CN108872971B - Target positioning method and device based on motion single array - Google Patents
Target positioning method and device based on motion single array Download PDFInfo
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Abstract
The invention relates to a target positioning method and a target positioning device based on a single motion array, which are characterized by collecting signal data of a target radiation source in at least two observation gaps, and constructing an observation station receiving array data model which comprises signal frequency and time delay received in each observation gap and an array flow vector generated by the target radiation source in each observation gap; and then, an observation station is used for receiving the array data model and the signal data, a target cost function of the position of the target radiation source is constructed, the position of the target radiation source is solved according to the target cost function, the position of the solved target radiation source is accurate, the positioning precision is high, and the low-aperture target radiation source can approach the lower boundary of Cramer Rao particularly under the conditions of low signal-to-noise ratio, low sample data volume and small aperture.
Description
Technical Field
The invention belongs to the technical field of direct positioning in passive positioning, and particularly relates to a target positioning method and device based on a moving single array.
Background
Compared with the traditional two-step positioning method, the method does not need to estimate parameters such as DOA, TDOA and the like in advance, and directly uses the original data to carry out nonlinear estimation on the position of the target in a maximum likelihood mode and the like, thereby reducing the loss of target information in the parameter estimation process and having higher positioning accuracy under low signal-to-noise ratio.
For example, chinese patent application publication No. CN105929389A proposes "a direct positioning method based on external radiation source delay and doppler frequency", which converts time domain data into frequency domain data by calculating fourier coefficients of received signals, then constructs a gaussian maximum likelihood estimator for the received data converted into the frequency domain, then converts the problem of extracting target location information from the data into the problem of solving the maximum eigenvalue of the information matrix, and finally obtains the estimation of the target location by geographic grid search. However, this approach does not solve the problem of position estimation of the target radiation source by the moving observatory.
Disclosure of Invention
The single-station positioning device intercepts and measures the radiation information of a target radiation source through a single moving observation station, and obtains the position information of a target. Compared with a multi-station passive positioning system, the single-station moving positioning system does not need a large amount of communication data transmission, has the advantages of simple structure, flexible equipment and the like, and has wide application prospect in many civil and military fields such as navigation, aviation, satellite positioning early warning, guided anti-radiation weapons, electronic reconnaissance and the like.
Therefore, the invention aims to provide a target positioning method and device based on a moving single array, which are used for solving the problem of position estimation of a moving observation station on a target radiation source.
For the problem of single-station positioning of movement, the direct positioning method is applied to a single-station positioning model of movement, so that the positioning precision can be effectively improved. Because the array receiver composed of multiple array elements has better directivity, the arrival azimuth angle of the target signal can be measured more accurately, and meanwhile, the receiver can output the signal-to-noise ratio which is in direct proportion to the number of the array elements. In a single-station positioning model, how to improve the accuracy of single-station direct positioning by using a multi-array system is a key problem in the single-station direct positioning.
Therefore, the invention provides a target positioning method based on a moving single array, which comprises the following steps:
1) acquiring signal data of a target radiation source in at least two observation gaps, and constructing an observation station receiving array data model which comprises the frequency and time delay of a signal received in each observation gap and an array flow vector generated by the target radiation source in each observation gap;
2) and receiving the array data model and the signal data by using the observation station, constructing a target cost function of the target radiation source position, and solving the target radiation source position according to the target cost function.
The method adopts the single motion array to obtain the signal data of the target radiation source in the observation gap, receives the array data model by constructing the observation station, then constructs the target cost function of the position of the target radiation source by using the data model, and solves the position of the target radiation source, and the solved position of the target radiation source is accurate and has higher positioning precision.
As a further limitation to the array flow vector, step 1) further comprises: according to the obtained observation time of each observation gap and the time delay of the signal of the target radiation source to each array element relative to the reference array element, constructing an array flow vector generated by the target radiation source in each observation gap, wherein the array flow vector is as follows:
in the formula, ak(p) array flow vector, ω, generated for the k-th observation interval for the target radiation source0Is the digital angular frequency, tau, of the carrier wavekMAnd T is the time delay of the signal of the target radiation source projected to the Mth array element relative to the selected reference array element, and is the observation time of each observation interval.
