A positioning and velocity measurement method based on two-way iterative shrinkage of measurement-results

Abstract

The present invention discloses a positioning and velocity measurement method based on two-way iterative contraction of measurement results, belonging to the field of passive positioning and velocity measurement. The method represents variables such as the position, velocity, and measurement error of the target radiation source in interval form, and adopts the method of two-way iterative contraction of results, that is, after obtaining the results by using the double iterative algorithm based on interval analysis, substituting them into the TDOA / FDOA measurement equation again to inversely deduce a new joint time-frequency difference measurement interval, and then substituting it back into the algorithm for solution, further shrinking the interval area of positioning and velocity measurement. An interval-form positioning and velocity measurement result that definitely contains the true solution can be obtained. Compared with the single-point numerical form in the prior art, the interval-form positioning and velocity measurement result of the present invention can ensure the positioning and velocity measurement accuracy while making the positioning and velocity measurement result reliable. In addition, it reduces the computational complexity and can be applied to multi-system joint positioning and velocity measurement scenarios such as wireless sensor networks, radar detection, and dead reckoning.

Description

Technical Field

[0001] The present invention relates to a positioning and velocity measurement method based on two-way iterative shrinkage of measurement-results, and belongs to the field of passive positioning and velocity measurement. Background Art

[0002] At present, the widely used global positioning system belongs to cooperative positioning, that is, there is communication between the radiation source and the positioning system. However, in reality, there are also situations where there is no communication between the radiation source and the positioning system, and it is necessary to locate the target.

[0003] Currently, the more common methods of passive positioning and velocity measurement are the time difference of arrival (TDOA) positioning method, the frequency difference of arrival (FDOA) technology, and their combined positioning and velocity measurement TDOA / FDOA technology, etc. Since the position and velocity of the radiation source have a highly non-linear relationship with the time difference of arrival and the frequency difference of arrival of the observed quantities, the Newton-Gauss iterative method is often used in the solution. The Newton-Gauss iterative method is applicable to mixed observed quantities, but it cannot give an analytical solution of the radiation source position, and it needs a reliable iterative value to converge to the global optimum.

[0004] In order to be able to calculate the analytical solution of the fixed target radiation source position, a two-step positioning method based on TDOA measurement is proposed. First, by introducing variables related to the radiation source position, the non-linear equations about the TDOA observed quantities are transformed into linear equations, and then the least squares weighted method is used to solve the position and related variables of the radiation source. Finally, the position of the radiation source can be estimated through the relationship between the auxiliary variables and the position of the radiation source.

[0005] Another existing method to solve the difficulty in solving due to the highly non-linear TDOA and FDOA measurement equations is to use effective double-iteration source positioning and velocity estimation of the time of arrival and the frequency difference of arrival measurements. In this way, not only can the calculation cost be significantly reduced, but also the accuracy of the position and velocity of the radiation source estimated by the double-iteration method is close to the Cramer-Rao lower bound.

[0006] However, the above positioning and velocity measurement technologies are all represented, calculated, and solved for positioning and velocity measurement in the form of single-point numerical values. Although the positioning effect is improved to a certain extent, it is impossible to obtain a deterministic positioning result, that is, it is impossible to obtain accurate position and velocity results. Summary of the Invention

[0007] In order to improve the positioning accuracy of the positioning and velocity measurement technology, the present invention provides a positioning and velocity measurement method based on two-way iterative shrinkage of measurement-results, characterized in that the method includes:

[0008] Step 1: Obtain the initial position interval [u] and the initial velocity interval of the target radiation source according to prior knowledge

[0009] Step 2: Use N observation stations to perform TDOA and FDOA positioning and velocity measurement on the target radiation source in a two-dimensional scenario, and obtain the initial joint time-frequency difference measurement interval [m o ;

[0010] Step 3: Update the position interval, including:

[0011] Assume that the velocity of the target radiation source is known and is the midpoint of the initial velocity interval midpoint Expand the first-order Taylor series of the initial joint time-frequency difference measurement interval at the midpoint of the initial position interval, and perform a contraction estimation on the initial position interval to obtain the updated position interval

