Method for locating moving target based on time delay and doppler under calibration target cooperation

Abstract

The application discloses a kind of calibration target cooperation under the positioning method of mobile target based on time delay and doppler, it is related to radio reflection positioning technical field, including steps: by each receiver respectively by mobile target and calibration target reflected signal is received, and the time delay and doppler information conversion is extracted into propagation distance and distance rate measurement value;According to the distance relationship of the propagation node in each signal propagation link, the propagation distance difference model and the distance rate difference model between targets are respectively constructed;Approximate conversion is carried out after two difference models are respectively equivalent after rewriting by introducing auxiliary variable, and pseudo-linear equation is piled based on two approximate conversion results;Semi-positive programming problem is constructed based on pseudo-linear equation, and the position and speed estimation of mobile target is obtained by substituting propagation distance measurement value and distance rate measurement value to solve semi-positive programming problem.The application breaks through the dependence of prior art on strict time synchronization and direct path, and improves the positioning robustness under complex shielding environment.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radio reflection positioning, and particularly relates to a mobile target positioning method based on time delay and Doppler under calibration target cooperation. BACKGROUND

[0002] In recent years, multi-static positioning systems have become a research hotspot in the fields of radar, navigation and wireless sensing due to their advantages in positioning accuracy, anti-interference ability and concealment. Compared with traditional single-base positioning systems, multi-static architecture can effectively utilize spatial diversity gain by deploying transmitters and receivers separately, significantly improving the accuracy and robustness of target positioning. This technology has been widely applied to key scenarios such as high-precision navigation of autonomous vehicles, target search and tracking in disaster rescue, and passive detection in military reconnaissance.

[0003] In multi-static positioning systems, the position estimation of a target usually relies on measurement parameters such as time delay (TD), differential time delay (DTD), Doppler shift or angle of arrival (AoA) extracted from received signals. Among them, the time delay-based ellipse positioning method is one of the most common solutions. The basic principle is that each bistatic TD measurement value defines an ellipse or ellipsoid surface with the transmitter and receiver as the foci in two-dimensional or three-dimensional space, and the intersection of the ellipses / ellipsoids formed by the measurement data of multiple transceiver pairs is the estimated value of the target position. Existing research mainly focuses on two typical scenarios: one is the cooperative positioning system where the transmitter positions are known, and the other is the non-cooperative (such as external radiation source or passive positioning) system where the transmitter positions are unknown.

[0004] In the case where the transmitter positions are known, existing algorithms (such as maximum likelihood estimation, least squares, etc.) can approach the Cramér-Rao Lower Bound (CRLB) under the assumption of strict synchronization between transceivers, achieving high positioning accuracy. However, in practical applications, it is often difficult to maintain high-precision time synchronization between widely deployed receiver nodes, especially in complex environments such as urban canyons, underwater or underground spaces. Synchronization errors can significantly reduce positioning performance. To address this problem, the main solution of existing technology is the time delay difference (DTD) based positioning method: by calculating the autocorrelation time delay difference between the direct wave and the target reflected wave signal, the dependence on absolute time synchronization is reduced. However, this method requires the receiver to be able to simultaneously capture the direct wave and reflected wave signals, while in actual scenarios, the direct path may be missing due to obstacles or signal attenuation. SUMMARY

[0005] In order to realize the multi-base target positioning under the severe conditions of unknown transmitter position, unsynchronized receivers and missing direct path due to occlusion, the application proposes a mobile target positioning method based on time delay and Doppler under the calibration target cooperation, including the following steps:

[0006] S1: Construct a multi-base positioning system containing an unknown position transmitter, a plurality of known position receivers, a mobile target with unknown position and speed, and a calibration target with known fixed position;

[0007] S2: Receive the signals reflected by the mobile target and the calibration target respectively through each receiver, extract the time delay measurement value and the Doppler frequency shift measurement value of the corresponding target, and convert them into propagation distance measurement value and distance rate measurement value respectively;

[0008] S3: According to the distance relationship of the propagation nodes in each signal propagation link, construct the propagation distance difference model and the distance rate difference model between the targets respectively;

[0009] S4: Through the introduction of auxiliary variables, the propagation distance difference model and the distance rate difference model are approximately converted after equivalent rewriting, and the pseudo-linear equations are stacked based on the two approximate conversion results;

[0010] S5: Based on the pseudo-linear equations, construct a semi-definite programming problem, and solve the semi-definite programming problem by substituting the propagation distance measurement value and the distance rate measurement value to obtain the position and speed estimation of the mobile target.

