A method for obtaining terminal ballistic parameters combining ballistic shock wave and explosion wave

Abstract

This invention provides a method for obtaining terminal ballistic parameters by combining ballistic shock wave and explosion wave data. This method solves the technical problem that existing acoustic measurement methods can only obtain the location and time of the explosion, but not the projectile velocity and trajectory direction, thus hindering accurate assessment of projectile performance. The method comprises the following steps: N acoustic measurement points (N≥2) are set up around a predetermined explosion point; the acoustic measurement points sequentially acquire the arrival direction and time of the ballistic shock wave, and the arrival direction and time of the explosion wave; the explosion point location and explosion time are obtained from the acquired explosion wave arrival direction and time; and the trajectory direction and projectile velocity are calculated from the acquired ballistic shock wave arrival direction, time, and explosion point location. This invention enables the acquisition of terminal ballistic parameters such as explosion point location, explosion time, projectile velocity, and trajectory direction, providing crucial data support for accurate projectile performance assessment.

Description

Technical Field

[0001] This invention relates to a method for obtaining terminal ballistic parameters of a supersonic projectile, specifically a method for obtaining terminal ballistic parameters by combining ballistic shock waves and explosion waves. Background Technology

[0002] As a supersonic missile approaches the ground, its low altitude and complex terrain such as mountains and hills obstruct its view, resulting in a small radar cross-section and significant ground clutter interference. Therefore, radar struggles to acquire the missile's terminal trajectory parameters. Optical measurement methods are susceptible to interference from smoke and fog, making it difficult to obtain clear images under continuous attack, leading to measurement failure. Furthermore, the small field of view of optical measurements means that significant deviations beyond the field of view can also cause measurement failure, making it impossible to acquire the missile's terminal trajectory parameters.

[0003] Distributed acoustic measurement methods are commonly used for measuring the location of targets over large areas due to their all-weather operation, immunity to smoke and fog, and wide measurement range. Current acoustic measurement methods involve using multiple microphones to receive the acoustic signals generated by a target explosion or high-speed impact with the ground, utilizing the time difference between the microphones to locate the target. However, this method can only obtain the location and time of the explosion, but not the projectile's velocity and trajectory, thus making it impossible to accurately assess the projectile's performance. Summary of the Invention

[0004] The purpose of this invention is to solve the technical problem that existing acoustic measurement methods can only obtain the location of the explosion point and the time of explosion, but cannot obtain the velocity and trajectory of the projectile, thus making it impossible to accurately evaluate the performance of the projectile. The invention provides a method for obtaining terminal trajectory parameters by combining the ballistic shock wave and the explosion wave.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for obtaining terminal ballistic parameters combining ballistic shock wave and explosion wave, characterized by the following steps:

[0007] Step 1: Set up N acoustic measurement points around the predetermined blast point, where N≥2; the acoustic measurement points sequentially acquire the direction of arrival of the ballistic shock wave and the arrival time of the ballistic shock wave, as well as the direction of arrival of the explosion wave and the arrival time of the explosion wave.

[0008] Step 2: Obtain the location of the explosion point and the time of explosion by acquiring the direction of arrival and arrival time of the explosion wave;

[0009] Step 3: Calculate the trajectory direction and projectile velocity using the obtained trajectory shock wave arrival direction, trajectory shock wave arrival time, and detonation point location.

[0010] Furthermore, step 1 specifically includes:

[0011] N acoustic measurement points are set up around the predetermined blast point, where N≥2; the acoustic measurement points are located at known positions s. i =[x i ,y i ,z i ] T , i∈{1,2,…,N},[·] T This represents the transpose operation, with the explosion point position set as s, and the distance from explosion point s to the acoustic measurement point s. i The distance is d i Acoustic measurement point s i The corresponding shock wave separation point is p i Shock wave separation point p i To acoustic measurement point s i The distance is r i Shock wave separation point p i The distance to the explosion point s is l i The acoustic measurement points sequentially receive shock wave separation points p on the trajectory of the supersonic projectile. i The ballistic shock wave and the explosion wave generated by the explosion are obtained sequentially, including the direction of arrival of the ballistic shock wave and the arrival time of the ballistic shock wave, as well as the direction of arrival of the explosion wave and the arrival time of the explosion wave.