As a further limitation to the observatory receive array data model, the observatory receive array data model is as follows:
rk(t)＝bkak(p)sk(t-τk)ej2πft+nk(t)
in the formula, rk(t) array data received at the kth observation interval station at time t, bkIs the propagation coefficient of the signal of the target radiation source reaching the observation station in the k observation interval, ak(p) array flow vector, n, generated for the k observation interval for the target radiation sourcek(t) Gaussian noise, τ, for the kth observation gap at time tkThe time delay of the signal of the radiation source reaching the observation station in the k observation interval is defined, f is the frequency of the signal received by the observation station in the k observation interval, sk(t-τk) Is (t-tau)k) Time of flightAnd (4) signals emitted by the target radiation source in the k-th observation interval.
As a further limitation on the signal frequency, the signal frequency received at each observation gap is as follows:
f＝fc·(1+μk(p))
where f is the frequency of the signal received in each observation interval, fcIs the signal carrier frequency, mu, of the target radiation sourcek(p) Doppler effect generated by relative movement of observation station and target radiation source, c propagation velocity of electromagnetic wave, pkFor the position of the observation station in the k-th observation interval, vkTo observe the velocity of the station within the k observation gap,
is v iskP is the position of the target radiation source.
As a further limitation to the objective cost function, the objective cost function in step 2) is the minimum mean square error of the array data received by the observation station, and is calculated as follows:
wherein Q (p) is the target cost function, rkFor the signal data vector of the target radiation source of the k-th observation interval, bkIs the propagation coefficient of the signal of the target radiation source reaching the observation station in the k observation interval, ak(p) an array flow vector generated for the source of the target radiation at the kth observation interval,
fcis the signal carrier frequency of the target radiation source,
μk(p) Doppler Effect, T, produced by relative movement of the observation station and the target radiation sourcesFor the sampling interval in the k-th observation interval, τkIs the time delay, s, of the signal of the radiation source reaching the observation station in the k observation intervalkThe signal vector emitted by the target radiation source for the k-th observation interval.
Further, in the solving process of the target cost function, the target cost function is converted into a maximized cost function which maximizes the eigenvalue of the conjugate matrix including the radiation source position information, and the maximized cost function is as follows:
wherein
In the formula (I), the compound is shown in the specification,
to maximize the cost function, VkFor a conjugate matrix containing information on the position of the radiation source, λmaxIs the maximum eigenvalue, v, of the conjugate matrixkIs an intermediate variable, ak(p) an array flow vector generated for the source of the target radiation at the kth observation interval,
fcis the signal carrier frequency, mu, of the target radiation sourcek(p) Doppler Effect, T, produced by relative movement of the observation station and the target radiation sourcesFor the sampling interval in the k-th observation interval, τkIs the time delay, s, of the signal of the radiation source reaching the observation station in the k observation intervalkIs the signal vector emitted by the target radiation source.
Further, a coordinate value corresponding to the maximum eigenvalue of the conjugate matrix is searched by using the two-dimensional geographic grid as the position coordinate of the target radiation source.
In order to solve the above technical problem, the present invention further provides a target positioning device based on a single motion array, including an observation station receiving array data model construction unit and a calculation unit, wherein:
the observation station receiving array data model construction unit is used for: acquiring signal data of a target radiation source in at least two observation gaps, and constructing an observation station receiving array data model which comprises the frequency and time delay of a signal received in each observation gap and an array flow vector generated by the target radiation source in each observation gap;
the computing unit is to: and receiving the array data model and the signal data by using the observation station, constructing a target cost function of the target radiation source position, and solving the target radiation source position according to the target cost function.
