Large maneuvering target modeling and tracking method based on improved Singer model

Abstract

The invention provides a large maneuvering target modeling and tracking method based on an improved Singer model. According to the method, the jerk of a target is introduced as a state variable, a state model is established, the observability of the nonlinear state model is verified, the accelerated speed and the line-of-sight angular rate of the strong maneuvering target are estimated through the information of the relative distance, the relative speed and the line-of-sight angular rate obtained by a seeker, and simulation is carried out for the guidance process. It is proved that the target acceleration and the line-of-sight rate estimated by the method are high in precision, and the maneuvering target interception performance is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of tracker guidance control, and in particular relates to a large maneuvering target modeling and tracking method based on an improved Singer model. Background Art

[0002] Improving the estimation accuracy of the target state and achieving stable, reliable and accurate target tracking are of great practical significance. However, the target maneuvering acceleration cannot be directly measured, whether through the tracker's own seeker or ground measurement equipment, so it is necessary to use measurable information to estimate the target maneuvering acceleration. In addition, in order to perform precise guidance, it is also necessary to estimate the line of sight angular rate based on the measurement information provided by the seeker. Many existing models cannot accurately describe the target's motion state, especially the target's acceleration information. Summary of the invention

[0003] The present invention aims at the estimation of target acceleration and the design of filter in the process of large maneuvering target tracking, and proposes a large maneuvering target modeling and tracking method based on improved Singer model.

[0004] The present invention is implemented by the following technical scheme. The present invention proposes a large maneuvering target modeling and tracking method based on an improved Singer model, and the method comprises the following steps:

[0005] Step 1: Based on the positional relationship between the target and the tracker, derive the relative motion equation between the tracker and the target in the line of sight coordinate system;

[0006] Step 2: Using the Singer model, introduce the state variable of jerk in the line-of-sight coordinate system and establish the twelfth-order state model of the target;

[0007] Step 3: Conduct observability analysis on the target’s twelve-order state model;

[0008] Step 4: Based on the twelfth-order state model, a tracking filter model is established, and an extended Kalman filter is designed through the relative distance, relative speed and line of sight angle information measured by the seeker to estimate the target acceleration and line of sight angular rate;

[0009] Step 5: Use the estimated line-of-sight angular rate to perform guidance simulation.

[0010] Furthermore, in step 1, a coordinate system is established according to the relative motion relationship between the tracker and the target, wherein: xyz represents the three coordinate axes of the inertial coordinate system of the launch point, x 4 y 4 z 4 Represents the three coordinate axes of the line of sight coordinate system, R represents the relative distance between the tracker and the target, qε and q β They represent altitude and azimuth respectively.

[0011] Furthermore, in step 1, the target-tracker sight line vector is expressed as

[0012] r=p t -p (1)

[0013] Among them, p t and p represent the position vectors of the target and tracker in the inertial coordinate system, respectively;

[0014] Differentiating equation (1) with respect to time, we get

[0015]

[0016] Among them, dr / dt and δr / δt represent the relative time derivative of the line of sight vector in the inertial coordinate system and the line of sight coordinate system, respectively, ω x Represents the angular velocity of the sight coordinate system relative to the inertial coordinate system, V t and V represent the target and tracker velocity vectors respectively; the above formula is written in the projection form in the line of sight coordinate system as:

[0017]

[0018] in,

[0019]

[0020] Substituting formula (4) into formula (3), we can get

[0021]

[0022] Taking the derivative of (5) with respect to time, we get

[0023]

[0024] Projected to the line of sight coordinate system, where

[0025]

[0026] Substituting (5) into the equation, the equation of motion can be simplified as follows:

[0027]

[0028] Among them, a r 、a ε and a β is the component of the tracker acceleration on the three axes of the line of sight coordinate system, a tr 、a tε and a tβIt is the component of target acceleration on the three axes of the line of sight coordinate system.