[0011] The application uses the difference processing of the measurement values of the calibration target reflected signal and the mobile target reflected signal to eliminate the systematic error caused by the clock offset of the transmitter-receiver and the asynchronous carrier frequency, breaks through the dependence of the prior art on strict time synchronization and direct path, and improves the positioning robustness in complex occlusion environment (such as urban building group, canyon or underground space).

[0012] Further, in the S2 step, the propagation distance measurement value and the distance rate measurement value are converted by the following way: processing the received signal, extracting the time delay measurement value and the Doppler frequency shift measurement value of the corresponding target, according to the signal propagation speed and the carrier frequency , taking the product of the propagation speed and the time delay measurement value of the corresponding target as the target propagation distance measurement value, and taking the product of the propagation speed and the Doppler frequency shift measurement value of the corresponding target divided by the carrier frequency as the distance rate measurement value, wherein is the calibration target or moving target .

[0013] Furthermore, in the step S3, the propagation distance difference model and the distance rate difference model are constructed in the following manner:

[0014] According to the transmitter position in the current signal propagation link , No. Receiver locations and moving target location The positional relationship between them is used to construct the propagation distance model and distance rate model of the moving target. The formula is expressed as follows:

[0015] ,

[0016] Where, The signal is sent from the transmitter to the moving target and then reflected by the The propagation distance measurement value of the signal propagation link received by each receiver, For the transmitter and The true value of the distance offset error caused by clock asynchrony between receivers, The signal is sent from the transmitter to the moving target and then reflected by the The propagation distance measurement noise on the signal propagation link received by each receiver, The signal is sent from the transmitter to the moving target and then reflected by the The distance rate measurement value on the signal propagation link received by each receiver, is the speed of the moving target, For the transmitter and The true value of the range rate offset error caused by the different carrier frequencies between receivers, The signal is sent from the transmitter to the moving target and then reflected by the The distance rate measurement noise on the signal propagation link received by the receiver, T is the matrix transpose, represents the Euclidean norm;

[0017] According to the transmitter position in the current signal propagation link , No. Receiver positions and calibration target position The positional relationship between them is used to construct the propagation distance model and distance rate model of the calibration target. The formula is expressed as follows:

[0018] ,

[0019] Where, The signal is sent from the transmitter to the calibration target and then reflected by the The propagation distance measurement value of the signal propagation link received by each receiver, The signal is sent from the transmitter to the calibration target and then reflected by the The propagation distance measurement noise on the signal propagation link received by each receiver, The signal is sent from the transmitter to the calibration target and then reflected by the The distance rate measurement value on the signal propagation link received by each receiver, The signal is sent from the transmitter to the calibration target and then reflected by the The range rate measurement noise on the signal propagation link received by each receiver;

[0020] The propagation distance difference model is constructed based on the difference between the propagation distance model of the moving target and the calibration target. The distance rate difference model is constructed based on the difference between the distance rate model of the moving target and the calibration target. The formula is expressed as follows:

[0021] ,

[0022] Where, The signal is sent by the transmitter, reflected by the moving target and the calibration target, and then The difference in propagation distances of the two signal propagation links received by a receiver, is the measurement noise of the propagation distance difference, The signal is sent by the transmitter, reflected by the moving target and the calibration target, and then The distance rate difference between the two signal propagation links received by a receiver, is the measurement noise of the range rate difference.

[0023] Furthermore, in the step S4, the auxiliary variable includes the unknown position of the transmitter in the difference model. The items are selected as independent variables to simplify the difference model, including and .

[0024] Furthermore, in step S4, the pseudo linear equation is obtained specifically through the following steps:

[0025] According to the auxiliary variables, the propagation distance difference model and the distance rate difference model are equivalently rewritten as:

[0026] ,

[0027] Will Move to the left side of the propagation distance difference model equation, square both sides of the equation and ignore the second-order noise term to obtain the propagation distance difference conversion model:

[0028] ,

[0029] Let Move the distance rate difference value model equation left side, and multiply both sides of the equation by , and rewrite the formula according to the propagation distance difference value model equivalent Substitute and ignore the second-order noise term, get the distance rate difference value conversion model:

[0030] ,

[0031] Stack the two difference value conversion models into matrix form to get the pseudo-linear equation:

[0032] ,

[0033] In the formula, is an unknown vector, is an introduced coefficient matrix, is an introduced coefficient vector, is an introduced noise coefficient matrix, is a measurement noise vector.

