A three-station hybrid target positioning method combining intra-station and inter-station measurements

Abstract

The application discloses a three-station mixed target positioning method combining intra-station / inter-station measurement, comprising the following steps: obtaining intra-station DOA measurement of each radar station, dividing the radar into one reference station and two receiving stations, obtaining inter-station TDOA measurement and FDOA measurement of the receiving station and the reference station; estimating X-axis coordinates of the target and the distance from the target to the reference station by using the DOA measurement and the TDOA measurement; correcting the X-axis coordinates of the target and the distance from the target to the reference station by using the FDOA measurement; determining Y-axis and Z-axis coordinates of the target by using the TDOA measurement and the corrected X-axis coordinates and the distance from the target to the reference station, and completing three-station target positioning. The method uses a satellite as a radiation source to emit a signal, uses a UAV as a receiving station to receive, and positions the target by using intra-station / inter-station multiple measurement information, so that target positioning can be realized by using only three UAVs as receiving stations. The method has a good engineering application prospect.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of target positioning, and relates to a three-station hybrid target positioning method combining intra-station and inter-station measurements. BACKGROUND

[0002] Multi-station radar high-precision target positioning is a unique advantage of distributed radar systems. Target positioning capability comes from the difference in the observation angle of multi-station radar to the target. Under the condition of a given number of radars, the more dispersed the observation angle of the radar to the target is, the higher the system spatial diversity gain is, and the higher the target positioning precision is; on the contrary, if the target is located in the same observation direction of the multi-station radar, the target cannot be effectively positioned. Target positioning has broad application prospects in military and civilian fields: in the military field, accurate estimation of the target position provides a strong guarantee for wartime intelligence acquisition, tracking and even final precision strike; and in the civilian field, accurate positioning can provide reliable help for communication, rescue, transportation and other livelihood services.

[0003] Target positioning is generally divided into active positioning and passive positioning. Active positioning refers to that a radar actively transmits a signal, which is irradiated by a target and then returned to a receiving end, that is, the transmission signal source is controllable, and it is a complete receiving-transmitting system, but the existence of the transmission source makes the radar poor in concealment and easy to be interfered by the enemy; passive positioning radar does not transmit a signal, but only receives the signal radiated by the target, and has good concealment, but when the target radiation intensity is low, the target cannot be positioned. The space-air cross-domain radar system adopts the mode of positioning the target by irradiating the task area with a high-orbit satellite and receiving with an unmanned aerial vehicle, and the radiation source is controllable. The enemy has to pay a great price to interfere with the high-orbit satellite of our side, and the space-air cross-domain radar system combines the respective advantages of active positioning and passive positioning, and can be used as a supplement to the positioning type. For distributed radar target positioning of one transmission and multiple receptions, time difference of arrival (TDOA) positioning requires at least four receiving stations, and in wartime environment, the number of receiving stations is a very valuable sensing resource, and it is necessary to study the target positioning problem under the condition of a given number of receiving stations. Therefore, the application studies three-station target positioning, and proposes a three-station hybrid target positioning method combining intra-station and inter-station measurements.

[0004] Unlike satellite navigation positioning technology, the position solution is completed at the user. In the radar target positioning problem, the relationship between the radar and the target is a non-cooperative relationship, and the premise of positioning is that the target has been detected, and the positioning solution is completed in the central processing center of the receiving end. According to the difference of the signal acquisition stage, the target positioning method can be divided into direct positioning method and indirect positioning method. The direct positioning method refers to directly combining the target signals of multiple receiving stations to directly estimate the target position at the signal level. If multiple radars observe the target at approximately the same angle, the target can also be positioned by using the phase information through signal phase correlation, which can significantly improve the positioning accuracy. In the direct positioning method, the target position can be achieved by multi-dimensional search or optimization relaxation method, but the multi-dimensional search method faces the problems of phase ambiguity and large amount of calculation, and the optimization relaxation method needs to adjust the parameters and balance between convex relaxation approximation and positioning accuracy. The indirect positioning method is to extract indirect measurements such as distance, Doppler, angle, etc. from the signal, and then measure the target at the measurement level according to the extracted measurements. Since the positioning process is isolated in the indirect positioning method, and a closed-form solution of the target position can be obtained, this method has become the mainstream method of research.