[0029] Furthermore, in step 2, a twelve-order state model of the target is established, specifically:

[0030] Substituting formula (5) into formula (8) yields

[0031]

[0032] Among them, v r 、v ε and v β is the component of the tracker's relative velocity vector on the three axes of the line of sight coordinate system; in order to obtain more accurate acceleration information of large maneuvering targets, the jerk is selected as the state variable, and the Singer model is adopted, and the state variable is selected as:

[0033]

[0034] In summary, we can get the twelve-order state model as shown in formula (11):

[0035]

[0036] Where W r , W ε , W β is a Gaussian white noise with variance Q, λ r , ε , β is the target maneuvering frequency; select the relative distance r, relative speed High and low angle q ε and azimuth q β As a measurement quantity.

[0037] Furthermore, in step 3, according to Lemma 1, we can know the judgment condition that the twelve-order state model is locally weakly observable, specifically:

[0038] Lemma 1 For the twelve-order state model, we have:

[0039] Σ:

[0040] dG is the element of dL f (…(L f (g i ))) finite linear combination of the form

[0041] dG=[dg 1 … dg m dL f (g i ) … dL f (…(L f(g i )))]

[0042]

[0043] If the dimension of dG at any x is n, then Σ is said to satisfy the observability rank condition, that is, Σ is locally weakly observable. For the twelfth-order state model, we can obtain

[0044]

[0045] dH=[h 01 h 02 h 03 h 04 h 11 h 12 h 13 h 14 h 21 h 22 h 23 h 24 ]

[0046] From the above calculation results, we can get rank(dH)=12, the twelfth-order state model satisfies the observability rank condition, that is, the twelfth-order state model is locally weakly observable.

[0047] Furthermore, in step 4, it can be known from formula (5) According to the measurement information of the seeker, the relative distance r and relative speed can be measured. High and low angle q ε and azimuth q β , therefore, the measurement matrix is:

[0048]

[0049] Based on the above, the model of the tracking filter can be obtained as follows:

[0050]

[0051] Where X∈R 12 and Y∈R 4 is the measured output of the filter, W and V are the system noise and measurement noise, and both are Gaussian white noise.

[0052] Furthermore, the steps of designing an extended Kalman filter based on the tracking filter model are specifically as follows:

[0053] The first step is to linearize the twelfth-order state model and obtain the Jacobian matrix φ k :

[0054]

[0055] The second step is to predict the state prior estimate x k+1|k :

[0056] x k+1|k =f(x k|k ) (14)

[0057] The third step is to predict the prior estimate of the covariance matrix P k+1|k :

[0058] P k+1|k =φ k P k|k φ k T +Q (15)

[0059] The fourth step is to calculate the state gain matrix K based on the obtained prior estimate k+1 :

[0060] K k+1 =P k+1|k H k+1 T (H k+1 P k+1|k H k+1 T +R) -1 (16)

[0061] The fifth step is to obtain the state posterior estimate x according to the state gain matrix correction k+1|k+1 :

[0062] x k+1|k+1 =x k+1|k +K k+1 (z k+1 -Hx k+1|k ) (17)

[0063] The sixth step is to obtain the covariance posterior estimate P according to the state gain matrix correction k+1|k+1 .

[0064] Furthermore, the covariance posterior estimate P k+1|k+1 for:

[0065] P k+1|k+1 =(IK k+1 H)P k+1|k (18).

[0066] The present invention also proposes an electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the large maneuvering target modeling and tracking method based on the improved Singer model are implemented.

[0067] The present invention also proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of a large maneuvering target modeling and tracking method based on an improved Singer model.

[0068] Beneficial effects of the present invention:

[0069] The present invention proposes a method combining the Singer model with nonlinear filtering, introduces the target's acceleration as a state variable, establishes a state model, verifies the observability of the nonlinear state model, estimates the acceleration and line of sight angular velocity of a strong maneuvering target through the relative distance, relative velocity and line of sight angular velocity information obtained by the seeker, and simulates the guidance process, proving that the target acceleration and line of sight angular velocity estimated by the proposed method have high accuracy, thereby improving the performance of intercepting maneuvering targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0071] Figure 1 It is a schematic diagram of the positional relationship between the tracker and the target;

[0072] Figure 2 This is a schematic diagram of the estimation of the high and low angle line of sight angular rates when the maximum overload is 20g;

[0073] Figure 3 This is a schematic diagram of the azimuth line of sight angular rate estimation when the maximum overload is 20g;