[0034] Further, the formula expression of the semi-definite programming problem in the S5 step is:

[0035] ,

[0036] In the formula, is an optimization variable corresponding to the unknown vector , is an auxiliary matrix variable introduced in the semi-definite programming problem, is a weight matrix introduced in the semi-definite programming problem, is the trace of the matrix.

[0037] Further, the constraint conditions of the semi-definite programming problem include:

[0038] ,

[0039] In the formula, is the 2L+2th element in , is the 2L+4th element in , is the element at the position of the 2L+1th row and the 2L+1th column in , is the element at the position of the 2L+1th row and the 2L+2th column in , is the element matrix of the 1st to Lth rows and the 1st to Lth columns in , is the element matrix of the 1st to Lth rows and the 1st to Lth columns in The elements matrix of the first to Lth rows and L+1th to 2Lth columns.

[0040] Further, the unknown position transmitter is an external radiation source. Wherein The covariance matrix of the measurement noise vector The expected symbol is sought.

[0041] Further, the unknown position transmitter is an external radiation source.

[0042] Compared with the prior art, the present application has at least the following beneficial effects:

[0043] (1) The present application proposes a mobile target positioning method based on time delay and Doppler under the cooperation of a calibration target, which uses the difference processing of the measurement values of the calibration target reflection signal and the mobile target reflection signal to eliminate systematic errors caused by the clock offset of the transmitter-receiver and the asynchronous carrier frequency, breaks through the dependence on strict time synchronization and direct path in the prior art, and improves the positioning robustness in complex shielding environments (such as urban building groups, valleys or underground spaces);

[0044] (2) By introducing auxiliary variables to equivalently reconstruct the highly nonlinear differential measurement model, the original complex optimization problem is converted into a pseudo-linear equation, combined with the semi-definite programming (SDP) solving algorithm, the calculation complexity is reduced while ensuring the positioning accuracy approaching the Cramer-Rao lower bound (CRLB), and the efficient joint estimation of the mobile target position and velocity is realized;

[0045] (3) Compatible with the external radiation source (such as a broadcast tower or a communication base station) with unknown position as an opportunity transmitter, not only reduces the system deployment cost, but also expands the application potential in special scenes such as military passive reconnaissance, disaster rescue hidden search and rescue, etc. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 It is a step diagram of a mobile target positioning method based on time delay and Doppler under the cooperation of a calibration target;

[0047] Figure 2 It is a comparison diagram of the MSE of the coordinate position estimation of the target by the method of the present application and CRLB with respect to the distance measurement noise power;

[0048] It is a comparison diagram of the MSE of the target moving speed estimation by the method of the present application and CRLB with respect to the distance measurement noise power; Figure 3 It is a comparison diagram of the MSE of the target moving speed estimation by the method of the present application and CRLB with respect to the distance measurement noise power;

[0049] Figure 4 ​​​a comparison chart of the MSE of the target coordinate position estimation varying with the number of receivers in the case of

[0050] Figure 5 a comparison chart of the MSE of the target moving speed estimation varying with the number of receivers in the case of DETAILED DESCRIPTION

[0051] The following is a specific embodiment of the present application and further describes the technical solutions of the present application in conjunction with the drawings, but the present application is not limited to these embodiments.

[0052] According to the first specific embodiment of the present application, it is considered that in the conventional multistatic positioning system, the target position estimation usually depends on the time delay (TD), the time delay difference (DTD) or the Doppler frequency shift and other measurement parameters. Among them, the cooperative positioning method based on the known position transmitter can approach the Cramer-Rao lower bound (CRLB) under strict time synchronization conditions, but in actual deployment, it is difficult for the widely distributed receiver nodes to maintain high-precision clock synchronization, especially in complex environments such as urban canyons, underwater or underground, and synchronization errors will cause the positioning performance to deteriorate significantly. In view of the synchronization problem, the existing technology uses a positioning method based on the time delay difference (DTD) of the direct wave and the reflected wave to reduce the synchronization dependence, but this method requires the receiver to simultaneously capture the direct wave and the reflected wave signal. In actual application scenarios, the absence of the direct path caused by building shielding, terrain obstruction or signal attenuation makes such a method completely ineffective. In addition, the passive positioning technology using unknown position external radiation sources (such as broadcast base stations) can expand the application scenario, but its highly nonlinear model has high complexity in solving, and it has insufficient robustness in the shielding environment. The above defects seriously restrict the practicality of the multistatic positioning system in harsh scenes such as military reconnaissance and disaster rescue. In order to solve the above problems, the present application proposes a mobile target positioning method based on time delay and Doppler under the calibration target cooperation, as shown in Figure 1 , including the following steps:

[0053] S1: constructing a multistatic positioning system containing a transmitter with unknown position, a plurality of receivers with known position, a mobile target with unknown position and speed, and a calibration target with known fixed position;

[0054] S2: receiving the signals reflected by the mobile target and the calibration target by each receiver, extracting the time delay measurement value and the Doppler frequency shift measurement value of the corresponding target from the signals, and converting them into the propagation distance measurement value and the distance rate measurement value, respectively;

[0055] S3: constructing the propagation distance difference model and the distance rate difference model between the targets according to the distance relationship of the propagation nodes in each signal propagation link;

[0056] ​S4: Approximate conversion of the propagation distance difference model and the distance rate difference model by introducing auxiliary variables for equivalent rewriting, and based on the two approximate conversion results, pile up pseudo-linear equations;

[0057] S5: Based on the pseudo-linear equations, construct a semi-definite programming problem, and by substituting the propagation distance measurement value and the distance rate measurement value, solve the semi-definite programming problem to obtain the position and velocity estimation of the moving target.

[0058] For the positioning of moving targets in various working condition scenes, the present application first constructs a multi-base positioning system assisted by a calibration target, sets an unknown position transmitter (external radiation source, which can be a broadcast signal tower or a communication base station), the real position coordinates of which in L-dimensional space are , which is clock-asynchronous with the receiver; a receiver with a known position and clock-asynchronous, the real position coordinates of which in L-dimensional space are an unknown position and moving speed moving target, the real position coordinates and moving speed of which in L-dimensional space are and respectively. To assist positioning and clock synchronization, the present application also introduces a stationary calibration target with a known position, the real position coordinates of which in L-dimensional space are The signal transmitted by the transmitter can be reflected by the calibration target and then received by the receiver. It should be noted that in the present embodiment, vector or matrix parameters are represented by bold symbols, and scalar parameters are represented by regular body symbols.

[0059] When the transmitter sends a signal, due to the obstruction between the transmitter and each receiver, the direct signal cannot be detected by the receiver, and can only be received by the receiver after being reflected by the moving target and the calibration target. At this time, the receiver processes the received reflected signal to extract the time delay measurement value and the Doppler shift measurement value of the corresponding target (moving target or calibration target) for subsequent semi-definite programming problem solving. Specifically, according to the signal propagation speed and the carrier frequency , the product of the propagation speed and the time delay measurement value of the corresponding target is the propagation distance measurement value of the target (D ), and the product of the propagation speed and the Doppler shift measurement value of the corresponding target divided by the carrier frequency is the distance rate measurement value (v ), wherein is the calibration target or the moving target .

[0060] At the same time, according to the transmitter position in the current signal propagation link , No. Receiver locations and moving target location The positional relationship between them is used to construct the propagation distance model and distance rate model of the moving target. The formula is expressed as follows:

[0061] ,

[0062] ,

[0063] Where, The signal is sent from the transmitter to the moving target and then reflected by the The propagation distance measurement value of the signal propagation link received by each receiver, For the transmitter and The true value of the distance offset error caused by clock asynchrony between receivers, The signal is sent from the transmitter to the moving target and then reflected by the The propagation distance measurement noise on the signal propagation link received by each receiver, The signal is sent from the transmitter to the moving target and then reflected by the The distance rate measurement value on the signal propagation link received by each receiver, is the speed of the moving target, For the transmitter and The true value of the range rate offset error caused by the different carrier frequencies between receivers, The signal is sent from the transmitter to the moving target and then reflected by the The distance rate measurement noise on the signal propagation link received by the receiver, T is the matrix transpose, represents the Euclidean norm.

[0064] According to the transmitter position in the current signal propagation link , No. Receiver positions and calibration target position The positional relationship between them is used to construct the propagation distance model and distance rate model of the calibration target. The formula is expressed as follows:

[0065] ,

[0066] ,

[0067] Where, The signal is sent from the transmitter to the calibration target and then reflected by the a propagation distance measurement on the signal propagation link received by the receiver, a propagation distance measurement noise on the signal propagation link received by the receiver, a propagation distance measurement on the signal propagation link received by the receiver, a propagation distance measurement noise on the signal propagation link received by the receiver, a distance rate measurement on the signal propagation link received by the receiver, a distance rate measurement noise on the signal propagation link received by the receiver.