[0005] The premise of target positioning is that the target parameters are identifiable to the current radar system. For the air (three-dimensional) target positioning problem, excluding the ill-conditioned observation configuration, TDOA positioning requires at least four stations, and the differential will consume an additional common receiving station. In addition, target positioning is closely related to the number of radar stations, radar-target geometric configuration, signal-to-noise ratio (SNR), etc. If the positioning accuracy index requirement is to be met, the above multiple factors need to be optimized in combination with the radar system parameters. The ellipsoid positioning estimator proposed by Chan and Ho is a classic two-stage TDOA positioning method. In the first stage, the reference distance (the distance from the reference radar to the target) is combined with the target position to form an augmented parameter vector, and the augmented parameter vector is estimated by linearizing the nonlinear equation set. In the second stage, the relationship between the reference distance and the target position is used to update the target positioning result. Further, in 2004, Ho and Parith modified the method into an iterative form, making it applicable to the case where there is a position error in the receiving station. Under the condition that the position error of the receiving station is small, the method can approach the Cramer-Rao lower bound of parameter estimation, and when the position error is large, the introduction of nonlinearity will cause the positioning accuracy to decrease. Therefore, researchers have tried to replace the second stage with a first-order Taylor approximation technique, which has achieved certain accuracy improvement. However, this method introduces the reference distance into the augmented parameter vector, so at least five receiving stations are required to meet the requirement of parameter identification. Therefore, the literature points out that the estimate of the reference distance can be first introduced into the augmented parameter vector to reduce the number of receiving stations required.

[0006] Although the above method can reduce the number of TDOA positioning receiving stations to at least four stations. However, for real-time reconnaissance and surveillance, the number of receiving stations is a very valuable resource. Under the permitted conditions, we hope to meet the positioning index requirements with the least number of receiving stations, or even at the cost of a certain degree of positioning accuracy loss in exchange for the reduction of the number of stations. In these cases, it is necessary to study three-station target positioning. If multiple-station target positioning is performed using TDOA measurements, at least four receiving stations are required. If there are only three receiving stations, the part of the target parameters that cannot be identified needs to be estimated through other additional measurements.

[0007] To this end, the present application combines the intra- / inter-station multi-measurement information, estimates the reference distance and the target X coordinate within the station, so that the estimation of the remaining target parameters can be achieved by three stations, and proposes a three-station hybrid target positioning method combining intra- / inter-station measurements, to provide more accurate target position information for strategic, reconnaissance and guidance applications. SUMMARY

[0008] The technical problem solved by the present application is to overcome the shortcomings of the prior art and to provide a three-station hybrid target positioning method combining intra- / inter-station measurements, to provide a solution for the three-station target positioning problem.

[0009] The technical solutions provided by the present application are as follows:

[0010] In a first aspect, a three-station hybrid target positioning method combining intra- / inter-station measurements comprises:

[0011] Obtaining intra-station DOA measurements of each radar station, dividing the radar into one reference station and two receiving stations, obtaining inter-station TDOA measurements and FDOA measurements of the receiving station-reference station;

[0012] Estimating the target X-axis coordinate and the distance from the target to the reference station using the DOA measurements and the TDOA measurements;

[0013] Correcting the target X-axis coordinate and the distance from the target to the reference station using the FDOA measurements;

[0014] Determining the target Y-axis and Z-axis coordinates using the TDOA measurements and the corrected X-axis coordinate and the distance from the target to the reference station, to complete the three-station target positioning.

[0015] In combination with the first aspect, the obtaining of the intra-station DOA measurements comprises:

[0016] Suppose that the space-air distributed radar network is composed of a single high-orbit satellite-borne radar and K unmanned aerial vehicle-borne radars, the high-orbit satellite-borne radar transmits signals, the unmanned aerial vehicle-borne radars only receive signals, the number of receiving radars K=3; the satellite navigation position is located at Considering the limited positioning accuracy of GNSS, the satellite's true position a and navigation position a o The relationship between them is described as a = a o +Δa=[x a ,y a ,z a ] T In the formula, Δa is the satellite navigation position error, and the satellite velocity is v. a The navigation position of the i-th UAV is located at Real location s i and navigation location The relationship is In the formula Δs i Let be the position error of the i-th UAV, and let v be the speed of the UAV. s ;

[0017] Assume the aerial target in the scene is located at u = [x, y, z] T The actual receiving cone angle of the target observed by the i-th UAV is:

[0018]

[0019] In the formula, e1 = [1, 0, 0] T DOA measurement is expressed as:

[0020]

[0021] in This indicates the noise level of the DOA measurement.