[0012] Furthermore, step 2 specifically includes the following sub-steps:

[0013] Step 2.1: Based on the direction of arrival of the explosion wave obtained in Step 1, obtain the explosion point s relative to the acoustic measuring point s. i unit vector k i :

[0014]

[0015] in: The pitch angle of the explosion point measured at the i-th acoustic measurement point;

[0016] The azimuth angle of the explosion point measured at the i-th acoustic measurement point;

[0017] Step 2.2: Calculate the estimated location s of the explosion point using the weighted least squares method according to the following formula.

[0018]

[0019] in:

[0020] G is a matrix that integrates the direction of arrival information of the explosion wave.

[0021] G = [2(k2-k1),…,2(k N -k1),U1,…,U N];

[0022] U i The matrix constructed by the direction of the explosion wave:

[0023]

[0024] W is a weight matrix that integrates information on the direction of arrival of the explosion wave and the distance from the explosion point to the measuring point.

[0025] W = TQT T ;

[0026]

[0027] 0 1×2 A row vector with two elements equal to 0. 2×2 It is a 2x2 matrix with all elements equal to 0, and 02 is the zero vector;

[0028] Q is the measurement error vector. The covariance matrix, d n1 =c(t) b,n -t b,1 ), n∈{2,…,N}, d n1 For the nth acoustic measurement point s n The distance to the explosion point s is the difference between the distance from the first acoustic measurement point s1 to the explosion point s, where c is the speed of sound propagation, and t is the velocity of sound. b,n and t b,1 These are the nth acoustic measurement points s n When the explosion wave obtained from the first acoustic measurement point s1 arrives, Δ(·) represents the error of the corresponding measurement value;

[0029] h is a vector that combines the direction of arrival of the blast wave, the location of the acoustic measurement point, and the distance difference between the acoustic measurement point and the blast point.

[0030] Step 2.3: Based on the acoustic measurement point s in Step 1 i When the explosion wave arrives, the unit vector k obtained in step 2.1 is also present. i And the estimation of the explosion point location s obtained in step 2.2 The estimated time of the explosion was calculated. And on Calculate the average value to obtain an estimate of the explosion time t.

[0031]

[0032] in: For d i The estimate, tb,i For the i-th acoustic measurement point s i When the explosion wave was obtained.

[0033] Furthermore, step 3 specifically includes the following sub-steps:

[0034] Step 3.1: Based on the direction of arrival of the ballistic shock wave obtained in Step 1, obtain the shock wave separation point p. i Relative to acoustic measurement point s i unit vector b i :

[0035] b i =[cosφ i cosθ i ,cosφ i sinθ i ,sinφ i ] T

[0036] Where: φ i The elevation angle of the ballistic shock wave measured at the i-th acoustic measurement point;

[0037] θ i The azimuth angle of the ballistic shock wave measured at the i-th acoustic measurement point;

[0038] Step 3.2: Calculate the estimated shock wave separation point location p1 using the weighted least squares method according to the following formula.

[0039]

[0040] in:

[0041] A is a matrix that integrates the direction of arrival information of the ballistic shock wave, A = [(b2-b1), ..., (b N -b1),2(b2-b1),…,2(b N -b1),V1];

[0042] V i The matrix constructed for the direction of arrival of the ballistic shock wave:

[0043]

[0044] W1 is a weight matrix that integrates information on the direction of arrival of the ballistic shock wave, the distance from the shock wave separation point to the detonation point, the distance from the shock wave separation point to the acoustic measurement point, the positions of the shock wave separation point and the acoustic measurement point, and the ballistic direction. W1 = Q1.