[0074] Figure 4 This is a schematic diagram of the estimated acceleration in the y-axis direction when the maximum overload is 20g;

[0075] Figure 5 This is a schematic diagram of the estimated acceleration in the z-axis direction when the maximum overload is 20g;

[0076] Figure 6 This is a schematic diagram of the off-target amount of 100 Monte Carlo simulation experiments. DETAILED DESCRIPTION

[0077] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0078] Combination Figure 1-Figure 6 The present invention proposes a large maneuvering target modeling and tracking method based on an improved Singer model, the method comprising the following steps:

[0079] Step 1: Based on the positional relationship between the target and the tracker, derive the relative motion equation between the tracker and the target in the line of sight coordinate system;

[0080] In step 1, a coordinate system is established based on the relative motion relationship between the tracker and the target, such as Figure 1 As shown in the coordinate system, xyz represents the three coordinate axes of the inertial coordinate system of the launch point, x 4 y 4 z 4 Represents the three coordinate axes of the line of sight coordinate system, R represents the relative distance between the tracker and the target, q ε and q β They represent altitude and azimuth respectively.

[0081] In step 1, the target-tracker sight line vector is expressed as

[0082] r=p t -p (1)

[0083] Among them, p t and p represent the position vectors of the target and tracker in the inertial coordinate system, respectively;

[0084] Differentiating equation (1) with respect to time, we get

[0085]

[0086] Among them, dr / dt and δr / δt represent the relative time derivative of the line of sight vector in the inertial coordinate system and the line of sight coordinate system, respectively, ω x Represents the angular velocity of the sight coordinate system relative to the inertial coordinate system, V t and V represent the target and tracker velocity vectors respectively; the above formula is written in the projection form in the line of sight coordinate system as:

[0087]

[0088] in,

[0089]

[0090] Substituting formula (4) into formula (3), we can get

[0091]

[0092] Taking the derivative of (5) with respect to time, we get

[0093]

[0094] Projected to the line of sight coordinate system, where

[0095]

[0096] Substituting (5) into the equation, the equation of motion can be simplified as follows:

[0097]

[0098] Among them, a r 、a ε and a β is the component of the tracker acceleration on the three axes of the line of sight coordinate system, a tr 、a tε and a tβ It is the component of target acceleration on the three axes of the line of sight coordinate system.

[0099] Step 2: Using the Singer model, introduce the state variable of jerk in the line-of-sight coordinate system and establish the twelfth-order state model of the target;

[0100] In step 2, the twelve-order state model of the target is established as follows:

[0101] Substituting formula (5) into formula (8) yields

[0102]

[0103] Among them, v r 、v ε and v β is the component of the tracker's relative velocity vector on the three axes of the line of sight coordinate system; in order to obtain more accurate acceleration information of large maneuvering targets, the jerk is selected as the state variable, and the Singer model is adopted, and the state variable is selected as:

[0104]

[0105] In summary, we can get the twelve-order state model as shown in formula (11):

[0106]

[0107] Where W r , Wε , W β is a Gaussian white noise with variance Q, λ r , ε , β is the target maneuvering frequency; select the relative distance r, relative speed High and low angle q ε and azimuth q β As a measurement quantity.

[0108] Step 3: Conduct observability analysis on the target’s twelve-order state model;

[0109] Observability is the premise for the reliable operation of the filter. In order to prove the effectiveness of the proposed model, the observability analysis of the model (11) proposed in the present invention is carried out. According to Lemma 1, the judgment condition for the local weak observability of the twelve-order state model is as follows:

[0110] Lemma 1 For the twelve-order state model, we have:

[0111] Σ:

[0112] dG is the element of dL f (…(L f (g i ))) finite linear combination of the form

[0113] dG=[dg 1 … dg m dL f (g i ) … dL f (…(L f (g i )))]

[0114]

[0115] If the dimension of dG at any x is n, then Σ is said to satisfy the observability rank condition, that is, Σ is locally weakly observable. For the twelfth-order state model, we can obtain

[0116]

[0117] dH=[h 01 h 02 h 03 h 04 h 11 h 12 h 13 h 14 h 21 h 22 h 23 h 24 ]

[0118] From the above calculation results, we can get rank(dH)=12, the twelfth-order state model satisfies the observability rank condition, that is, the twelfth-order state model is locally weakly observable.