[0012] Step 4: Update the velocity interval, including:

[0013] Assume that the position of the target radiation source is known and is the midpoint u of the initial position interval [u m = mid([u]), expand the first-order Taylor series of the initial joint time-frequency difference measurement interval at the midpoint of the initial velocity interval, and perform a contraction estimation on the initial velocity interval to obtain the updated velocity interval

[0014] Step 5: Replace the initial velocity interval with the updated velocity interval obtained in Step 4, substitute it into Steps 3 and 4, and continue to contract the position interval and the velocity interval until convergence, and finally obtain the position estimation interval and the velocity estimation interval

[0015] Step 6: Substitute the obtained position estimation interval and the velocity estimation interval back into the TDOA / FDOA measurement equation to obtain a new joint time-frequency difference measurement interval [m'];

[0016] Step 7: Take the intersection of the new joint time-frequency difference measurement interval and the initial joint time-frequency difference measurement interval, and then replace the initial joint time-frequency difference measurement interval with the intersection and substitute it into Step 3;

[0017] Step 8: Repeat Steps 3 to 7 until the position estimation interval and the velocity estimation interval Converge, end the loop, and obtain the final positioning and velocity measurement results.

[0018] Optionally, it is characterized in that the second step includes:

[0019] According to the 3σ error principle, intervalize the time difference measurement value τ and frequency difference measurement value f obtained by TDOA and FDOA positioning and velocity measurement, that is:

[0020]

[0021]

[0022] The initial joint time-frequency difference measurement interval is: [m o = [[τ o T ,[f o T T ;

[0023] Among them, is the time difference measurement interval, is the frequency difference measurement interval, τ j1 is the arrival time difference between the signal arriving at the j-th observation station and the first observation station, f j1 is the arrival frequency difference between the signal arriving at the j-th observation station and the first observation station, and σ is the standard deviation of the corresponding variable.

[0024] Optionally, the third step includes:

[0025] Assume that the velocity of the radiation source is known and is the midpoint of the initial velocity interval Expand the first-order Taylor series of the joint time-frequency difference true value m o ∈[m o = [[τ o T ,[f o T T near the midpoint of the initial position interval of the radiation source, and obtain:

[0026]

[0027]

[0028] Among them, J1 is the Jacobian interval matrix, m o is the true value of the joint time-frequency difference measurement, τ o is the set of time differences between the signal arriving at each observation station and the first observation station, f o is the set of frequency differences between the signal arriving at each observation station and the first observation station, ​​​​​​The time-frequency difference estimation measurement u obtained by substituting the midpoints of the position interval and the speed interval into the TDOA / FDOA equation o is the true value of the target position, and

[0029] is the true value of the target speed; 1,m Substitute the midpoints of the interval variables in the Jacobian interval matrix J1 to form J

[0030] to replace J1;

[0031]

[0032] where, is the updated position interval.

[0033] Optionally, the step four includes:

[0034] Assume that the position of the radiation source is known and is the midpoint u m = mid([u]) of the initial position interval. Expand the first-order Taylor series of the true value m o of the joint time-frequency difference measurement around the midpoint of the speed interval of the radiation source to obtain:

[0035]

[0036]

[0037] where J2 is the Jacobian matrix;

[0038] Use the midpoints J 2,m of the interval variables in the Jacobian interval matrix J2 to form to replace J2,

[0039]

[0040] where, is the updated speed interval.

