 2, it is characterised in that when the observation data are that polar coordinates observe data When, the formula of the fusion entropy is：
    <mrow> <msub> <mi>H</mi> <mi>N</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>|</mo> <mi>r</mi> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mi>l</mi> <mi>n</mi> <mrow> <mo>(</mo> <msup> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> <mi>e</mi> </mrow> <mo>)</mo> </mrow> <mi>N</mi> </msup> <mo>|</mo> <msub> <mi>R</mi> <mrow> <mi>N</mi> <mo>,</mo> <mi>x</mi> <mi>y</mi> </mrow> </msub> <mo>|</mo> <mo>)</mo> </mrow> </mrow>
    Wherein, x and y is respectively the horizontally and vertically position of target in rectangular coordinate system, and [r a] is more radar target observation systems N portions internal loopback radars composition polar coordinates observation data, r=[rn]1×N, a=[an]1×N, rnAnd anRespectively n-th thunder Up to detection target range and azimuth, RN,xyUnder conditions of being observed in polar coordinates, target rectangular co-ordinate location estimation covariance Matrix, | | it is determinant of a matrix, H is the information content of the target rectangular co-ordinate position obtained using the observation of more radar polar coordinates.
  5. 5. measure according to claim 4, it is characterised in that the covariance matrix and the carat of parameter Estimation are beautiful The relation of sieve lower bound is：
    <mrow> <msub> <mi>R</mi> <mrow> <mi>N</mi> <mo>,</mo> <mi>&amp;lambda;</mi> <mi>y</mi> </mrow> </msub> <mo>&amp;GreaterEqual;</mo> <msub> <mi>CRLB</mi> <mi>N</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>|</mo> <mi>r</mi> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>I</mi> <mi>N</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>|</mo> <mi>r</mi> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> </mrow>
    Wherein, the IN(x, y | r, a) it is Fisher information square.
  6. 6. measure according to claim 5, it is characterised in that it is described fusion entropy lower bound be：
    <mrow> <msub> <mi>H</mi> <mi>N</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>|</mo> <mi>r</mi> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>&amp;GreaterEqual;</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mi>l</mi> <mi>n</mi> <mrow> <mo>(</mo> <msup> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> <mi>e</mi> </mrow> <mo>)</mo> </mrow> <mi>N</mi> </msup> <mo>|</mo> <msubsup> <mi>I</mi> <mi>N</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>(</mo> <mrow> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>|</mo> <mi>r</mi> <mo>,</mo> <mi>a</mi> </mrow> <mo>)</mo> <mo>|</mo> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
  7. 7. measure according to claim 6, it is characterised in that the Fi sher information matrixs IN(x, y | r, a) have Body is：
    <mrow> <msub> <mi>I</mi> <mi>N</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>|</mo> <mi>r</mi> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <msup> <mo>&amp;part;</mo> <mn>2</mn> </msup> <mi>ln</mi> <mi> </mi> <mi>f</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>&amp;rsqb;</mo> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mi>E</mi> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <msup> <mo>&amp;part;</mo> <mn>2</mn> </msup> <mi>ln</mi> <mi> </mi> <mi>f</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <mi>y</mi> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mi>E</mi> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <msup> <mo>&amp;part;</mo> <mn>2</mn> </msup> <mi>ln</mi> <mi> </mi> <mi>f</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> <mo>&amp;part;</mo> <mi>y</mi> </mrow> </mfrac> <mo>&amp;rsqb;</mo> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mi>E</mi> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <msup> <mo>&amp;part;</mo> <mn>2</mn> </msup> <mi>ln</mi> <mi> </mi> <mi>f</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
    Wherein, f (r, is a) joint probability density function of multiple radar system observation.
  8. 8. measure according to claim 7, it is characterised in that the joint probability density letter of N portions radar observation Number, it is specially：
    <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Pi;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mfrac> <mn>1</mn> <mrow> <msqrt> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msqrt> <msubsup> <mi>&amp;sigma;</mi> <mi>n</mi> <mi>r</mi> </msubsup> </mrow> </mfrac> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mi>r</mi> <mi>n</mi> </msub> <mo>-</mo> <msub> <mi>r</mi> <mrow> <mi>n</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <msup> <mrow> <mo>(</mo> <msubsup> <mi>&amp;sigma;</mi> <mi>n</mi> <mi>r</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <mfrac> <mn>1</mn> <mrow> <msqrt> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msqrt> <msubsup> <mi>&amp;sigma;</mi> <mi>n</mi> <mi>a</mi> </msubsup> </mrow> </mfrac> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mi>a</mi> <mi>n</mi> </msub> <mo>-</mo> <msub> <mi>a</mi> <mrow> <mi>n</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <msup> <mrow> <mo>(</mo> <msubsup> <mi>&amp;sigma;</mi> <mi>n</mi> <mi>a</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
    Wherein, rn,0For n-th radar detection target actual distance, an,0For n-th radar detection target real angle, wherein WithThe distance and bearing angle observation noise criteria of respectively n-th radar is poor.
  9. A kind of 9. measurement apparatus of the information content of more thunders based on comentropy, it is characterised in that including：
    Fusion Model establishes unit, for for more radar target observation systems, establishing unified more radar observation information fusion moulds Type；
    Fusion entropy model establishes unit, for according to the observation information Fusion Model, establishing the fusion entropy mould of multiple radar system Type；
    Metric element, for according to the fusion entropy model, being measured to the information content of more radar target observation systems.
  10. 10. measurement apparatus according to claim 9, it is characterised in that the measurement fusion model is：
    Ψ=g (z1,z2,…,zN)
    Wherein, g is information fusion method, zn(n=1,2 ... N) for the multi-section radar of more radar target observation systems observation number According to；Work as znFor echo sequence when, emerging system output Ψ be testing result, that is, judge target whether there is；Work as znFor what is exported after detection Point mark, then fusion results Ψ is target locating result；As observed quantity znFor target feature vector when, fusion output Ψ for know Other result.
  11. 11. measure according to claim 9, it is characterised in that fusion entropy model establishes unit and establishes fusion entropy mould Type, specifically include：
    According to the definition of conditional information entropy and the measurement fusion model, multiple radar system is merged into the uncertain of the result of decision Degree is represented with conditional entropy, is defined as merging entropy, its specific formula is：
    H(Ψ|z1:N)=- ∫ ∫ p (z1:N,Ψ)log p(Ψ|z1:N)dΨdz1:N
    =-∫ ∫ p (z1:N)p(Ψ|z1:N)log p(Ψ|z1:N)dΨdz1:N
    Wherein, observation collection z1:N={ z1,z2,...,zN, each measurement vector zn(n=1,2 ..., N) represent N portions radar fusion Radar n is to the observation of same target, p (z in system1:N) be the radar observation of N portions joint probability density function, H (Ψ | z1:N) For the fusion entropy of N portions radar system, represent to observe z in input1,z2,…,zNUnder conditions of, export Ψ average uncertainty.
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