[0022] In conjunction with the first aspect, the division of the radar into one reference station and two receiving stations, and the acquisition of TDOA and FDOA measurements between the receiving station and the reference station, includes:

[0023] The true bistatic distance received by the i-th UAV after being launched from a high-orbit satellite and passing over the target is expressed as:

[0024] b i =||ua||2+||us i ||2

[0025] After distance difference,

[0026] r i1 =b i -b1=r i -r1

[0027] In the formula r i =||us i ||2 represents the distance from the target to the i-th UAV, then the TDOA measurement is written as:

[0028]

[0029] where c represents the speed of light, Δt i1 represents the differential time delay measurement noise;

[0030] The true bistatic Doppler is:

[0031]

[0032] where v t is the target instantaneous velocity, λ is the wavelength,

[0033]

[0034] ψ T and are the transmit and receive velocity cone angles respectively, after Doppler differencing,

[0035]

[0036] The FDOA measurement is:

[0037]

[0038] where represents the FDOA measurement noise.

[0039] In combination with the first aspect, the step of estimating the target X-axis coordinate and the distance from the target to the reference station by using the DOA measurement and the TDOA measurement comprises: considering that the influence of the radar position error on the observation angle is very small, i.e.:

[0040]

[0041] and r i = r i1 +r1, it is obtained that:

[0042]

[0043] The parameter vector is defined as All the measurements of the receiving radars are arranged in a matrix form and written as:

[0044] h a =G a v1

[0045] In the formula:

[0046]

[0047] and

[0048]

[0049] Using noisy measurement vectors and respectively instead of noiseless measurement vectors and r1 = [r 21 ,r 31 ] T The least squares problem is then established as:

[0050]

[0051] The LS solution of part of the target parameters v1 is:

[0052]

[0053] In combination with the first aspect, the step of correcting the X-axis coordinate of the target and the distance from the target to the reference station using the FDOA measurement includes: the i-th part receives the FDOA measurement of the radar and the reference radar, which can be written as:

[0054]

[0055] The velocity cone angle of the positive side-looking array and the array plane cone angle are equal, and there are Therefore, due to the existence of the common term (v s +v t ) / λ, the constraint between the FDOA measurements is:

[0056]

[0057] Substituting into the above constraint expression between FDOA measurements, we get:

[0058]

[0059] That is:

[0060]

[0061] Substituting and into the above constraint expression between FDOA measurements, we get:

[0062] h a = G a v1

[0063] In the formula, G a is corrected as:

[0064]

[0065] and

[0066]

[0067] In combination with the first aspect, the step of determining the target Y-axis and Z-axis coordinates by using the TDOA measurements and the corrected X-axis coordinates and the distance from the target to the reference station to complete the three-station target positioning comprises:

[0068] The TDOA measurement r i1 = r i -r1is arranged as r i1 +r1= r i , and squaring both sides, we get:

[0069]

[0070] Substitute and , we get:

[0071]

[0072] wherein and The TDOA measurements from all receiving stations are arranged in matrix form:

[0073]

[0074] In the formula v2 = [y, z] T ,

[0075]

[0076] and

[0077]

[0078] According to the Gauss-Markov theorem, minimize wherein The weighted least squares (WLS) estimate of the remaining parameter v2 is:

[0079]

[0080] In the formula is the TDOA vector, and the weight matrix W is

[0081] W = (AQ t A T +BQ s B T ) -1

[0082] In the formula Q t = c 2 E[ΔtΔt T ] and Q s = E[ΔsΔs T], wherein Δt = [Δt 21 ,…,Δt K1 ] T and

[0083] A≈I K-1

[0084]

[0085] Finally, the three-station target positioning result is expressed as

[0086] In a second aspect, a three-station hybrid target positioning device combining intra- / inter-station measurements comprises:

[0087] one or more processors;

[0088] a storage device configured to store one or more programs,

[0089] when the one or more programs are executed by the one or more processors, the one or more processors implement the three-station hybrid target positioning method combining intra- / inter-station measurements according to the first aspect.