[0041] Optionally, the step six includes:

[0042] Take the upper limit u sup and the lower limit u inf of the position estimation interval and substitute them back into the TDOA equation to obtain the maximum value τ sup and the minimum value τ inf of the time difference of arrival of a signal from each observation station to the first observation station, forming a new time difference interval, i.e., [τ'] = [τinf , τ sup , the TDOA equation is as follows:

[0043]

[0044] where c is the signal propagation speed, is the time difference between the signal arriving at the j-th observation station and the first observation station, is the position of the j-th observation station, u o is the estimated position of the target;

[0045] Take the upper limit and the lower limit of the velocity estimation interval and substitute them back into the FDOA equation to obtain f sup , f inf , that is, [f'] = [f inf , f sup , the FDOA equation is as follows:

[0046]

[0047] where c is the signal propagation speed and f0 is the signal carrier center frequency, is the unit vector from o to u is the estimated velocity of the target, is the velocity of the j-th observation station;

[0048] Jointly constitute the lower limit m' inf = [τ inf , f inf and the upper limit m' sup = [τ sup , f sup of the time-frequency difference interval, and use them as the new joint time-frequency difference interval [m'] = [[τ'] T , [f'] T T , where [τ'] = [τ inf , τ sup , [f'] = [f inf , f sup .

[0049] Optionally, the prior knowledge includes: the base station coverage area.

[0050] Optionally, the convergence condition is: both the interval midpoint and the interval width are constant.

[0051] Optionally, the number of base stations N = 4.

[0052] ​The second object of the present invention is to provide a positioning and velocity measurement system, including:

[0053] A radiation source information acquisition module, configured to acquire data information of a target radiation source;

[0054] A data processing module, which processes the data information of the target radiation source by using the above-mentioned positioning and velocity measurement method to obtain the final positioning and velocity measurement results;

[0055] An output display module, configured to output and display the positioning and velocity measurement results.

[0056] Optionally, the output display module includes: a display screen.

[0057] The beneficial effects of the present invention are as follows:

[0058] (1) In the present invention, variables such as the position data, velocity data, and TDOA / FDOA measurement errors of the target radiation source are expressed in the form of intervals, and a positioning and velocity measurement result in the form of an interval that surely contains the true solution can be obtained. Compared with the single-point numerical form in the prior art, the intervalized positioning and velocity measurement result of the present invention can ensure the positioning and velocity measurement accuracy while also making the positioning and velocity measurement results reliable.

[0059] (2) The present invention adopts a two-way iterative contraction method for alternately solving the position interval and the velocity interval, which not only effectively avoids the problem of difficult solution caused by the highly nonlinear TDOA and FDOA measurement equations, but also reduces the computational complexity.

[0060] (3) After obtaining the result by using the double iterative algorithm based on interval analysis in the present invention, the result is substituted into the TDOA / FDOA measurement equation again to inversely deduce a new joint time-frequency difference measurement interval, and then substituted back into the algorithm for solution, further shrinking the interval area of the positioning and velocity measurement, so that the interval result has higher certainty and effectively improves the positioning and velocity measurement accuracy.

[0061] (4) The present invention is applicable to multi-system joint positioning and velocity measurement. Since its output result is an interval result, it can perform multi-system collaborative work through the intersection of interval results, and can be applied to multiple scenarios such as wireless sensor networks, radar detection, and dead reckoning, and has low requirements and complexity for equipment. Description of the Drawings

[0062] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0063] Figure 1 It is a comparison diagram of the RMSE of the radiation source position before and after the measurement-result two-way iterative shrinkage in the second embodiment of the present invention;

[0064] Figure 2 It is a comparison diagram of the estimated area of the radiation source position before and after the measurement-result two-way iterative shrinkage in the second embodiment of the present invention;

[0065] Figure 3 It is a comparison diagram of the deviation of the radiation source position before and after the measurement-result two-way iterative shrinkage in the second embodiment of the present invention;

[0066] Figure 4 It is a containment diagram of the position estimation results under different true values before the measurement-result two-way iterative shrinkage in the second embodiment of the present invention;

[0067] Figure 5 It is a containment diagram of the position estimation results under different true values after the measurement-result two-way iterative shrinkage in the second embodiment of the present invention;

[0068] Figure 6 It is a comparison diagram of the RMSE of the radiation source velocity estimation before and after the measurement-result two-way iterative shrinkage in the second embodiment of the present invention;

[0069] Figure 7 It is a comparison diagram of the estimated area of the radiation source velocity before and after the measurement-result two-way iterative shrinkage in the second embodiment of the present invention;