As a further definition of the observatory receive array data model construction unit, the observatory receive array data model construction unit is further to: according to the obtained observation time of each observation gap and the time delay of the signal of the target radiation source to each array element relative to the reference array element, constructing an array flow vector generated by the target radiation source in each observation gap, wherein the array flow vector is as follows:
in the formula, ak(p) array flow vector, ω, generated for the k-th observation interval for the target radiation source0Is the digital angular frequency, tau, of the carrier wavekMAnd T is the time delay of the signal of the target radiation source projected to the Mth array element relative to the selected reference array element, and is the observation time of each observation interval.
As a further limitation to the observatory receive array data model, the observatory receive array data model is as follows:
rk(t)＝bkak(p)sk(t-τk)ej2πft+nk(t)
in the formula, rk(t) array data received at the kth observation interval station at time t, bkIs the propagation coefficient of the signal of the target radiation source reaching the observation station in the k observation interval, ak(p) array flow vector, n, generated for the k observation interval for the target radiation sourcek(t) Gaussian noise, τ, for the kth observation gap at time tkThe time delay of the signal of the radiation source reaching the observation station in the k observation interval is defined, f is the frequency of the signal received by the observation station in the k observation interval, sk(t-τk) Is (t-tau)k) The signal emitted by the target radiation source in the k-th observation interval at the moment.
As a further limitation on the signal frequency, the signal frequency received at each observation gap is as follows:
f＝fc·(1+μk(p))
where f is the frequency of the signal received in each observation interval, fcIs the signal carrier frequency, mu, of the target radiation sourcek(p) Doppler effect generated by relative movement of observation station and target radiation source, c propagation velocity of electromagnetic wave, pkFor the position of the observation station in the k-th observation interval, vkTo observe the velocity of the station within the k observation gap,
is v iskP is the position of the target radiation source.
As a further limitation, the objective cost function is the minimum mean square error of the array data received by the observation station, and is calculated as follows:
wherein Q (p) is as defined aboveTarget cost function, rkFor the signal data vector of the target radiation source of the k-th observation interval, bkIs the propagation coefficient of the signal of the target radiation source reaching the observation station in the k observation interval, ak(p) an array flow vector generated for the source of the target radiation at the kth observation interval,
fcis the signal carrier frequency of the target radiation source,
μk(p) Doppler Effect, T, produced by relative movement of the observation station and the target radiation sourcesFor the sampling interval in the k-th observation interval, τkIs the time delay, s, of the signal of the radiation source reaching the observation station in the k observation intervalkThe signal vector emitted by the target radiation source for the k-th observation interval.
Further, in the solving process of the target cost function, the target cost function is converted into a maximized cost function which maximizes the eigenvalue of the conjugate matrix including the radiation source position information, and the maximized cost function is as follows:
wherein
In the formula (I), the compound is shown in the specification,
to maximize the cost function, VkFor a conjugate matrix containing information on the position of the radiation source, λmaxIs the maximum eigenvalue, v, of the conjugate matrixkIs an intermediate variable, ak(p) generated for the k-th observation interval for the target radiation sourceThe vector of the flow of the array is,
fcis the signal carrier frequency, mu, of the target radiation sourcek(p) Doppler Effect, T, produced by relative movement of the observation station and the target radiation sourcesFor the sampling interval in the k-th observation interval, τkIs the time delay, s, of the signal of the radiation source reaching the observation station in the k observation intervalkIs the signal vector emitted by the target radiation source.
Further, a coordinate value corresponding to the maximum eigenvalue of the conjugate matrix is searched by using the two-dimensional geographic grid as the position coordinate of the target radiation source.
Drawings
FIG. 1 is a schematic flow chart of the method of the present invention for direct positioning of a moving single array;
FIG. 2 is a schematic view of the kinematic single station positioning of the present invention;
FIG. 3 is a schematic diagram of the geographical position relationship between a target radiation source and an observation station;
FIG. 4 is a graphical comparison of the positioning error curves for the method of the present invention and the two-step positioning method at different signal-to-noise ratios;
FIG. 5 is a schematic diagram comparing the positioning error curves of the method of the present invention with a two-step positioning method for different sample point numbers;
FIG. 6 is a schematic diagram comparing the positioning error curves of the method of the present invention and the two-step positioning method at different circular array radius wavelength ratios.