[0090] In a third aspect, a readable storage medium has a computer program stored thereon, which, when executed by a processor, implements the three-station hybrid target positioning method combining intra- / inter-station measurements according to the first aspect.

[0091] In a fourth aspect, a computer program product comprises a computer program which, when executed, performs the three-station hybrid target positioning method combining intra- / inter-station measurements according to the first aspect.

[0092] The three-station hybrid target positioning method combining intra- / inter-station measurements according to the present application has the following beneficial effects:

[0093] (1) The three-station hybrid target positioning method combining intra- / inter-station measurements according to the present application innovatively estimates the reference distance and the target X coordinate using DOA measurements and TDOA measurements, and uses FDOA measurements to assist in improving the parameter estimation accuracy. This method reduces the number of required DOA measurements, can reduce system cost, and is easy to implement in engineering.

[0094] (2) The three-station hybrid target positioning method combining intra- / inter-station measurements according to the present application is a target positioning method under three-station position uncertainty. This method estimates the target Y and Z coordinates by constructing a pseudo-linear equation set under the condition that the receiving station position is unknown. This method only requires three receiving stations to complete target positioning, has good robustness, and has good engineering application prospects. BRIEF DESCRIPTION OF DRAWINGS

[0095] Figure 1 This is a flowchart of a three-station hybrid target localization method based on combined in-station / inter-station measurements according to the present invention;

[0096] Figure 2 This is a scatter plot of the target location estimation in an embodiment of the present invention;

[0097] Figure 3 This is a comparison of target positioning accuracy in the embodiments of the present invention. Detailed Implementation

[0098] The features and advantages of the present invention will become clearer and more apparent from the following detailed description.

[0099] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments.

[0100] The three-station hybrid target localization method based on combined in-station / inter-station measurements in this invention can be applied to the field of target localization. For example... Figure 1 As shown, this method first estimates the reference distance and target X-coordinate by combining DOA and TDOA measurements; then, it uses FDOA measurements to improve the accuracy of parameter estimation; finally, by combining the estimated target parameters and constructing a pseudo-linear equation system using inter-station TDOA measurements through parameter "compression," the target is located. This method requires only three receiving stations to achieve target positioning and has good prospects for engineering applications.

[0101] The implementation steps are as follows:

[0102] Step 1: Obtain intra-station DOA measurements and inter-station TDOA+FDOA measurements.

[0103] Assume a space-air distributed radar network consists of a single high-orbit satellite-borne radar and K unmanned aerial vehicle (UAV)-borne radars. The high-orbit satellite-borne radar transmits signals, while the UAV-borne radars only receive signals. To focus on the three-station target localization, we assume the number of receiving radars, K = 3. The satellite navigation position is located at... Given the limited positioning accuracy of the Global Navigation Satellite System (GNSS), the actual satellite position 'a' and the navigation position 'a' are... o The relationship can be described as a = a o +Δa=[x a ,y a ,z a ] T In the formula, Δa is the satellite navigation position error, and the satellite velocity is v. aSimilarly, the i-th UAV navigation position is located at Real position s i and navigation position The relationship is where Δs i is the i-th UAV position error, and the UAV velocity is v s The definitions of intra-station measurements and inter-station measurements are given below:

[0104] a) Intra-station DOA measurement

[0105] Intra-station measurement mainly refers to the target direction of arrival (DOA) measurement obtained by the receiving radar antenna array. Assuming that the aerial target in the scene is located at u = [x, y, z] T , the real receiving cone angle of the i-th UAV observing the target is:

[0106]

[0107] where e1 = [1, 0, 0] T . Due to the limited angle measurement accuracy, the real receiving cone angle is affected by measurement noise, and the DOA measurement can be expressed as:

[0108]

[0109] where represents the DOA measurement noise.