[0045] Q1 is the measurement error vector ε=[Δs T ,Δτ 21 ,…,Δτ N1,ε1,...,ε N ] T The covariance matrix, ε i =[Δθ i ,Δφ i ] T , τ j1 =c(t) s,j -t s,1 ), j∈{2,…,N}, t s,j and t s,1 The j-th acoustic measurement point s j When the ballistic shock wave obtained from the first acoustic measurement point s1 arrives;

[0046] z represents the fusion of the trajectory shock wave arrival direction, impact point, and acoustic measurement point location, as well as the acoustic measurement point s. j The vector of distance difference between s1 and their respective shock wave separation points.

[0047]

[0048] r 21 Let r be the difference between the distance from the second acoustic measurement point s2 to the corresponding shock wave separation point p2 and the distance from the first acoustic measurement point s1 to the corresponding shock wave separation point p1. N1 For the Nth acoustic measurement point s N to the corresponding shock wave separation point p N The difference between the distance from the first acoustic measurement point s1 and the distance from the corresponding shock wave separation point p1;

[0049] Based on the estimation of the shock wave separation point position p1 The calculation process involves sequentially calculating the estimated positions of the remaining shock wave separation points to obtain the position p of each shock wave separation point. i Estimate

[0050] Step 3.3: Based on the estimated location s of the explosion point obtained in Step 2.2 The position p of each shock wave separation point obtained in step 3.2 i Estimate The estimated corresponding ballistic direction is calculated. And for all Calculate the average value to obtain an estimate of the ballistic direction u.

[0051]

[0052] in: The symbol ||·|| denotes the 2-norm of a vector;

[0053] Step 3.4: Let the weight matrix W1 = BQ1BT Repeat steps 3.2-3.3 to obtain the updated estimate of the ballistic direction u.

[0054] in,

[0055]

[0056] 0 1×3 A row vector with 3 elements equal to 0. 1×(N-1) A row vector with N-1 elements all equal to 0. 2×3 A matrix with 2 rows and 3 columns, all elements being 0. 2×(N-1) For a matrix consisting of 2 rows and N-1 columns, all elements are 0, I (N-1)×(N-1) It is an N-1 dimensional identity matrix. The estimated trajectory direction u obtained in step 3.3

[0057] Step 3.5: Based on the updated ballistic direction u estimated in Step 3.4 and the unit vector b obtained in step 3.1 i The corresponding shock wave separation point position p is calculated. i Estimation of projectile velocity And for all Calculate the average value to obtain an estimate of the projectile's velocity v.

[0058]

[0059] in:

[0060] Further, in step 1, N = 2; the acoustic measuring points use microphone array signals to sequentially acquire the direction of arrival of the ballistic shock wave and the arrival time of the ballistic shock wave, as well as the direction of arrival of the explosion wave and the arrival time of the explosion wave.

[0061] The beneficial effects of this invention are:

[0062] 1. This invention provides a method for obtaining terminal ballistic parameters by combining ballistic shock wave and explosion wave. It integrates the arrival direction and time of ballistic shock wave and the arrival direction and time of explosion wave, and realizes the acquisition of the detonation point position, explosion time, projectile velocity and ballistic direction. The acquired terminal ballistic parameters are diverse, providing technical support for evaluating projectile performance and debris search under large deviation conditions.

[0063] 2. This invention uses the weighted least squares method to directly calculate the location of the explosion point and the shock wave separation point. It has a closed-form solution, and the calculation method is fast and efficient. It can be processed online in real time and is easy to apply and promote.

[0064] 3. This invention not only utilizes the ballistic shock wave direction obtained from acoustic measurement points, but also integrates the obtained ballistic shock wave arrival time to locate the shock wave separation point, thus realizing the acquisition of the ballistic direction of the supersonic projectile using acoustic means.