[0068] Then, using the known position of the calibration target as an error scale (or spatial reference frame), systematic bias errors are separated and cancelled by differencing, including the fixed distance bias due to clock asynchrony between the transmitter and receiver, which is the same for all reflection paths, and the fixed distance rate bias due to carrier frequency asynchrony between the transmitter and receiver, which is only an error term because the calibration target is stationary. Here, the difference between the propagation distance models of the moving target and the calibration target is:

[0069] ,

[0070] which, after expansion, becomes:

[0071] ,

[0072] and simplifying, the propagation distance difference model is:

[0073] ,

[0074] where, is the propagation distance difference of the two signal propagation links from the transmitter, reflected by the moving target and the calibration target, and received by the receiver, is the measurement noise of the propagation distance difference. In this way, is cancelled, leaving only the geometric distance combination and the differential noise.

[0075] And by subtracting the distance rate models of the moving target and the calibration target:

[0076] ,

[0077] which, after expansion, becomes:

[0078] ,

[0079] ​​Simplify the distance rate difference model:

[0080] ,

[0081] is the distance rate difference of the two signal propagation links, one from the transmitter, reflected by the moving target and the calibration target, and received by the first receiver, and the other from the transmitter, reflected by the moving target and the calibration target, and received by the second receiver, is the measurement noise of the distance rate difference. Similarly, is canceled out, leaving only the Doppler geometry term and the differential noise.

[0082] Here, the present application eliminates by differential operation, so as to avoid the direct path obstruction problem (such as urban obstruction, terrain obstruction) completely by relying only on the reflected path signals of the target and the calibration target, and converts the original measurement model containing offset error into a pure geometry model + noise.

[0083] Since the difference model after difference still has double nonlinear coupling, where: the propagation distance difference model contains the nested norm term of the unknown position of the moving target and the unknown position of the transmitter , the distance rate difference model contains the position-velocity coupling term, which has strong nonlinearity due to the fractional structure. Therefore, the present application introduces auxiliary variables with the term containing the unknown position of the transmitter in the difference model as an independent variable, simplifies the difference model, including and , and reconstructs the difference model under the equivalent rewriting of the difference model:

[0084] ,

[0085] ,

[0086] Here, the present application absorbs by the introduced , converts the unknown position of the transmitter into a scalar parameter, and decouples the strong correlation between position and velocity by the introduced to represent the radial velocity of the moving target relative to the transmitter.

[0087] Then, the propagation distance difference model is moved and squared:

[0088] ,

[0089] Neglecting the second-order noise term , the propagation distance difference conversion model is obtained by expanding the geometry term: ​​

[0090] .

[0091] For the distance rate difference model, it is obtained by moving to the left side of the distance rate difference model equation and multiplying both sides of the equation by , and rewriting the formula according to the propagation distance difference model equivalent is substituted and the second-order noise term is ignored, the distance rate difference conversion model (or by directly deriving the propagation distance difference conversion model with respect to time) is obtained:

[0092] .

[0093] Then, in order to build a mathematical unified framework and realize efficient global optimization, the present application stacks the two conversion models into a matrix form here, thereby integrating the two independent equations into a single matrix equation to obtain the required pseudo-linear equation , wherein:

[0094] is an unknown vector;

[0095] is an introduced coefficient matrix, and a vector composed of the first row elements of the coefficient matrix is , a vector composed of the first row elements of the coefficient matrix is , is a zero vector of dimension;

[0096] is an introduced coefficient vector, and the first element of the coefficient vector is , a vector composed of the first row elements of the coefficient vector is ;

[0097] is an introduced noise coefficient matrix, defined as , wherein represents a column vector composed of distance difference measurements, represents a column vector composed of distance rate difference measurements, represents a diagonal matrix with as the diagonal element, , is a distance difference value measurement given by the th receiver, is a distance rate difference value measurement given by the th receiver, is a zero matrix of dimension, is the full 1 -vector of the velocities;

[0098] Let denote the measurement noise vector, , , Let denote the range difference measurement noise given by the kth receiver, Let denote the range rate difference measurement noise given by the kth receiver.

[0099] Then, based on the pseudo-linear equations, the non-convex problem can be transformed into a convex optimization problem using the convex relaxation technique, and a semi-definite programming problem can be constructed as follows:

[0100] ,

[0101] ,

[0102] ,

[0103] ,

[0104] where, is the optimization variable corresponding to the position vector is the auxiliary matrix variable introduced in the semi-definite programming problem to convert the non-convex problem into a semi-definite programming problem; is the weight matrix introduced in the semi-definite programming problem, is the covariance matrix of the measurement noise vector is the expected sign; is the trace of a matrix; is the 2L+2th element in is the 2L+4th element in is the element at the position of the 2L+1th row and 2L+1th column in is the element at the position of the 2L+1th row and 2L+2th column in is the element matrix of the 1st to Lth rows and 1st to Lth columns in is the element matrix of the 1st to Lth rows and L+1th to 2Lth columns in By solving the semi-definite programming problem using the interior point method, the estimates of the moving target position and velocity can be obtained.