[0070] Figure 8 It is a deviation diagram of the radiation source velocity before and after the measurement-result two-way iterative shrinkage in the second embodiment of the present invention;

[0071] Figure 9 It is a containment diagram of the velocity estimation results under different true values before the measurement-result two-way iterative shrinkage in the second embodiment of the present invention;

[0072] Figure 10 It is a containment diagram of the velocity estimation results under different true values after the measurement-result two-way iterative shrinkage in the second embodiment of the present invention. Detailed implementation manners

[0073] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be further described in detail below in conjunction with the accompanying drawings.

[0074] Embodiment 1:

[0075] This embodiment provides a positioning and velocity measurement method based on measurement-result two-way iterative shrinkage, including:

[0076] Step 1: Obtain the initial position interval [u] and the initial velocity interval of the target radiation source according to prior knowledge

[0077] Step 2: Use N observation stations to perform TDOA and FDOA positioning and velocity measurement on the target radiation source in the two-dimensional scenario to obtain the initial joint time-frequency difference measurement interval [m o ;

[0078] Step 3: Update the position interval, including:

[0079] Assume that the velocity of the target radiation source is known and is the midpoint of the initial velocity interval ; Expand the first-order Taylor series of the initial joint time-frequency difference measurement interval at the midpoint of the initial position interval, and perform a contraction estimation on the initial position interval to obtain the updated position interval

[0080] Step 4: Update the velocity interval, including:

[0081] Assume that the position of the target radiation source is known and is the midpoint u of the initial position interval [u m = mid([u]), expand the first-order Taylor series of the initial joint time-frequency difference measurement interval at the midpoint of the initial velocity interval, and perform a contraction estimation on the initial velocity interval to obtain the updated velocity interval

[0082] Step 5: Replace the initial velocity interval with the updated velocity interval obtained in Step 4, substitute it into Steps 3 and 4, and continue to contract the position interval and the velocity interval until convergence, and finally obtain the position estimation interval and the velocity estimation interval

[0083] Step 6: Substitute the obtained position estimation interval and the velocity estimation interval back into the TDOA / FDOA measurement equation to obtain a new joint time-frequency difference measurement interval [m'];

[0084] Step 7: Take the intersection of the new joint time-frequency difference measurement interval and the initial joint time-frequency difference measurement interval, and then substitute the intersection instead of the initial joint time-frequency difference measurement interval into Step 3;

[0085] Step 8: Repeat Steps 3 to 7 until the position estimation interval and the velocity estimation interval converge, end the loop, and obtain the final positioning and velocity measurement results.

[0086] Embodiment 2:

[0087] This embodiment provides a positioning and velocity measurement method based on two-way iterative contraction of measurement-results, including:

[0088] Step 1: Obtain the initial position interval [u] and the initial velocity interval of the target radiation source according to prior knowledge

[0089] Step 2: Use N observation stations to perform TDOA and FDOA positioning and velocity measurement on the target radiation source in a two-dimensional scenario, and obtain the initial joint time-frequency difference measurement interval [m o ;

[0090] According to the 3σ error principle, intervalize the time difference measurement value τ and the frequency difference measurement value f obtained by TDOA and FDOA positioning and velocity measurement, that is:

[0091]

[0092]

[0093] Among them, is the time difference measurement interval, is the frequency difference measurement interval, τ j1 is the arrival time difference between the signal arriving at the j-th observation station and the 1st observation station, f j1 is the arrival frequency difference between the signal arriving at the j-th observation station and the 1st observation station, and σ is the standard deviation of the corresponding variable.