[0065] 4. In this invention, terminal ballistic parameters can be obtained by selecting two acoustic measurement points, which reduces the difficulty of deployment and implementation in the field, improves the ease of use of the measurement system, facilitates large-scale testing, and is suitable for rapid deployment and mobile measurement in large areas of the field. Attached Figure Description

[0066] Figure 1 This is a schematic diagram of the terminal ballistic parameter acquisition model according to an embodiment of the method for acquiring terminal ballistic parameters by combining ballistic shock wave and explosion wave of the present invention;

[0067] Figure 2 This is a schematic diagram of the elevation and azimuth angles of the explosion point and the elevation and azimuth angles of the ballistic shock wave, measured using acoustic measuring point s1 as an example in this embodiment of the invention. Detailed Implementation

[0068] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0069] A method for obtaining terminal ballistic parameters combining ballistic shock wave and explosion wave, specifically including the following steps:

[0070] Step 1, as follows Figures 1-2 As shown, two acoustic measurement points are set up around the predetermined blast point; a ground coordinate system is established with s1 as the origin, and the two acoustic measurement points are located at the known position s. i =[x i ,y i ,z i ] T , i∈{1,2},[·] T This represents the transpose operation, with the explosion point position set as s, and the distance from explosion point s to the acoustic measurement point s. i The distance is d i Acoustic measurement point s i The corresponding shock wave separation point is p i Shock wave separation point p i To acoustic measurement point s i The distance is r i Shock wave separation point p i The distance to the explosion point s is l iThe shock cone angle is α, and its relationship with the projectile velocity v and the sound wave propagation speed c is sinα = c / v; two acoustic measuring points first receive the shock wave separation point p on the trajectory of the supersonic projectile. i The ballistic shock wave is emitted, and the direction of arrival and time of arrival of the ballistic shock wave are obtained. Then, the explosion wave generated by the explosion is received, and the direction of arrival and time of arrival of the explosion wave are obtained. In this embodiment, the acoustic measuring point uses a microphone array signal to sequentially obtain the direction of arrival and time of arrival of the ballistic shock wave, the direction of arrival and time of arrival of the explosion wave.

[0071] Step 2: Based on the direction of arrival and arrival time of the explosion wave obtained in Step 1, determine the location of the explosion point and the time of explosion.

[0072] Step 2.1: Based on the direction of arrival of the explosion wave obtained in Step 1, obtain the explosion point s relative to the acoustic measuring point s. i unit vector k i :

[0073]

[0074] in: The pitch angle of the explosion point measured at the i-th acoustic measurement point; The azimuth angle of the explosion point measured at the i-th acoustic measurement point; by Figure 1 It can be known that ss i =d i k i (k2-k1) T (k2+k1)=0, then:

[0075] 2(k2-k1) T s = (k2 - k1) T (s1+s2-d 21 k1)

[0076] Where, d 21 =d2-d1=c(t) b,2 -t b,1 ), d 21 Let t be the difference between the distance from the second acoustic measurement point s2 to the explosion point s and the distance from the first measurement point s1 to the explosion point s. b,2 and t b,1 The arrival times of the explosion waves obtained from the second acoustic measuring point s2 and the first acoustic measuring point s1 are respectively;

[0077] Step 2.2: Use the weighted least squares method to calculate the estimated location s of the explosion point. The specific process is as follows:

[0078] Matrix U is constructed by the direction of the explosion wave. i Make each column vector equal to the unit vector k iOrthogonal, and matrix U i The column vectors are orthogonal to each other, that is... but: in, I 2×2 It is the identity matrix, and 02 is the zero vector; And 2(k2-k1) in step 2.1 T s = (k2 - k1) T (s1+s2-d 21 If k1) is represented by a matrix, then: G T s = h, where G is the matrix fusing the direction of arrival information of the blast wave, G = [2(k2-k1), U1, U2], and h is the vector fusing the direction of arrival of the blast wave, the distance difference between acoustic measurement point s2 and acoustic measurement point s1 to the explosion point s, and the position of the acoustic measurement point.