Detailed Description
The following further describes embodiments of the present invention with reference to the drawings.
The embodiment of the target positioning method based on the moving single array comprises the following steps:
1) and acquiring signal data of a target radiation source in at least two observation gaps, and constructing an observation station receiving array data model which comprises the frequency and time delay of the signal received in each observation gap and the array flow vector generated by the target radiation source in each observation gap.
Specifically, now, consider a positioning scenario of a target as shown in fig. 2, assuming that there is a stationary target radiation source to be positioned, the position vector is p, the bandwidth of the transmitted signal s (t) is W, and the carrier frequency is fc. A certain M array element antenna array is installed on a moving observation station, data of a radiation source is sampled in K observation gaps, the observation time of each observation gap is T, and p is usedkAnd vk(K1.., K) represents the position and velocity of the observation station within the K-th observation interval. The data model received by the observation station at time t is:
rk(t)＝bkak(p)sk(t-τk)ej2πft+nk(t)
in the formula: bkRepresenting the propagation coefficient of the signal arriving at the observation station at the k-th observation interval; a isk(p) represents the array flow pattern vector generated by the radiation source at the k-th observation interval, which can be expressed as:
wherein, taukMThe time delay of the radiation source signal projected to the Mth array element relative to the selected reference array element. n isk(t) means mean 0 and variance σ2Gaussian noise of (omega)0A digital angular frequency of a carrier; tau iskRepresenting the time delay of the radiation source signal reaching the observation station in the k observation interval; f represents the frequency of the signal received by the observation station in the k-th observation interval, and can be expressed as:
f＝fc·(1+μk(p))
in the formula, muk(p) represents the Doppler effect generated by the relative motion of the target radiation source and the observation station, and can be represented as:
wherein c represents the propagation velocity of electromagnetic waves, vkFor observation station in k observation intervalThe speed of the internal air flow is controlled,
is v iskP is the position of the target radiation source. Due to fcThe frequency of the signal obtained after the digital down-conversion processing is known quantity is:
to be able to directly locate the target radiation source, two assumptions need to be made here:
(1) the time delay of the signal in each observation gap is sufficiently short, i.e. τkT, such that the instantaneous position p of the observation stationkVelocity vkAnd a signal propagation delay taukMay be considered constant over the observation time;
(2) the target radiation source is a narrow-band signal and satisfies the condition W & lt fc。
The signal may be represented in the form of a complex envelope as follows:
where u (t) is the amplitude of the received signal,
is the phase of the received signal. For far-field narrow-band signals, u (t) and
all remain unchanged, with only phase changes due to the difference in the path lengths of the spatial source signals to the array elements.
Let d be the array element spacing and λ be the signal wavelength, which can be expressed as d/λ < f for narrow band signalsc/W。
It can be seen that the assumption of narrow band depends not only on the relative bandwidth of the signal, but also on the ratio of array element spacing to wavelength. From the above assumptions, the following equation can be derived for a narrowband signal:
the following can be obtained:
suppose the observation station samples a time interval T in the k observation intervalsSampling snapshot times of NsThe above formula is expressed in vector form:
rk＝bkak(p)FkDksk+nk
in the above formula:
2) and constructing a target cost function by utilizing the array data receiving model of the observation station, namely, the minimum mean square error of the array data received by the observation station, and converting the target cost function into a maximized cost function which enables the characteristic value of the conjugate matrix containing the radiation source position information to be maximum.