[0105] ​​​​​​​​​​​According to the second specific embodiment of the present invention, in order to verify the feasibility and effectiveness of the method of the present invention, this embodiment verifies the method of the present invention through a simulation test.

[0106] Assume that there are 6 receivers with known positions in a three-dimensional space, i.e. a three-dimensional coordinate system ( ) and a calibration target with a known position, and a moving target with an unknown position. The real Cartesian coordinate position of the receiver with a known position in three-dimensional space is is randomly generated, and its scalar component in the X-axis direction of the three-dimensional coordinate system Meters (indicating that the component is randomly generated within the interval (-1000, 1000) meters), its scalar component in the Y-axis direction of the three-dimensional coordinate system Meters, its scalar component in the Z-axis direction of the three-dimensional coordinate system Meters; the true Cartesian coordinate position of the calibration target with known position in three-dimensional space is randomly generated, and its scalar component in the X-axis direction of the three-dimensional coordinate system Meters, its scalar component in the Y-axis direction of the three-dimensional coordinate system Meters, its scalar component in the Z-axis direction of the three-dimensional coordinate system Meters; the real Cartesian coordinate position of the unknown moving target in three-dimensional space is assumed to be , the real Cartesian coordinate position is also randomly generated, and its scalar component in the X-axis direction of the three-dimensional coordinate system is Meters, its scalar component in the Y-axis direction of the three-dimensional coordinate system Meters, its scalar component in the Z-axis direction of the three-dimensional coordinate system meters, and its moving speed is assumed to be It is also randomly generated, and its scalar component in the X-axis direction of the three-dimensional coordinate system is Meters / second, its scalar component in the Y-axis direction of the three-dimensional coordinate system Meters / second, its scalar component in the Z-axis direction of the three-dimensional coordinate system meters per second; unknown distance offset is set to is randomly generated, where meters, unknown range rate offset Assume it to be randomly generated, where m / s. The noise of the distance measurement from the target to the receiver is assumed to have a mean of 0 and a covariance matrix of Gaussian noise, where represents the variance of the distance measurement noise, for The distance measurement noise of the signal reflected from the target to the receiver is assumed to have a mean of 0 and a covariance matrix of Gaussian noise, where represents the variance of the range rate measurement noise; the range measurement noise of the signal reflected from the calibration target to the receiver is assumed to have a mean of 0 and a covariance matrix of Gaussian noise, where Represents the variance of the distance measurement noise; the distance measurement noise of the signal reflected by the target to the receiver is assumed to have a mean of 0 and a covariance matrix of Gaussian noise, where represents the variance of the range rate measurement noise; assuming .

[0107] Based on the above parameter settings, simulation experiments tested the performance of the proposed method under different distance measurement noise power and different sensor numbers. The mean squared error (MSE) describing positioning performance in both cases was calculated by running 1000 Monte Carlo experiments on 10 random scenarios. The Cramer-Rao lower bound (CRLB) was also introduced for comparison.

[0108] Figure 2 The method of the present invention and CRLB are given. Comparison diagram of the MSE of the target coordinate position estimation as the distance measurement noise power changes, Figure 3 The method of the present invention and CRLB are given. Comparison chart of the MSE of target moving speed estimation with the change of distance measurement noise power under the condition of .

[0109] Figure 4 The method of the present invention and CRLB are given. Comparison chart of the MSE of the target coordinate position estimation as the number of receivers changes. Figure 5 The method of the present invention and CRLB are given. Comparison chart of the MSE of target moving speed estimation as the number of receivers changes in the case of .

[0110] from Figure 2 、 Figure 3 It can be seen from the figure that when the distance measurement noise power changes, the method of the present invention can achieve the positioning accuracy of CRLB when the distance measurement noise power is small. Figure 4 、 Figure 5As can be seen from the above, when the number of receivers changes, the positioning accuracy of the method of the application can reach the CRLB when the target number exceeds 5, and in addition, the MSE of the target position estimation of the method of the application is significantly reduced as the number of receivers increases, which means that the positioning accuracy of the target of the method of the application is significantly improved as the number of receivers increases.