[0079] Measurement error vector The covariance matrix is ​​Q. The weight matrix W is obtained by fusing information on the direction of arrival of the blast wave and the distance from the blast point to the measuring point: W = TQT T

[0080] in, 0 2×2 This is a 2x2 matrix with all elements equal to 0, where 02 is the zero vector, and Δ(·) represents the error of the corresponding measurement; finally, combined with G... T s=h and W=TQT T The estimated location s of the explosion point was obtained using the weighted least squares method. for:

[0081]

[0082] Step 2.3: Based on the acoustic measurement point s in Step 1 i The unit vector k obtained in step 2.1 i And the estimation of the explosion point location s obtained in step 2.2 Get d i Estimate Combining the arrival time of the explosion wave obtained in step 1, an estimate of the explosion time is calculated. And the obtained Calculate the average value to obtain an estimate of the explosion time t.

[0083]

[0084] in, t b,i For the i-th acoustic measurement point s i When the acquired explosion wave arrived;

[0085] Step 3: Estimate the trajectory of the ballistic shock wave, the arrival time of the ballistic shock wave obtained in Step 1, and the location s of the detonation point obtained in Step 2.2. Calculate the trajectory and projectile velocity

[0086] Step 3.1: Based on the direction of arrival of the ballistic shock wave obtained in Step 1, obtain the shock wave separation point p. i Relative to acoustic measurement point s i unit vector b i :

[0087] b i =[cosφ i cosθ i ,cosφ i sinθ i ,sinφ i ] T

[0088] Where: φ i The elevation angle of the ballistic shock wave measured at the i-th acoustic measurement point; θ i The ballistic shock wave azimuth angle is measured at the i-th acoustic measurement point; then the difference between the distance from the second acoustic measurement point s2 to the corresponding shock wave separation point p2 and the distance from the first acoustic measurement point s1 to the corresponding shock wave separation point p1 can be obtained:

[0089]

[0090] Where, τ 21 =c(t) s,2 -t s,1 ), t s,2 and t s1 The arrival times of the ballistic shock waves obtained from the second acoustic measuring point s2 and the first acoustic measuring point s1 are respectively. Depend on Figure 1 It can be seen that r i b i =p i -s i r2(b2+b1)=r2b1+r1b1+r 21 b1; then, using the orthogonality between vectors, we obtain (b2-b1). T (b2+b1)=0、(b2-b1) T (s-p1)=0, then:

[0091] 2(b2-b1) T p1 = (b2 - b1) T (s1+s2-r 21 b1)

[0092] (b2-b1) T p1 = (b2 - b1) T s

[0093] Step 3.2: Use the weighted least squares method to calculate the estimated location p1 of the shock wave separation point. The specific process is as follows:

[0094] Matrix V is constructed based on the direction of arrival of the ballistic shock wave. i Make each column vector of it equal to the unit vector b i Orthogonal, and matrix V i The column vectors are orthogonal to each other, that is... get: in, Will And 2(b2-b1) in step 3.1 T p1 = (b2 - b1) T (s1+s2-r 21 b1), (b2-b1) T p1 = (b2 - b1) T Representing s using a matrix, the equation for solving the shock wave separation point p1 corresponding to the acoustic measurement point s1 is: A T p1 = z, where A is the matrix fusing ballistic shock wave direction of arrival information, A = [(b2-b1), 2(b2-b1), V1], and z is the vector fusing ballistic shock wave direction of arrival, impact point and acoustic measurement point positions, and the distance difference between acoustic measurement points s2 and s1 to their respective shock wave separation points.

[0095] Measurement error vector ε=[Δs T ,Δτ 21 ,ε1,ε2] T The covariance matrix is ​​Q1, ε i =[Δθ i ,Δφ i ] T Δ(·) represents the error of the corresponding measurement value, and the weight matrix W1 is obtained by fusing the ballistic shock wave arrival direction, the distance from the shock wave separation point to the detonation point, the distance from the shock wave separation point to the acoustic measurement point, the positions of the shock wave separation point and the acoustic measurement point, and the ballistic direction information. W1 = Q1, combined with A T Given p1 = z and W1 = Q1, the estimated location p1 of the shock wave separation point is calculated using the weighted least squares method. for:

[0096]

[0097] Based on the above estimation of the shock wave separation point location p1 The calculation process involves estimating the shock wave separation point location p2.