Specifically, under the observation station receiving array data model of direct positioning of a single moving station, the estimation of the target position can be regarded as utilizing the received data rkThe radiation source position coordinates p are estimated. The problem of positioning the radiation source is converted into a solution by constructing a cost function, and the minimum mean square error of the target position is estimated to be the minimum value of the following cost function:
b to minimize the above formulakCan be obtained by:
bk＝[(ak(p)FkDksk)H(ak(p)FkDksk)]-1×(ak(p)FkDksk)Hrk
＝(ak(p)FkDksk)Hrk
without loss of generality, for any k, assume:
||sk||2＝1,||ak(p)||2＝1
the cost function can therefore be expressed as:
since | | | rk||2Independently of the parameters, the minimization of Q (p) can be achieved by maximization
To realize that:
in the formula:
maximizing a cost function
Conversion to the selection sum skCorresponding VkThus, the maximum cost function is as follows:
3) and searching through a two-dimensional geographic grid to enable the coordinate value corresponding to the maximum characteristic value of the conjugate matrix to be the position coordinate of the radiation source.
By performing a two-dimensional grid-type spatial index, find
The maximum corresponding coordinate value is the position coordinate of the radiation source, namely:
the specific process is as follows:
(1) firstly, dividing a grid according to known conditions, and determining the wide range x E [ x ] of a scenemin,xmax]，y∈[ymin,ymax]Divided into uniform M equal parts, total M2A plurality of grid points;
(2) at each grid point (x)m,yn) Where M, n is less than or equal to M, calculating the time delay parameter tau required at each pointksum-Doppler frequency difference parameter fk；
(3) Constructing a maximum cost function of the grid points according to the receiving array data model of the observation station, and calculating the obtained time delay parameter tauksum-Doppler frequency difference parameter fkSubstituting the maximum cost function to calculate the maximum characteristic value of the grid point;
(4) and (3) obtaining the maximum characteristic value of the cost function through searching of two dimensions of x and y, wherein the corresponding coordinate value (x, y) is the position coordinate of the target.
4) The method of the invention is simulated by a simulation experiment. Define the root mean square error as:
setting simulation parameters: assuming that there is a static emission source, the carrier frequency f of the emissioncThe propagation speed c of a gaussian signal with the bandwidth of 300kHz at 0.5GHz is the speed of light. Observation station and target siteAs shown in fig. 3, the position of the radiation source is (5500m,2500m), the observation station moves in the positive direction of the x-axis at a speed of 300m/s along y-500 m, the ratio of the radius of the circular array of the observation array to the wavelength is 1, the observation interval is 3.33s, and the number of observations is set to 10. The method is compared with a Taylor series iteration two-step positioning method (the Taylor series iteration two-step positioning method adopts the Taylor series method to perform positioning calculation according to the obtained time delay parameter and Doppler parameter) in a simulation mode. FIG. 4 is a comparison of the positioning error curves of the present invention with other methods at different signal-to-noise ratios; FIG. 5 is a comparison of the positioning error curves of the two-step positioning method of the present invention with different sample point numbers; FIG. 6 is a comparison of the positioning error curves for the two-step positioning method of the present invention at different radial wavelength ratios of the circular array; simulation experiments show that the positioning performance of the method is obviously superior to that of a two-step positioning method, and the method can better approach CRLB (Cramer-Lo lower bound); with the improvement of the signal-to-noise ratio, the sample data size and the circular array aperture, the RMSE (root mean square error) of different methods is reduced and is consistent with the descending trend of the CRLB. Compared with a two-step positioning method, the method has higher positioning accuracy under the conditions of low signal-to-noise ratio, low sample data volume and small aperture.
Compared with the traditional single-station positioning method, the direct positioning method can better inhibit the influence of noise, improve the positioning accuracy and approach the lower boundary of Cramer-Rao particularly under the conditions of low signal-to-noise ratio, low sample data size and small aperture.
The invention also provides a target positioning device based on the motion single array, which comprises an observation station receiving array data model construction unit and a calculation unit, wherein:
the observation station receiving array data model construction unit is used for: and acquiring signal data of a target radiation source in at least two observation gaps, and constructing an observation station receiving array data model which comprises the frequency and time delay of the signal received in each observation gap and the array flow vector generated by the target radiation source in each observation gap.
The computing unit is to: and receiving the array data model and the signal data by using the observation station, constructing a target cost function of the target radiation source position, and solving the target radiation source position according to the target cost function.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.