[0110] b) Inter-station TDOA+FDOA measurement

[0111] Determining one UAV-borne radar as the reference station and the other two UAV-borne radars as the receiving stations, the inter-station measurement mainly refers to the time difference of arrival (TDOA) measurement and the frequency difference of arrival (FDOA) measurement obtained by the receiving stations and the reference station. First, the real bistatic distance received by the i-th UAV from the high-orbit satellite after passing through the target can be expressed as:

[0112] b i = ||u-a||2+||u-s i ||2 Equation 3

[0113] After distance difference,

[0114] r i1 = b i -b1 = r i -r1 Equation 4

[0115] where r i = ||u-s i||2denotes the distance from the target to the ith UAV. Considering that TDOA measurements and range-difference of arrival (RDOA) measurements differ only by a multiplicative factor, we do not strictly distinguish between these two types of measurements in the sequel. The TDOA measurement can then be written as:

[0116]

[0117] where c denotes the speed of light, Δt i1 denotes the differential time delay measurement noise.

[0118] Similarly, the true bistatic Doppler is:

[0119]

[0120] where v t is the target instantaneous velocity, λ is the wavelength of the transmitted signal,

[0121]

[0122] ψ T and are the transmit and receive velocity cone angles, respectively, and after Doppler differencing,

[0123]

[0124] The FDOA measurement can be written as:

[0125]

[0126] where denotes the FDOA measurement noise.

[0127] Step 2. Estimate the target partial parameters, i.e., the target X-coordinate and the target distance to the reference station, using the DOA measurements and the TDOA measurements.

[0128] The target localization is split into two parts. First, consider that the radar position error has a small effect on the observed angle, i.e.,

[0129]

[0130] and r i = r i1 + r1, we have:

[0131]

[0132] is the true receive cone angle of the ith UAV observing the target, is the receive cone angle of the ith UAV observing the target without considering the measurement noise;

[0133] Definition of parameter vector All the received radar measurements are arranged into a matrix form, which can be written as:

[0134] h a = G a v1 Equation 12

[0135] In which:

[0136]

[0137] And:

[0138]

[0139] Replace the noise-free measurement vector and with the noisy measurement vector and r1 = [r 21 ,r 31 ] T , the least squares (LS) problem can be established as:

[0140]

[0141] The least squares solution of the partial target parameter v1 is:

[0142]

[0143] Step 3, use FDOA measurement to assist in improving the estimation accuracy of the target partial parameter in step 2.

[0144] The FDOA measurement of the i-th receiving radar and the reference radar is written as:

[0145]

[0146] On the other hand, the velocity cone angle and the array plane cone angle of the forward-looking array are equal, and there is Therefore, due to the existence of the common term (v s +v t ) / λ, the FDOA measurements can be constrained as:

[0147]

[0148] Substitute (10) into (18) to get:

[0149]

[0150] That is:

[0151]

[0152] The formula (11) and formula (20) are arranged in matrix form, and the following is obtained:

[0153] h a = G a v1 Formula 21

[0154] In the formula G a is corrected to:

[0155]

[0156] and

[0157]

[0158] Compared with step 2, step 3 introduces the FDOA measurement equation at the same time, without the target DOA measurement of the reference station. It is worth emphasizing that the Doppler estimation accuracy needs to be high enough to utilize the FDOA measurement to assist parameter estimation.

[0159] Step 4, the target Y-axis and Z-axis coordinates are determined by using the inter-station TDOA measurement, and the three-station target positioning is completed.

[0160] The pseudo-linear equation set is constructed by using the inter-station TDOA measurement to position the target. In order to linearize the equation, the reference distance needs to be added to the parameter vector to be estimated, and then four unknown parameters are included in the aerial target positioning, and at least five receiving stations can support the parameter identifiable condition. If the reference distance and the target X coordinate are estimated by using the intra-station measurement, then the minimum number of receiving stations can be reduced to three stations.