[0098] Step 3.3: Based on the estimated location s of the explosion point obtained in Step 2.2 The position p of each shock wave separation point obtained in step 3.2 i Estimate The estimated corresponding ballistic direction is calculated. And for all Calculate the average value to obtain an estimate of the ballistic direction u.

[0099]

[0100] in, The symbol ||·|| denotes the 2-norm of a vector;

[0101] Step 3.4: Let the weight matrix W1 = BQ1B T Repeat steps 3.2-3.3 to obtain the updated estimate of the ballistic direction u. in, 0 1×2 A row vector with two elements equal to 0. 1×3 A row vector with 3 elements equal to 0. 2×2 A matrix consisting of 2 rows and 2 columns, all of which are 0. 2×3 This is a 2x3 matrix where all elements are 0. The estimated trajectory direction u obtained in step 3.3

[0102] Step 3.5, from Figure 1 It can be seen that sinα=-u T b i Based on the updated ballistic direction u estimated in step 3.4 and the unit vector b obtained in step 3.1 i Combining this with sinα = c / v from step 1, the corresponding shock wave separation point position p can be calculated. i Estimation of projectile velocity And for all Calculate the average value to obtain an estimate of the projectile's velocity v.

[0103]

[0104] in:

[0105] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions within the technical scope disclosed in the present invention should be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for obtaining terminal ballistic parameters combining ballistic shock wave and explosion wave, characterized in that, Includes the following steps: Step 1: Set up N acoustic measurement points around the predetermined blast point, where N≥2; the acoustic measurement points are located at known positions s. i =[x i ,y i , z i ] T , i∈{1,2,…,N},[·] T This represents the transpose operation, with the explosion point position set as s, and the distance from explosion point s to the acoustic measurement point s. i The distance is d i Acoustic measurement point s i The corresponding shock wave separation point is p i Shock wave separation point p i To acoustic measurement point s i The distance is r i Shock wave separation point p i The distance to the explosion point s is l i The acoustic measurement points sequentially receive shock wave separation points p on the trajectory of the supersonic projectile. i The ballistic shock wave and the explosion wave generated by the explosion are obtained sequentially, along with the direction and time of arrival of the ballistic shock wave and the direction and time of arrival of the explosion wave. Step 2: Obtain the location of the explosion point and the time of explosion by acquiring the direction of arrival and arrival time of the explosion wave; Step 3: Calculate the trajectory direction and projectile velocity using the acquired shock wave arrival direction, shock wave arrival time, and impact point location; this includes the following sub-steps: Step 3.1: Based on the direction of arrival of the ballistic shock wave obtained in Step 1, obtain the shock wave separation point p. i Relative to acoustic measurement point s i unit vector b i : b i =[cosφ i cosθ i , cosφ i sinθ i , sinφ i ] T ; Wherein: φ i The elevation angle of the ballistic shock wave measured at the i-th acoustic measurement point; θ i The azimuth angle of the ballistic shock wave measured at the i-th acoustic measurement point; Step 3.2: Calculate the estimated shock wave separation point location p1 using the weighted least squares method according to the following formula. : ； in: A is a matrix that integrates ballistic shock wave direction of arrival information. ; V i The matrix constructed for the direction of arrival of the ballistic shock wave: ； W1 is a weighted matrix that integrates information on the trajectory shock wave direction of arrival, the distance from the shock wave separation point to the impact point, the distance from the shock wave separation point to the acoustic measurement point, the positions of the shock wave separation point and the acoustic measurement point, and the trajectory direction. ; Q1 is the measurement error vector. The covariance matrix, , , j∈{2,…,N}, t s,j and t s,1 The j-th acoustic measurement point s j When the ballistic shock wave arrives at the first acoustic measurement point s1; c is the propagation speed of the sound wave, and Δ(·) represents the error of the corresponding measurement value; To integrate the trajectory shock wave direction of arrival, impact point, and acoustic measurement point location, acoustic measurement point s j The vector of distance difference between s1 and their respective shock wave separation points. , , r 21 Let r be the difference between the distance from the second acoustic measurement point s2 to the corresponding shock wave separation point p2 and the distance from the first acoustic measurement point s1 to the corresponding shock wave separation point p1. N1 For the Nth acoustic measurement point s N to the corresponding shock wave separation point p N The difference between the distance from the first acoustic measurement point s1 and the distance from the corresponding shock wave separation point p1; Based on the estimation of the shock wave separation point position p1 The calculation process involves sequentially calculating the estimated positions of the remaining shock wave separation points to obtain the position p of each shock wave separation point. i Estimate ; Step 3.3: Based on the estimated location s of the explosion point obtained in Step 2 The position p of each shock wave separation point obtained in step 3.2 i Estimate The estimated trajectory direction is calculated. And for all Calculate the average value to obtain an estimate of the ballistic direction u. : ； in: ,symbol The 2-norm of a vector; Step 3.4: Let the weight matrix... Repeat steps 3.2-3.3 to obtain the updated estimate of the ballistic direction u. ; in, ; , 0 1×3 A row vector with 3 elements equal to 0. 1×(N-1) A row vector with N-1 elements all equal to 0. 2×3 A matrix with 2 rows and 3 columns, all elements being 0. 2×(N-1) For a matrix consisting of 2 rows and N-1 columns, all elements are 0, I (N-1)×(N-1) It is an N-1 dimensional identity matrix. The estimated trajectory direction u obtained in step 3.3 ; Step 3.5: Based on the updated ballistic direction u estimated in Step 3.4 and the unit vector b obtained in step 3.1 i The corresponding shock wave separation point position p is calculated. i Estimation of projectile velocity And for all Calculate the average value to obtain an estimate of the projectile's velocity v. : ； in: .