[0119] Step 4: Based on the twelfth-order state model, a tracking filter model is established, and an extended Kalman filter is designed through the relative distance, relative speed and line of sight angle information measured by the seeker to estimate the target acceleration and line of sight angular rate;

[0120] In step 4, we can know from formula (5) According to the measurement information of the seeker, the relative distance r and relative speed can be measured. High and low angle q ε and azimuth q β , therefore, the measurement matrix is:

[0121]

[0122] Based on the above, the model of the tracking filter can be obtained as follows:

[0123]

[0124] Where X∈R 12 and Y∈R 4 is the measured output of the filter, W and V are the system noise and measurement noise, and both are Gaussian white noise.

[0125] The specific steps for designing an extended Kalman filter based on the tracking filter model are:

[0126] The first step is to linearize the twelfth-order state model and obtain the Jacobian matrix φ k :

[0127]

[0128] H k It is linear in itself and does not need Taylor expansion.

[0129] The second step is to predict the state prior estimate x k+1|k :

[0130] x k+1|k =f(x k|k ) (14)

[0131] The third step is to predict the prior estimate of the covariance matrix P k+1|k :

[0132] P k+1|k =φ k P k|k φk T +Q (15)

[0133] The fourth step is to calculate the state gain matrix K based on the obtained prior estimate k+1 :

[0134] K k+1 =P k+1|k H k+1 T (H k+1 P k+1|k H k+1 T +R) -1 (16)

[0135] The fifth step is to obtain the state posterior estimate x according to the state gain matrix correction k+1|k+1 :

[0136] x k+1|k+1 =x k+1|k +K k+1 (z k+1 -Hx k+1|k ) (17)

[0137] The sixth step is to obtain the covariance posterior estimate P according to the state gain matrix correction k+1|k+1 .

[0138] The posterior estimate of the covariance P k+1|k+1 for:

[0139] P k+1|k+1 =(IK k+1 H)P k+1|k (18).

[0140] Step 5: Use the estimated line-of-sight angular rate to perform guidance simulation.

[0141] The present invention aims at the estimation of target acceleration and filter design problems in the process of tracking large maneuvering targets. The Singer model is adopted to introduce the state variable of jerk in the line of sight coordinate system, and the twelfth-order state model of the target is established, and the observability of the nonlinear twelfth-order state model is proved. Based on this model, combined with the extended Kalman filter, the estimation of target acceleration and line of sight angular rate is realized through the relative distance, relative speed and line of sight angle information measured by the seeker. The simulation results show that the combination of the established state model and filter can effectively improve the estimation accuracy of acceleration; at the same time, the guidance simulation using the estimated line of sight angular rate can better complete the task of intercepting large maneuvering targets.

[0142] Simulation part

[0143] In order to verify the effectiveness of the proposed twelfth-order state model for large maneuvering target acceleration estimation and line-of-sight angular rate extraction, for the reentry strong maneuvering target, the maneuvering frequency is 0.5 Hz and the maximum maneuvering acceleration is a max = ±20g of the screw maneuver was simulated.

[0144] Assume that the initial missile-target distance is R = 13900m and the initial speed of the target is v xt =-1.28×10 3 m / s,v yt =-1.49×10 3 m / s,v zt =0m / s, the initial velocity of the tracker is v x =1.026×10 3 m / s,v y =1.117×10 3 m / s,v z = 0m / s. The measurement error of the missile-target distance R is 3σ = 50m, the measurement error of the relative speed V is 3σ = 10m / s, and the sight angle q ε and q β The measurement error is σ = 0.01°, from which the measurement noise variance matrix R can be calculated n , the system noise variance matrix is

[0145] Q n =diag[Q 1 Q 2 ... Q 12 ]