[0161] The formula r i1 = r i -r1 is arranged as r i1 +r1 = r i , and both sides are squared, and the following is obtained:

[0162]

[0163] Substituting and , the following is obtained:

[0164]

[0165] Among them and The TDOA measurements from all receiving stations are arranged in matrix form:

[0166]

[0167] In the formula v2 = [y, z] T ,

[0168]

[0169] and

[0170]

[0171] Then according to the Gauss-Markov theorem, minimize where The weighted least squares (WLS) estimate of the remaining parameter v2is:

[0172]

[0173] where is the TDOA vector, and the weighting matrix W is:

[0174] W = (AQ t A T +BQ s B T ) -1 Equation 30

[0175] where Q t = c 2 E[ΔtΔt T ] and Q s = E[ΔsΔs T ], where Δt = [Δt 21 ,…, Δt K1 ] T and

[0176] A ≈ I K-1 Equation 31

[0177]

[0178] Finally, the three-station target positioning result can be expressed as

[0179] The application also provides a three-station mixed target positioning device combining intra- / inter-station measurement, comprising:

[0180] one or more processors;

[0181] a storage device configured to store one or more programs,

[0182] when the one or more programs are executed by the one or more processors, the one or more processors implement the three-station mixed target positioning method combining intra- / inter-station measurement of the first aspect.

[0183] The above processor and storage device can be configured on any unmanned aerial vehicle carrying a radar.

[0184] It is understood that the above-described processor can be a CPU, and can also be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs) or other programmable logic devices, discrete gates or transistor logic, discrete hardware components, or the like. The general-purpose processor can be a microprocessor or any conventional processor, or the like. It is worth noting that the processor can be an advanced RISC machines (ARM) architecture processor.

[0185] The above-described storage device can include read-only memory and random access memory, and provide instructions and data to the processor. The memory can also include non-volatile random access memory. For example, the memory can also store device type information.

[0186] The storage device can be a volatile memory or a non-volatile memory, or can include both volatile and non-volatile memories. Among them, the non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically EPROM (EEPROM) or flash memory. The volatile memory can be random access memory (RAM) used as an external cache. By way of example but not limitation, many forms of RAM are available. For example, static random access memory (SRAM), dynamic random access memory (DRAM), synchronous DRAM (SDRAM), double data rate synchronous dynamic random access memory (DDR SDRAM), enhanced SDRAM (ESDRAM), synchlink DRAM (SLDRAM) and direct memory bus random access memory (direct rambus RAM, DRRAM).

[0187] The application further provides a readable storage medium, which stores a computer program, and the program is executed by a processor to implement the joint intra- / inter- station measurement three-station mixed target positioning method of the first aspect.

[0188] The application further provides a computer program product, which comprises a computer program (also referred to as code or instruction) that, when executed, performs the joint intra- / inter- station measurement three-station mixed target positioning method of the first aspect.

[0189] In the above embodiments, the implementation can be achieved by software, hardware, firmware or any combination thereof, entirely or partially. When implemented by software, the implementation can be achieved in the form of a computer program product, entirely or partially. The computer program product comprises one or more computer instructions. When the computer instructions are loaded and executed on a computer, the flow or function described in the embodiments of the application is generated, entirely or partially. The computer can be a general-purpose computer, a special-purpose computer, a computer network or other programmable devices. The computer instructions can be stored in a computer readable storage medium or transferred from one computer readable storage medium to another, for example, the computer instructions can be transferred from one website site, computer, server or data center to another website site, computer, server or data center by wire (such as coaxial cable, optical fiber, digital subscriber line (DSL) or wireless (such as infrared, wireless, microwave, etc.).

[0190] Those skilled in the art can realize that the apparatuses and algorithm steps of the examples described in conjunction with the embodiments disclosed herein can be realized by electronic hardware or a combination of computer software and electronic hardware. Whether the functions are realized in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

[0191] The implementation effect of the application is further illustrated by simulation experiments.

[0192] Suppose the orbit height of the high-orbit satellite is 36000km, the variance of the three-dimensional position error is 100m, and the three-dimensional coordinates of the three unmanned aerial vehicles are [200e 3 ,100e 3 ,15e 3 ] T m, [100e 3 ,200e 3 ,15.5e 3 ] Tm and [200e 3 ,100e 3 ,16e 3 ] T m, the variance of the three-dimensional position error is 4m, and the flight speed is 150 m / s. The aerial target is located at [250e 3 ,250e 3 ,5e 3 ] T m, and the speed is 62.5 m / s. Table 1 shows the results of the WLS-Ho method, the WLS-AOA / TDOA method, and the hybrid positioning method proposed in the present application under the condition that the target SNR is 20 dB:

[0193] It can be seen that, since the WLS-Ho method does not satisfy the parameter identifiable condition, it cannot position the target, and the positioning accuracy is very poor, with the positioning accuracy always being more than 10 5 meters; the WLS-AOA / TDOA positioning method estimates part of the target parameters using AOA / TDOA measurements, fills in the missing part of the target identifiable condition first, and then estimates the remaining target parameters, with the positioning accuracy being better than 1000 meters; the hybrid positioning method proposed in the present application further considers FDOA measurements, and uses the inter-station constraint relationship between FDOA measurements to improve the accuracy of target parameter estimation.