Claims (8)
1. A target positioning method based on a moving single array is characterized by comprising the following steps:
1) acquiring signal data of a target radiation source in at least two observation gaps, and constructing an observation station receiving array data model which comprises the frequency and time delay of a signal received in each observation gap and an array flow vector generated by the target radiation source in each observation gap;
2) receiving an array data model and the signal data by using an observation station, constructing a target cost function of a target radiation source position, and solving the target radiation source position according to the target cost function;
the step 1) further comprises the following steps: according to the obtained observation time of each observation gap and the time delay of the signal of the target radiation source to each array element relative to the reference array element, constructing an array flow vector generated by the target radiation source in each observation gap, wherein the array flow vector is as follows:
in the formula, ak(p) array flow vector, ω, generated for the k-th observation interval for the target radiation source0Is the digital angular frequency, tau, of the carrier wavekMThe time delay of the signal of the target radiation source relative to the selected reference array element when the signal is projected to the Mth array element;
the observation station receives the array data model as follows:
rk(t)＝bkak(p)sk(t-τk)ej2πft+nk(t)
in the formula, rk(t) array data received at the kth observation interval station at time t, bkIs the propagation coefficient of the signal of the target radiation source reaching the observation station in the k observation interval, ak(p) array flow vector, n, generated for the k observation interval for the target radiation sourcek(t) Gaussian noise, τ, for the kth observation gap at time tkThe time delay of the signal of the radiation source reaching the observation station in the k observation interval is defined, f is the frequency of the signal received by the observation station in the k observation interval, sk(t-τk) Is (t-tau)k) A signal emitted by a target radiation source of the k-th observation interval at the moment;
in step 2), the target cost function is the minimum mean square error of the array data received by the observation station, and the calculation formula is as follows:
wherein Q (p) is the target cost function, rkFor the signal data vector of the target radiation source of the k-th observation interval, bkIs the propagation coefficient of the signal of the target radiation source reaching the observation station in the k observation interval, ak(p) an array flow vector generated for the source of the target radiation at the kth observation interval,
fcis the signal carrier frequency of the target radiation source,
μk(p) Doppler Effect, T, produced by relative movement of the observation station and the target radiation sourcesFor the sampling interval in the k-th observation interval, τkIs the time delay, s, of the signal of the radiation source reaching the observation station in the k observation intervalkThe signal vector emitted by the target radiation source for the k-th observation interval.
2. The method of claim 1, wherein the received signal frequency in each observation interval is as follows:
f＝fc·(1+μk(p))
where f is the frequency of the signal received in each observation interval, fcIs the signal carrier frequency, mu, of the target radiation sourcek(p) Doppler effect generated by relative movement of observation station and target radiation source, c propagation velocity of electromagnetic wave, pkFor the position of the observation station in the k-th observation interval, vkTo observe the velocity of the station within the k observation gap,
is v iskP is the position of the target radiation source.
3. The method for locating a target according to claim 1, wherein in the solving of the target cost function, the target cost function is converted into a maximized cost function that maximizes an eigenvalue of a conjugate matrix containing radiation source position information, and the maximized cost function is as follows:
wherein
In the formula (I), the compound is shown in the specification,
to maximize the cost function, VkFor a conjugate matrix containing information on the position of the radiation source, λmaxIs the maximum eigenvalue, v, of the conjugate matrixkIs an intermediate variable, ak(p) an array flow vector generated for the source of the target radiation at the kth observation interval,
fcis the signal carrier frequency, mu, of the target radiation sourcek(p) Doppler Effect, T, produced by relative movement of the observation station and the target radiation sourcesFor the sampling interval in the k-th observation interval, τkIs the time delay, s, of the signal of the radiation source reaching the observation station in the k observation intervalkIs the signal vector emitted by the target radiation source.
4. The method of claim 3, wherein the coordinate value corresponding to the maximum eigenvalue of the conjugate matrix is found by searching the two-dimensional geographic grid as the position coordinate of the target radiation source.