[0094] Step 3: Update the position interval, including:

[0095] Assume that the velocity of the target radiation source is known and is the midpoint of the initial velocity interval Shrink and estimate the initial position interval by expanding a section of the Taylor series of the initial joint time-frequency difference measurement interval at the midpoint of the initial position interval to obtain the updated position interval Expand the first-order Taylor series of the joint time-frequency difference true value m

[0096] ∈[m0 o =[[τ o o T ,[f o T T near the midpoint of the initial position interval of the radiation source to obtain:

[0097]

[0098]

[0099] Among them, J1 is the Jacobian interval matrix, m o is the true value of the joint time-frequency difference measurement, τ​​​​o is the set of time differences between the arrival of the signal at each observation station and at the first observation station, f o is the set of frequency differences between the arrival of the signal at each observation station and at the first observation station, is the time-frequency difference estimation measurement obtained by substituting the midpoints of the position interval and the velocity interval into the TDOA / FDOA equation, u o is the true value of the target position, is the true value of the target velocity;

[0100] Form J by using the midpoints of the interval variables in the Jacobian interval matrix J1 1,m to replace J1;

[0101] Obtain the least squares solution for the radiation source position estimation through formula transformation:

[0102]

[0103] where, is the updated position interval.

[0104] Step Four: Update the velocity interval, including:

[0105] Assume that the position of the target radiation source is known and is the midpoint u of the initial position interval [u] m = mid([u]), expand a section of the Taylor series of the initial joint time-frequency difference measurement interval at the midpoint of the initial velocity interval to perform a contraction estimation on the initial velocity interval, and obtain the updated velocity interval

[0106] Expand the first-order Taylor series of the joint time-frequency difference m o near the midpoint of the velocity interval of the radiation source to obtain:

[0107]

[0108]

[0109] where J2 is the Jacobian matrix,

[0110] Form J by using the midpoints of the interval variables in the Jacobian interval matrix J2 2,m to replace J2, is the time-frequency difference estimation measurement obtained by substituting the midpoints of the position interval and the velocity interval into the TDOA / FDOA equation, and obtain the least squares solution for the radiation source velocity estimation:

[0111]

[0112] where, is the updated velocity interval.

[0113] Step Five: Replace the initial speed range with the updated speed range obtained in Step Four, substitute it into Steps Three and Four, and continue to shrink the position range and speed range until convergence, finally obtaining the position estimation range and the speed estimation range

[0114] Step Six: Substitute the obtained position estimation range and the speed estimation range back into the TDOA / FDOA measurement equation to obtain a new joint time-frequency difference measurement range [m'];

[0115] Take the upper limit u sup and the lower limit u inf of the position estimation range and substitute them back into the TDOA equation to obtain τ sup , τ inf , that is, [τ'] = [τ inf , τ sup , and the TDOA equation is:

[0116]

[0117] Take the upper limit and the lower limit of the speed estimation range and substitute them back into the FDOA equation to obtain f sup , f inf , that is, [f'] = [f inf , f sup , and the FDOA equation is:

[0118]

[0119] Jointly constitute the lower limit m' inf = [τ inf , f inf and the upper limit m' sup = [τ sup , f sup of the time-frequency difference range, and use it as the new joint time-frequency difference range [m'] = [[τ'] T , [f'] T T , where [τ'] = [τ inf , τ sup , [f'] = [f inf , f sup .

[0120] ​Step 7: Take the intersection of the new joint time-frequency difference measurement interval and the initial joint time-frequency difference measurement interval, and then substitute the intersection for the initial joint time-frequency difference measurement interval into Step 3;

[0121] Step 8: Repeat Steps 3 to 7 until the position estimation interval and the velocity estimation interval converge, end the loop, and obtain the final positioning and velocity measurement results.

[0122] To further illustrate the beneficial effects that the present invention can bring, the following simulation experiments were carried out:

[0123] (1) Experimental environment setup: In this simulation experiment, it is set that the position coordinates of the radiation source moving in the two-dimensional plane are (5000, 8000) m, the velocity is (50, 80) m / s, the signal propagation speed c = 299792458 m / s, and the center frequency of the carrier f = 2 GHz.