2. The method for obtaining terminal ballistic parameters of the combined ballistic shock wave and explosion wave according to claim 1, characterized in that, Step 2 specifically includes the following sub-steps: Step 2.1: Based on the direction of arrival of the explosion wave obtained in Step 1, obtain the explosion point s relative to the acoustic measuring point s. i unit vector k i : Where: φi is the pitch angle of the explosion point measured by the i-th acoustic measuring point; The azimuth angle of the explosion point measured at the i-th acoustic measurement point; Step 2.2: Calculate the estimated location s of the explosion point using the weighted least squares method according to the following formula. : ； in: G is a matrix that integrates the direction of arrival information of the explosion wave. ; U i The matrix constructed by the direction of the explosion wave: ； W is a weight matrix that integrates information on the direction of arrival of the explosion wave and the distance from the explosion point to the measuring point. ; ; , 0 1×2 A row vector with two elements equal to 0. 2×2 It is a 2x2 matrix with all elements equal to 0, and 02 is the zero vector; Q is the measurement error vector. The covariance matrix, d n1 =c(t b,n -t b,1 ), n∈{2,…,N}, d n1 For the nth acoustic measurement point s n The difference between the distance to the explosion point s and the distance from the first acoustic measurement point s1 to the explosion point s, t b,n and t b,1 These are the nth acoustic measurement points s n When the explosion wave obtained from the first acoustic measurement point s1 arrives; h is a vector that combines the direction of arrival of the blast wave, the location of the acoustic measurement point, and the distance difference between the acoustic measurement point and the blast point. ; Step 2.3: Based on the acoustic measurement point s in Step 1 i When the explosion wave arrives, the unit vector k obtained in step 2.1 is also present. i And the estimation of the explosion point location s obtained in step 2.2 The estimated time of the explosion was calculated. and to Calculate the average value to obtain an estimate of the explosion time t. : ； in: , For d i The estimate, t b,i For the i-th acoustic measurement point s i When the explosion wave was obtained.

3. The method for obtaining terminal ballistic parameters of the combined ballistic shock wave and explosion wave according to claim 2, characterized in that: In step 1, N=2; the acoustic measuring points use microphone array signals to sequentially acquire the direction of arrival of the ballistic shock wave and the arrival time of the ballistic shock wave, as well as the direction of arrival of the explosion wave and the arrival time of the explosion wave.

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