[0146] in,

[0147] Q 1 =10^(-14), Q 2 =10^(-14), Q 3 =10^(-12), Q 4 =10^(-14), Q 5 =10^(-12),

[0148] Q 6 =10^(-14), Q 7 =10^(2), Q 8 =10^(2), Q 9 =10^(2), Q 10 =1,Q 11 =1,Q 12 =1

[0149] The above tracker and target information are used for simulation, and three aspects of analysis are mainly carried out, namely, line of sight angular rate estimation, acceleration estimation and miss distance analysis. Through simulation, it can be concluded that when the maximum overload is 20g, the estimated line of sight angular rate and target acceleration accuracy are higher by using the model proposed by the present invention. Through 100 Monte Carlo simulation experiments, the miss distance is within 0.06m, which can effectively intercept strong maneuvering targets, has important engineering application value, and lays the foundation for the design of guidance law.

[0150] The present invention also proposes an electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the large maneuvering target modeling and tracking method based on the improved Singer model are implemented.

[0151] The present invention also proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of a large maneuvering target modeling and tracking method based on an improved Singer model.

[0152] The memory in the embodiments of the present application may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. Among them, the non-volatile memory may be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), or a flash memory. The volatile memory may be a random access memory (RAM), which is used as an external cache. By way of example and not limitation, many forms of RAM are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), and direct RAM bus RAM (DR RAM). It should be noted that the memory of the method described in the present invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0153] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions may be transmitted from a website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (digital subscriber line, DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) mode to another website site, computer, server or data center. The computer-readable storage medium may be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated. The available medium may be a magnetic medium (eg, a floppy disk, a hard disk, a magnetic tape), an optical medium (eg, a high-density digital video disc (DVD)), or a semiconductor medium (eg, a solid state disc (SSD)).

[0154] In the implementation process, each step of the above method can be completed by an integrated logic circuit of hardware in a processor or an instruction in the form of software. The steps of the method disclosed in conjunction with the embodiment of the present application can be directly embodied as a hardware processor for execution, or a combination of hardware and software modules in a processor for execution. The software module can be located in a storage medium mature in the art such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, etc. The storage medium is located in a memory, and the processor reads the information in the memory and completes the steps of the above method in conjunction with its hardware. To avoid repetition, it is not described in detail here.

[0155] It should be noted that the processor in the embodiment of the present application can be an integrated circuit chip with signal processing capabilities. In the implementation process, each step of the above method embodiment can be completed by an integrated logic circuit of hardware in the processor or an instruction in the form of software. The above processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components. The methods, steps and logic block diagrams disclosed in the embodiments of the present application can be implemented or executed. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc. The steps of the method disclosed in the embodiment of the present application can be directly embodied as a hardware decoding processor to perform, or the hardware and software modules in the decoding processor can be combined and performed. The software module can be located in a mature storage medium in the field such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, etc. The storage medium is located in a memory, and the processor reads the information in the memory and completes the steps of the above method in combination with its hardware.

[0156] The above is a detailed introduction to a large maneuvering target modeling and tracking method based on an improved Singer model proposed in the present invention. In this article, specific examples are used to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea; at the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation method and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

Claims

1. A large maneuvering target modeling and tracking method based on an improved Singer model, characterized in that: The method comprises the following steps: Step 1: Based on the positional relationship between the target and the tracker, derive the relative motion equation between the tracker and the target in the line of sight coordinate system; Step 2: Using the Singer model, introduce the state variable of jerk in the line-of-sight coordinate system and establish the twelfth-order state model of the target; Step 3: Conduct observability analysis on the target’s twelve-order state model; Step 4: Based on the twelfth-order state model, a tracking filter model is established, and an extended Kalman filter is designed through the relative distance, relative speed and line of sight angle information measured by the seeker to estimate the target acceleration and line of sight angular rate; Step 5: Use the estimated line-of-sight angular rate to perform guidance simulation.

2. The method according to claim 1, characterized in that In step 1, a coordinate system is established based on the relative motion relationship between the tracker and the target, in which: xyz represents the three coordinate axes of the inertial coordinate system of the launch point, x4y4z4 represents the three coordinate axes of the line of sight coordinate system, R represents the relative distance between the tracker and the target, and q ε and q β They represent altitude and azimuth respectively.