[0124] Based on prior information such as the base station coverage area, the present invention initially estimates the initial position interval of the target as {[0, 10 4 , [0, 10 4} m, and the initial interval of the velocity as {[0, 100], [0, 100]} m / s. In this simulation, the base stations will be used to locate the moving radiation source. The number of base stations N = 4, and their position information is s1(20000, 20000) m, s2(0, 20000) m, s3(20000, 0) m, and s4(0, 0) m respectively. In the simulation, it is assumed that both the TDOA error and the FDOA error satisfy the 3σ error principle, and the number of Monte Carlo simulations is 10 3 , and thus, the simulation parameters are set.

[0125] (2) Selection of performance evaluation indicators: Four evaluation indicators are mainly selected.

[0126] The first is the area of the estimation interval of the position and velocity of the target radiation source, which can be defined as the product of subtracting the lower limits from the upper limits of the estimation results in each dimension. The unit of the position estimation interval is m 2 , the unit of the velocity estimation interval is m 2 / s 2 , and the smaller the interval width, the smaller the possible area where the target is located, and the better its performance is determined to be.

[0127] The second evaluation metric is the root mean squared error (RMSE) of the target radiation source's position and velocity. It is defined as the RMSE calculated by comparing the midpoints of the estimated intervals of the target's position and velocity obtained by the algorithm with the actual values of the target. Here, the unit of the position estimation error is m, and the unit of the velocity estimation error is m / s. Moreover, the smaller the RMSE, the better the performance.

[0128] The third evaluation metric is the bias, which refers to the difference between the true value and the output value of the target. The smaller the bias, the better the simulation performance.

[0129] The fourth evaluation metric is the inclusion rate, which refers to the probability that the true value of the target is included in the final estimated interval. The larger the inclusion rate, the better the simulation performance.

[0130] (3) First, study the performance of the position estimation results before and after the measurement-result two-way iterative shrinkage through the time difference measurement error. According to the 3σ error principle, intervalize the frequency difference measurement value f to obtain Perform performance analysis by taking different values of σ for the time difference measurement value τ, that is σ = 10 0.4(i-1) , i = 1, 2,..., 6, and performance comparison can be obtained, see Figures 1-3 ;

[0131] From Figure 1 and Figure 3 it can be seen that as the time difference measurement error increases, both the RMSE and the bias of the estimated position results increase, and before and after the measurement-result two-way iterative shrinkage, the changes in the RMSE and the bias are not significant. And from Figure 2 it can be seen that as the time difference measurement error increases, the area of the estimated position results also increases, but through the measurement-result two-way iterative shrinkage method, the area of the position estimation results decreases significantly. Therefore, the method of the present invention can improve the accuracy of positioning and speed measurement.

[0132] Next, study the inclusion rate of the method of the present invention from two aspects. First, as can be seen from Table 1, as the TDOA measurement error increases, the inclusion rate decreases, but in the case of a large error, a relatively good inclusion rate can still be maintained.

[0133] Table 1 Inclusion rates under different TDOA measurement errors

[0134]

[0135] On the other hand, set σ of the time difference measurement value to 30 m and σ of the frequency difference measurement value to 0.3 Hz. Randomly generate 300 coordinate points within the range of {[0, 10000], [0, 10000]} m as the true values of position estimation, substitute them into the algorithm for positioning, and count the positioning results before the two-way iterative contraction of the measurement-result as shown in Figure 4 shown, and the results after contraction are as shown in Figure 5 shown. It can be seen from the comparison of the two figures that after the two-way iterative contraction of the measurement-result, the area of the position estimation interval is significantly reduced, indicating that the positioning accuracy is effectively improved. After statistics, the inclusion rate before and after contraction is 0.99.