[0111] In summary, the application provides a mobile target positioning method based on time delay and Doppler under the cooperation of calibration targets, which uses the difference processing of the measured values of the calibration target reflection signal and the mobile target reflection signal to eliminate systematic errors caused by the clock offset of the transmitter-receiver and the different synchronization of the carrier frequency, breaks through the dependence of the prior art on strict time synchronization and direct path, and improves the positioning robustness in complex shielding environments (such as urban building groups, valleys or underground spaces).

[0112] By introducing auxiliary variables to equivalently reconstruct the highly nonlinear differential measurement model, the original complex optimization problem is converted into a pseudo-linear equation, and combined with the semi-definite programming (SDP) solving algorithm, the calculation complexity is reduced while ensuring that the positioning accuracy approaches the Cramer-Rao lower bound (CRLB), and efficient joint estimation of the position and velocity of the mobile target is realized.

[0113] Compatibility with unknown position external radiation sources (such as broadcast towers, communication base stations) as opportunity transmitters not only reduces the system deployment cost, but also expands the application potential in special scenarios such as military passive reconnaissance, disaster rescue and hidden search and rescue.

[0114] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the application are only used to explain the relative position relationship, motion condition, etc. between components in a certain specific posture (as shown in the drawings), and if the specific posture changes, the directional indications will also change accordingly.

[0115] In addition, the descriptions such as "first", "second", "one" and the like in the application are only for the purpose of description, and cannot be understood as indicating or implying the relative importance of the indicated technical features or implicitly indicating the number of the indicated technical features. Therefore, the features limited by "first", "second" can explicitly or implicitly include at least one of the features. In the description of the application, the meaning of "a plurality of" is at least two, such as two, three, etc., unless otherwise specifically limited.

[0116] In the present application, unless otherwise explicitly specified and limited, the terms "connection", "fixation" and the like should be understood in a broad sense, for example, "fixation" can be fixed connection, or detachable connection, or integral; can be mechanical connection, or electrical connection; can be directly connected, or indirectly connected through intermediate medium, can be internal communication of two elements or interaction relationship of two elements, unless otherwise explicitly limited. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0117] In addition, the technical solutions among various embodiments of the present application can be combined with each other, but it must be based on the fact that a person skilled in the art can realize it, when the combination of technical solutions appears contradictory or unachievable, it should be considered that the combination of technical solutions does not exist, nor is it within the protection scope required by the present application.

Claims

1. A method for calibrating target cooperative time delay and Doppler based mobile target localization, characterized in that, The method comprises the steps of: S1: constructing a multistatic positioning system comprising a transmitter with unknown position, a plurality of receivers with known positions, a moving target with unknown position and velocity, and a calibration target with known fixed position; S2: receiving signals reflected by the moving target and the calibration target respectively through each receiver, extracting time delay measurement and Doppler shift measurement of the corresponding target from the signals, and converting the measurements into propagation distance measurement and distance rate measurement respectively; S3: constructing a propagation distance difference model and a distance rate difference model between the targets according to the distance relationship of the propagation nodes in each signal propagation link; S4: approximately converting the propagation distance difference model and the distance rate difference model by introducing auxiliary variables after equivalent rewriting, and stacking pseudo-linear equations based on the two approximate conversion results; S5: constructing a semi-definite programming problem based on the pseudo-linear equations, and solving the semi-definite programming problem by substituting the propagation distance measurement and the distance rate measurement to obtain the position and velocity estimation of the moving target.

2. A time delay and Doppler based mobile target location method in cooperation with a calibration target according to claim 1, characterized in that, In the S2 step, the propagation distance measurement value and the distance rate measurement value are specifically converted by: processing the received signal to extract the time delay measurement value of the corresponding target and the Doppler shift measurement value , according to the signal propagation speed and the carrier frequency , the product of the propagation speed and the time delay measurement value of the corresponding target is the propagation distance measurement value of the target, and the product of the propagation speed and the Doppler shift measurement value of the corresponding target divided by the carrier frequency is the distance rate measurement value, wherein is a calibration target or a moving target .