[0194] Figure 2 Further, the scatter plot of the target position estimation of the hybrid positioning method proposed in the present application after 2000 experiments is given. The red pentagram represents the actual position of the target, and the blue dots represent the estimated position of the target in each experiment. It can be seen that the estimation deviation of the target position is about 2000 m, 2000 m, and 4000 m in the x, y, and z dimensions respectively, that is, the target position estimation is constrained in a cube with the target position as the center, and the length, width, and height are 2000 m, 2000 m, and 4000 m respectively.

[0195] Figure 3 Further, the relationship between the standard deviation of the target positioning accuracy of the three methods and the SNR is given, with the black line representing the WLS-Ho method, the blue line representing the WLS-AOA / TDOA method, and the red line representing the hybrid positioning method proposed in the present application. It can be seen that, due to the unidentifiable parameters, the positioning accuracy of the WLS-Ho method almost does not change with the SNR; the positioning accuracy of the WLS-AOA / TDOA method continuously improves with the improvement of the SNR; and the positioning accuracy of the hybrid positioning method proposed in the present application is better than that of the WLS-AOA / TDOA method due to the estimation of part of the parameters by the auxiliary FDOA measurements.

[0196] Table 1 Comparison of positioning results of the WLS-Ho method, the WLS-AOA / TDOA method, and the hybrid positioning method

[0197]

[0198] Simulation analysis and conclusion: the present application is aimed at the space-air network composed of high-orbit satellite and unmanned aerial radar, and the aerial target is positioned by using station measurement. It mainly includes three steps: 1) the LS problem about reference distance and target X coordinate estimation is established by using DOA measurement and TDOA measurement; 2) the target partial parameter estimation is assisted by using FDOA measurement; 3) the pseudo-linear equation set is constructed by using station TDOA measurement, and the target is positioned by using WLS method; the target positioning precision can be controlled within 1000 meters under the condition that the SNR is 20 dB, and the aerial target positioning is better realized.

[0199] The present application is described in detail above in combination with specific embodiments and exemplary examples, but these descriptions cannot be understood as limitations of the present application. Those skilled in the art understand that the technical solutions and embodiments of the present application can be variously replaced, modified or improved without departing from the spirit and scope of the present application, and these all fall within the scope of the present application. The protection scope of the present application is subject to the appended claims.

[0200] The contents not described in detail in the specification of the present application are the known technology of those skilled in the art.

Claims

1. A three-station hybrid target positioning method combining intra- / inter-station measurements, characterized in that, The method comprises the following steps: Obtaining DOA measurements of each radar station, dividing the radars into one reference station and two receiving stations, obtaining TDOA measurements and FDOA measurements between the receiving stations and the reference station; Estimating the X-axis coordinate of the target and the distance from the target to the reference station by using the DOA measurements and the TDOA measurements; Correcting the X-axis coordinate of the target and the distance from the target to the reference station by using the FDOA measurements; Determining the Y-axis and Z-axis coordinates of the target by using the TDOA measurements and the corrected X-axis coordinate and the distance from the target to the reference station, and completing the three-station target positioning.

2. The method of claim 1, wherein the method is a three-station hybrid TDOA / FDOA multistatic positioning method. The DOA measurements comprise: The space-air distributed radar network is composed of a single high-orbit spaceborne radar and K unmanned aerial radars. The high-orbit spaceborne radar transmits signals, and the unmanned aerial radars only receive signals. The number of receiving radars is K=3. The navigation position of the i-th unmanned aerial vehicle is located at i=1, 2, …, K, and the real position s i is related to the navigation position as where Δs i is the position error of the i-th unmanned aerial vehicle. The TDOA measurements comprise: wherein represents the DOA measurement noise, represents the true receive cone angle of the i-th drone observing the target. where u represents the aerial target position, u = [x, y, z] T , e1 = [1, 0, 0] T .