[0136] (4) Study the performance of the speed estimation results before and after the two-way iterative contraction of the measurement-result through the frequency difference measurement error. According to the 3σ error principle, intervalize the time difference measurement value τ to obtain Take different values of σ of the frequency difference measurement value f for performance analysis, that is σ = 0.5 * i, i = 1, 2,..., 6, and the performance comparison can be obtained. See Figures 6-8 :

[0137] From Figure 6 and Figure 8 it can be seen that as the frequency difference measurement error increases, both the RMSE and the bias of the estimated speed results increase, and before and after the two-way iterative contraction of the measurement-result, the changes in RMSE and bias are not significant. However, from Figure 7 it can be seen that as the frequency difference measurement error increases, the area of the estimated speed results also increases. It can be seen from the method of solving through the two-way iterative contraction of the measurement-result that the area of the speed estimation results after contraction is significantly lower than that before contraction, which also proves from the speed aspect that the method of solving through the two-way iterative contraction of the measurement-result can further improve the accuracy of the algorithm.

[0138] Similarly, the inclusion rate of the algorithm can be studied from two aspects.

[0139] First, it can be seen from Table 2 that as the FDOA measurement error increases, the inclusion rate decreases slightly, but still maintains a relatively good inclusion rate.

[0140] Table 2 Inclusion rate under different FDOA measurement errors

[0141]

[0142] On the other hand, set σ of the time difference measurement value to 30 m and σ of the frequency difference measurement value to 0.3 Hz. Randomly generate 300 coordinate points within the velocity range of {[0, 100], [0, 100]} m / s as the true values of velocity estimation, substitute them into the algorithm for velocity measurement, and count the velocity measurement results before the two-way iterative shrinkage of the measurement results of these 300 coordinate points as Figure 9 shown. The velocity measurement results after shrinkage are as Figure 10 shown. It can be seen from the comparison of the two figures that after shrinkage, the area of the velocity estimation interval is significantly reduced. Therefore, the accuracy of velocity estimation can be improved, and the inclusion rate before and after shrinkage is both 0.99.

[0143] Some steps in the embodiments of the present invention can be implemented by software, and the corresponding software program can be stored in a readable storage medium, such as an optical disc or a hard disk, etc.

[0144] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A positioning and velocity measurement method based on two-way iterative shrinkage of measurement-results, characterized in that, The method includes: Step 1: Obtain the initial position interval [u] and the initial velocity interval of the target radiation source according to prior knowledge Step 2: Use N observation stations to perform TDOA and FDOA positioning and velocity measurement on the target radiation source in a two-dimensional scenario to obtain the initial joint time-frequency difference measurement interval [m o ; Step 3: Update the position interval, including: Assume that the velocity of the target radiation source is known and is the midpoint of the initial velocity interval midpoint Expand the first-order Taylor series of the initial joint time-frequency difference measurement interval at the midpoint of the initial position interval, perform a contraction estimation on the initial position interval, and obtain an updated position interval Step 4: Update the velocity interval, including: Assume that the position of the target radiation source is known and is the midpoint \(u\) of the initial position interval \([u]\), i.e., \(u=\text{mid}([u])\). Expand the first-order Taylor series of the initial joint time-frequency difference measurement interval at the midpoint of the initial velocity interval to perform a contraction estimation on the initial velocity interval, and obtain an updated velocity interval. m ​ Step Five: Replace the initial speed interval with the updated speed interval obtained in Step Four, substitute it into Step Three and Step Four, and continue to shrink the position interval and the speed interval until convergence, and finally obtain the position estimation interval and the speed estimation interval Step 6: Substitute the obtained position estimation interval and the speed estimation interval back into the TDOA / FDOA measurement equation, and a new joint time-frequency difference measurement interval [m'] can be obtained; Step 7: Take the intersection of the new joint time-frequency difference measurement interval and the initial joint time-frequency difference measurement interval, and then substitute the intersection instead of the initial joint time-frequency difference measurement interval into Step 3; Step 8: Repeat Steps 3 to 7 until the position estimation interval and the speed estimation interval converge, end the loop, and obtain the final positioning and speed measurement results.

2. The positioning and speed measurement method according to claim 1, wherein Step 2 includes: According to the 3σ error principle, intervalize the time difference measurement value τ and the frequency difference measurement value f obtained by TDOA and FDOA positioning and velocity measurement, that is: The initial combined time-frequency difference measurement interval is: [m o = [[τ o T , [f o T T ;​​​ Among them, is the time difference measurement interval, is the frequency difference measurement interval, τ j1 is the time difference of arrival of the signal at the j-th observation station and the 1st observation station, f j1 is the frequency difference of arrival of the signal at the j-th observation station and the 1st observation station, and σ is the standard deviation of the corresponding variable.