3. The method according to claim 2, characterized in that In step 1, the target-tracker sight line vector is expressed as r=p t -p (1) Among them, p t and p represent the position vectors of the target and tracker in the inertial coordinate system, respectively; Differentiating equation (1) with respect to time, we get Among them, dr / dt and δr / δt represent the relative time derivative of the line of sight vector in the inertial coordinate system and the line of sight coordinate system, respectively, ω x Represents the angular velocity of the sight coordinate system relative to the inertial coordinate system, V t and V represent the target and tracker velocity vectors respectively; the above formula is written in the projection form in the line of sight coordinate system as: in, Substituting formula (4) into formula (3), we can get Taking the derivative of (5) with respect to time, we get Projected to the line of sight coordinate system, where Substituting (5) into the equation, the equation of motion can be simplified as follows: Among them, a r 、a ε and a β is the component of the tracker acceleration on the three axes of the line of sight coordinate system, a tr 、a tε and a tβ It is the component of target acceleration on the three axes of the line of sight coordinate system.

4. The method according to claim 3, characterized in that In step 2, a twelve-order state model of the target is established, specifically: Substituting formula (5) into formula (8) yields Among them, v r 、v ε and v β is the component of the tracker's relative velocity vector on the three axes of the line of sight coordinate system; in order to obtain more accurate acceleration information of large maneuvering targets, the jerk is selected as the state variable, and the Singer model is adopted, and the state variable is selected as: In summary, we can get the twelve-order state model as shown in formula (11): Where W r , W ε , W β is a Gaussian white noise with variance Q, λ r , ε , β is the target maneuvering frequency; select the relative distance r, relative speed High and low angle q ε and azimuth q β As a measurement quantity.

5. The method according to claim 4, characterized in that In step 3, according to Lemma 1, we can know the judgment conditions for the local weak observability of the twelfth-order state model, which are: Lemma 1 For the twelve-order state model, we have: dG is the element of dL f (…(L f (g i ))) finite linear combination of the form dG=[dg1…dg m dL f (g i )…dL f (…(L f (g i )))] If the dimension of dG at any x is n, then Σ is said to satisfy the observability rank condition, that is, Σ is locally weakly observable. For the twelfth-order state model, we can obtain dH=[h 01 h 02 h 03 h 04 h 11 h 12 h 13 h 14 h 21 h 22 h 23 h 24 ] From the above calculation results, we can get rank(dH)=12, the twelfth-order state model satisfies the observability rank condition, that is, the twelfth-order state model is locally weakly observable.

6. The method according to claim 5, characterized in that In step 4, we can know from formula (5) According to the measurement information of the seeker, the relative distance r and relative speed can be measured. High and low angle q ε and azimuth q β , therefore, the measurement matrix is: Based on the above, the model of the tracking filter can be obtained as follows: Where X∈R 12 and Y∈R 4 is the measured output of the filter, W and V are the system noise and measurement noise, and both are Gaussian white noise.

7. The method according to claim 6, characterized in that The specific steps for designing an extended Kalman filter based on the tracking filter model are: The first step is to linearize the twelfth-order state model and obtain the Jacobian matrix φ k : The second step is to predict the state prior estimate x k+1|k : x k+1|k =f(x k|k ) (14) The third step is to predict the prior estimate of the covariance matrix P k+1|k : P k+1|k =φ k P k|k φ k T +Q (15) The fourth step is to calculate the state gain matrix K based on the obtained prior estimate k+1 : K k+1 =P k+1|k H k+1 T (H k+1 P k+1|k H k+1 T +R) -1 (16) The fifth step is to obtain the state posterior estimate x according to the state gain matrix correction k+1|k+1 : x k+1|k+1 =x k+1|k +K k+1 (z k+1 -Hx k+1|k ) (17) The sixth step is to obtain the covariance posterior estimate P according to the state gain matrix correction k+1|k+1 .

8. The method according to claim 7, characterized in that The posterior estimate of the covariance P k+1|k+1 for: P k+1|k+1 =(I-K k+1 H)P k+1|k (18)。 9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 8 are implemented.

10. A computer-readable storage medium for storing computer instructions, characterized in that: When the computer instructions are executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

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