3. The method of claim 2, wherein the method is a three-station hybrid TDOA / FDOA method. The FDOA measurements comprise: The step of estimating the X-axis coordinate of the target and the distance from the target to the reference station by using the DOA measurements and the TDOA measurements comprises: where c represents the speed of light, At i1 denotes the differential delay measurement noise, r i1 = b i - b1= r i - r1, r i =||u-s i ||2, represents the distance from the target to the i-th drone; b i = ||u-a||2+||u-s i ||2, represents the real bistatic distance from the high orbit satellite, through the target, received by the ith UAV, where a represents the satellite real position, a = a o + Δa = [x a ,y a ,z a ] T , a o represents the satellite navigation position, and Δa represents the satellite navigation position error.

4. The method of claim 3, wherein the method is a three-station hybrid TDOA / FDOA multistatic positioning method. The step of correcting the X-axis coordinate of the target and the distance from the target to the reference station by using the FDOA measurements comprises: The FDOA measurements between the i-th receiving radar and the reference radar are written as: wherein denotes the FDOA measurement noise, where v a is the satellite velocity, v s is the velocity of the drone carrying the radar, v t is the target instantaneous velocity, λ is the wavelength of the transmitted signal, ψ T and are the emission and reception speed cone angles, respectively.

5. The method of claim 4, wherein the method is a three-station hybrid TDOA / FDOA multistatic positioning method. That is: Consider and r i = r i1 + r1, we get: Definition of parameter vector All the received radar measurements are arranged into a matrix form, written as: h a = G a v1 The step of determining the Y-axis and Z-axis coordinates of the target by using the TDOA measurements and the corrected X-axis coordinate and the distance from the target to the reference station, and completing the three-station target positioning comprises: The computer program product comprises a computer program, which, when executed, performs the three-station mixed target positioning method of the joint intra-station / inter-station measurements according to any one of claims 1 to 7. with noisy measurement vectors and replacing the noiseless measurement vectors and r1 = [r 21 , r 31 ] T The least squares problem is then set up as: The computer program product comprises a computer program, which, when executed, performs the three-station mixed target positioning method of the joint intra-station / inter-station measurements according to any one of claims 1 to 7.

6. The method of claim 5, wherein the method is a three-station hybrid TDOA / MTDOA method. The computer program product comprises a computer program, which, when executed, performs the three-station mixed target positioning method of the joint intra-station / inter-station measurements according to any one of claims 1 to 7. ​ The velocity cone angle and the array plane cone angle of the positive side-looking array are equal, and the velocity cone angle of the negative side-looking array is twice that of the positive side-looking array. Then, due to the common term (v s + v t ) / λ, the constraint between FDOA measurements is: Substituting the above constraint expression between FDOA measurements, we have: Substituting the above constraint expression between FDOA measurements, we have: Substituting the above constraint expression between FDO ​ The and Arranged in matrix form, we have: h a = G a v1 In the formula (I), G a Amended to read: ​ 7. The method of claim 6, wherein the method is a three-station hybrid TDOA / MTDOA method. ​ The TDOA measurement r i1 = r i - r1is arranged as r i1 + r1= r i and square both sides, we get: Substituting and yields: wherein and TDOA measurements from all receiving stations are collated into a matrix form: In the formulae v2 = [y, z] T , ​ Then, according to the Gauss-Markov theorem, the weighted least squares estimate of the remaining parameter v2is: where The weighted least squares estimate of the remaining parameter v2is: In the formula is a TDOA vector, and the weighting matrix W is: W = (AQ t A T +BQ s B T ) -1 where Q t = c 2 E[ΔtΔt T ] and Q s = E[ΔsΔs T ], where Δt = [Δt 21 ,…,Δt K1 ] T and A ≈ I K-1 The final three-station target location result is 8. A three-station hybrid target location device that combines intra- / inter- station measurements, characterized by, ​ ​ ​ ​ 9. A readable storage medium, characterized by, ​ 10. A computer program product, characterised in that, ​

Images