3. The positioning and speed measurement method according to claim 2, wherein Step 3 includes: Assume that the velocity of the radiation source is known and is the midpoint of the initial velocity interval The true value m of the joint time-frequency difference o ∈[m o = [[τ o T ,[f o T T is expanded around the midpoint of the initial position interval of the radiation source by the first-order Taylor series to obtain:​​​ Among them, J1 is the Jacobi interval matrix, and m o is the true value of the joint time-frequency difference measurement, τ o is the set of time differences between the signal arriving at each observation station and the first observation station, f o is the set of frequency differences between the signal arriving at each observation station and the first observation station, is the time-frequency difference estimation measurement obtained by substituting the midpoints of the position interval and the velocity interval into the TDOA / FDOA equation, u o is the true value of the target position, is the true value of the target velocity; Form J by using the midpoints of the interval variables in the Jacobian interval matrix J1 1,m to replace J1; Obtain the least squares solution of the radiation source position estimation through formula transformation: Among them, is the updated position interval.

4. The positioning and speed measurement method according to claim 3, characterized in that, Step 4 includes: Assume that the position of the radiation source is known and is the midpoint u of the initial position interval m = mid([u]), and the first-order Taylor series expansion of the true value m o of the joint time-frequency difference measurement is obtained by expanding around the midpoint of the velocity interval of the radiation source as follows: where J2 is the Jacobian interval matrix; Use the midpoint J of each interval variable in the Jacobi interval matrix J2 2,m to replace J2 The time-frequency difference estimation measurement obtained by substituting the midpoints of the position interval and the velocity interval into the TDOA / FDOA equation, and the least-squares solution for the radiation source velocity estimation is obtained: Among them, is the updated speed range.

5. The positioning and speed measurement method according to claim 4, wherein Step 6 includes: Take the upper limit u of the position estimation interval sup and the lower limit u inf and substitute them back into the TDOA equation to obtain the maximum value τ of the time difference of arrival of a signal from each observation station to the first observation station sup and the minimum value τ inf to form a new time difference interval, that is, [τ'] = [τ inf , τ sup , and the TDOA equation is as follows: where c is the signal propagation speed, is the time difference between the signal arriving at the j-th observation station and the first observation station, is the position of the j-th observation station, and u o is the estimated position of the target; Take the upper limit of the speed estimation interval and the lower limit and substitute them back into the FDOA equation to obtain f sup and f inf , that is, [f'] = [f inf , f sup , and the FDOA equation is: where c is the signal propagation speed and f0 is the signal carrier center frequency, is the unit vector from o to u, is the estimated velocity of the target, and is the velocity of the j-th observation station; Jointly constitute the lower limit m' of the time-frequency difference interval inf = [τ inf , f inf and the upper limit m' sup = [τ sup , f sup , and use it as the new joint time-frequency difference interval [m'] = [[τ'] T , [f'] T T , where, [τ'] = [τ inf , τ sup , [f'] = [f inf , f sup .​ 6. The positioning and speed measurement method according to claim 1, characterized in that, The prior knowledge includes: the coverage area of the base station.

7. The positioning and speed measurement method according to claim 1, characterized in that The convergence condition is that both the interval midpoint and the interval width are constant.

8. The positioning and speed measurement method according to claim 1, wherein The number of base stations N = 4.

9. A positioning and speed measurement system, characterized in that, Includes: A radiation source information acquisition module for acquiring data information of a target radiation source; A data processing module that uses the positioning and velocity measurement method according to any one of claims 1-8 to process the data information of the target radiation source to obtain final positioning and velocity measurement results; An output display module for outputting and displaying the positioning and velocity measurement results.

10. The positioning and speed measurement system according to claim 9, wherein The output display module includes: a display screen.

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