3. A time delay and Doppler based mobile target location method in cooperation with a calibration target according to claim 2, characterized in that, In the step S3, the propagation distance difference model and the distance rate difference model are constructed by the following method: According to the transmitter position in the current signal propagation link , No. Receiver locations and moving target location The positional relationship between them is used to construct the propagation distance model and distance rate model of the moving target. The formula is expressed as follows: ， Where, The signal is sent from the transmitter to the moving target and then reflected by the The propagation distance measurement value of the signal propagation link received by each receiver, For the transmitter and The true value of the distance offset error caused by clock asynchrony between receivers, The signal is sent from the transmitter to the moving target and then reflected by the The propagation distance measurement noise on the signal propagation link received by each receiver, The signal is sent from the transmitter to the moving target and then reflected by the The distance rate measurement value on the signal propagation link received by each receiver, is the speed of the moving target, For the transmitter and The true value of the range rate offset error caused by the different carrier frequencies between receivers, The signal is sent from the transmitter to the moving target and then reflected by the The distance rate measurement noise on the signal propagation link received by the receiver, T is the matrix transpose, represents the Euclidean norm; According to the position relationship between the transmitter position in the current signal propagation link , the first receiver position , and the calibration target position , a propagation distance model and a distance rate model of the calibration target are constructed, and the formula is expressed as: ， Where, The signal is sent from the transmitter to the calibration target and then reflected by the The propagation distance measurement value of the signal propagation link received by each receiver, The signal is sent from the transmitter to the calibration target and then reflected by the The propagation distance measurement noise on the signal propagation link received by each receiver, The signal is sent from the transmitter to the calibration target and then reflected by the The distance rate measurement value on the signal propagation link received by each receiver, The signal is sent from the transmitter to the calibration target and then reflected by the The range rate measurement noise on the signal propagation link received by each receiver; The propagation distance difference model is constructed based on the difference of the propagation distance model between the moving target and the calibration target, and the distance rate difference model is constructed based on the difference of the distance rate model between the moving target and the calibration target, which is expressed by the following formula: ， wherein is a difference in propagation distance of two signal propagation links of a signal transmitted by a transmitter, reflected by a moving target and a calibration target, and received by a first is a difference in propagation distance of two signal propagation links of a signal transmitted by a transmitter, reflected by a moving target and a calibration target, and received by a first is a measurement noise of the difference in propagation distance, is a difference in propagation distance of two signal propagation links of a signal transmitted by a transmitter, reflected by a moving target and a calibration target, and received by a first is a difference in propagation distance of two signal propagation links of a signal transmitted by a transmitter, reflected by a moving target and a calibration target, and received by a first is a measurement noise of the difference in propagation distance.

4. A time delay and Doppler based mobile target location method in cooperation with a calibration target according to claim 3, characterized in that, In the S4 step, the auxiliary variables are selected with terms containing the unknown position of the transmitter as independent variables to simplify the difference model, specifically including and and .

5. A time delay and Doppler based mobile target location method in cooperation with a calibration target according to claim 4, characterized in that, In the step S4, the pseudo-linear equations are obtained by the following steps: The propagation distance difference model and the distance rate difference model are equivalent rewritten as: ， The Moving to the left of the propagation distance difference model equation, squaring both sides of the equation and ignoring the second order noise term gives the propagation distance difference conversion model: ， The Moving to the distance rate difference model equation left side, and multiplying both sides of the equation by , and rewriting the formula according to the propagation distance difference model equivalence Substitute and ignore the second-order noise term, get the distance rate difference conversion model: ， The two difference conversion models are stacked into a matrix form to obtain the pseudo-linear equations: ， wherein is an unknown vector, is an introduced coefficient matrix, is an introduced coefficient vector, is an introduced noise coefficient matrix, is a measurement noise vector.

6. A time delay and Doppler based mobile target location method in cooperation with a calibration target according to claim 5, characterized in that, In the step S5, the semi-definite programming problem is expressed by the following formula: ， Where, corresponds to the unknown vector The optimization variables, is the auxiliary matrix variable introduced in the semi-positive programming problem, is the weight matrix introduced in the semi-definite programming problem, is the trace of the matrix.

7. A time delay and Doppler based mobile target location method in cooperation with a calibration target according to claim 6, characterized in that, The constraint conditions of the semi-definite programming problem include: ， wherein is the 2L+2th element in the middle row, is the 2L+4th element in the middle row, is the element at position 2L+1 row, 2L+1 column in the middle, is the element at position 2L+1 row, 2L+2 column in the middle, is the matrix of elements in the first to Lth row, first to Lth column in the middle, is the matrix of elements in the first to Lth row, L+1th to 2Lth column in the middle.

8. A time delay and Doppler based mobile target location method in cooperation with a calibration target according to claim 6, characterized in that, The wherein is a covariance matrix of the noise vector is the desired sought symbol.​ 9. The method of claim 1, wherein the method is a time delay and Doppler based mobile target location method with calibration target cooperation, characterized in that, The transmitter with unknown position is an external radiation source.

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