5. An object positioning device based on a single motion array is characterized by comprising an observation station receiving array data model construction unit and a calculation unit, wherein:
the observation station receiving array data model construction unit is used for: acquiring signal data of a target radiation source in at least two observation gaps, and constructing an observation station receiving array data model which comprises the frequency and time delay of a signal received in each observation gap and an array flow vector generated by the target radiation source in each observation gap;
the computing unit is to: receiving an array data model and the signal data by using an observation station, constructing a target cost function of a target radiation source position, and solving the target radiation source position according to the target cost function;
the observation station receiving array data model construction unit is further configured to: according to the obtained observation time of each observation gap and the time delay of the signal of the target radiation source to each array element relative to the reference array element, constructing an array flow vector generated by the target radiation source in each observation gap, wherein the array flow vector is as follows:
in the formula, ak(p) array flow vector, ω, generated for the k-th observation interval for the target radiation source0Is the digital angular frequency, tau, of the carrier wavekMThe time delay of the signal of the target radiation source relative to the selected reference array element when the signal is projected to the Mth array element;
the observation station receives the array data model as follows:
rk(t)＝bkak(p)sk(t-τk)ej2πft+nk(t)
in the formula, rk(t) array data received at the kth observation interval station at time t, bkIs the propagation coefficient of the signal of the target radiation source reaching the observation station in the k observation interval, ak(p) array flow vector, n, generated for the k observation interval for the target radiation sourcek(t) Gaussian noise, τ, for the kth observation gap at time tkThe time delay of the signal of the radiation source reaching the observation station in the k observation interval is defined, f is the frequency of the signal received by the observation station in the k observation interval, sk(t-τk) Is (t-tau)k) A signal emitted by a target radiation source of the k-th observation interval at the moment;
the target cost function is the minimum mean square error of array data received by the observation station, and the calculation formula is as follows:
wherein Q (p) is the target cost function, rkNumber of signals of target radiation source for k-th observation intervalData vector, bkIs the propagation coefficient of the signal of the target radiation source reaching the observation station in the k observation interval, ak(p) an array flow vector generated for the source of the target radiation at the kth observation interval,
fcis the signal carrier frequency of the target radiation source,
μk(p) Doppler Effect, T, produced by relative movement of the observation station and the target radiation sourcesFor the sampling interval in the k-th observation interval, τkIs the time delay, s, of the signal of the radiation source reaching the observation station in the k observation intervalkThe signal vector emitted by the target radiation source for the k-th observation interval.
6. The single motion array based object localization apparatus according to claim 5, wherein the received signal frequency at each observation interval is as follows:
f＝fc·(1+μk(p))
where f is the frequency of the signal received in each observation interval, fcIs the signal carrier frequency, mu, of the target radiation sourcek(p) Doppler effect generated by relative movement of observation station and target radiation source, c propagation velocity of electromagnetic wave, pkFor the position of the observation station in the k-th observation interval, vkTo observe the velocity of the station within the k observation gap,
is v iskP is the position of the target radiation source.
7. The device for object localization according to claim 5, wherein the solution of the objective cost function is to convert the objective cost function into a maximized cost function that maximizes the eigenvalue of the conjugate matrix containing the radiation source position information, and the maximized cost function is as follows:
wherein
In the formula (I), the compound is shown in the specification,
to maximize the cost function, VkFor a conjugate matrix containing information on the position of the radiation source, λmaxIs the maximum eigenvalue, v, of the conjugate matrixkIs an intermediate variable, ak(p) an array flow vector generated for the source of the target radiation at the kth observation interval,
fcis the signal carrier frequency, mu, of the target radiation sourcek(p) Doppler Effect, T, produced by relative movement of the observation station and the target radiation sourcesFor the sampling interval in the k-th observation interval, τkIs the time delay, s, of the signal of the radiation source reaching the observation station in the k observation intervalkIs the signal vector emitted by the target radiation source.
8. The device of claim 7, wherein the coordinate value corresponding to the maximum eigenvalue of the conjugate matrix is found by using two-dimensional geographic grid search as the position coordinate of the target radiation source.
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