A method for modeling and tracking large maneuvering targets based on forecast information

Abstract

This paper proposes a method for modeling and tracking large maneuvering targets based on an improved Singer model. This method introduces the target's jerk as a state variable, establishes a state model, and verifies the observability of this nonlinear state model. The method estimates the acceleration and line-of-sight angular velocity of a strongly maneuvering target using information such as relative range, relative velocity, and line-of-sight angular velocity obtained by the seeker. Simulations of the guidance process demonstrate that the proposed method accurately estimates the target acceleration and line-of-sight angular velocity, improving the performance of intercepting maneuvering targets.

Description

Technical Field

[0001] The present 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 accuracy of target state estimation and achieving stable, reliable, and precise target tracking is of great practical significance. However, the target's maneuvering acceleration cannot be directly measured, whether by the tracker's own seeker or ground-based measurement equipment. Therefore, it is necessary to estimate the target's maneuvering acceleration using measurable information. Furthermore, for 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 its acceleration information. Summary of the Invention

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

[0004] The present invention is achieved through the following technical solutions. The present invention proposes a large maneuvering target modeling and tracking method based on an improved Singer model, the method comprising 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 jerk as a state variable in the line-of-sight coordinate system to establish a 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. The extended Kalman filter is designed based on the relative distance, relative velocity 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 based on the relative motion relationship between the tracker and the target, in which: xyz represents the three coordinate axes of the launch point inertial coordinate system, 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.

[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 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 projection form of the above formula in the line of sight coordinate system is:

[0017]

[0018] in,

[0019]

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

[0021]

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

[0023]

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

[0025]

[0026] Substituting (5) into the equation, we can simplify the equation of motion to:

[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 tβ are the components of the 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. The Singer model is used, and the state variable is selected as:

[0033]

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

[0035]

[0036] Where W r 、W ε 、W β is Gaussian white noise with variance Q, λ r ,λ ε ,λ β is the target maneuvering frequency; select 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 conditions for the local weak observability of the twelfth-order state model, specifically:

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

[0039]

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

[0041] dG=[dg1…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 twelve-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 obtain rank(dH)=12, and the twelfth-order state model meets 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) that 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 white Gaussian noise.

[0052] Furthermore, the steps of designing an extended Kalman filter based on the tracking filter model are 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 the large maneuvering target modeling and tracking method based on the 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, and estimates the acceleration and line-of-sight angular velocity of a strongly maneuvering target through the relative distance, relative velocity, and line-of-sight angular velocity information obtained by the seeker. The guidance process is simulated, and it is proved that the target acceleration and line-of-sight angular velocity estimated by the proposed method are highly accurate, 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 following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

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

[0072] Figure 2 This is a schematic diagram of the estimation of angular rates at high and low angles of sight 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 overload is maximum 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 following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0078] Combine Figures 1-6 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 launch point inertial coordinate system, x4y4z4 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 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 projection form of the above formula in the line of sight coordinate system is:

[0087]

[0088] in,

[0089]

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

[0091]

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

[0093]

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

[0095]

[0096] Substituting (5) into the equation, we can simplify it to get the equation of motion:

[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 are the components of the target acceleration on the three axes of the line of sight coordinate system.

[0099] Step 2: Using the Singer model, introduce the jerk as a state variable in the line-of-sight coordinate system to establish a 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. The Singer model is used, and the state variable is selected as:

[0104]

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

[0106]

[0107] Where W r 、W ε 、W β is Gaussian white noise with variance Q, λr ,λ ε ,λ β is the target maneuvering frequency; select 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 this invention is carried out. According to Lemma 1, the judgment conditions for the local weak observability of the twelve-order state model are as follows:

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

[0111]

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

[0113] dG=[dg1…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 twelve-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 obtain rank(dH)=12, and the twelfth-order state model meets 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. The extended Kalman filter is designed based on the relative distance, relative velocity 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 white Gaussian noise.

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

[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 require 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 φ k 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 covariance estimate 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 addresses the problem of estimating target acceleration and designing filters during the tracking of large maneuvering targets. Using the Singer model, the state variable jerk is introduced in the line-of-sight coordinate system, a twelfth-order state model of the target is established, and the observability of this nonlinear twelfth-order state model is demonstrated. Based on this model, combined with an extended Kalman filter, the target acceleration and line-of-sight angular rate are estimated using the relative distance, relative velocity, and line-of-sight angle information measured by the seeker. Simulation results show that the combination of the established state model and filter can effectively improve the accuracy of acceleration estimation. At the same time, using the estimated line-of-sight angular rate for guidance simulation can effectively accomplish the task of intercepting large maneuvering targets.

[0142] Simulation part

[0143] In order to verify the effectiveness of the proposed twelve-order state model for large maneuvering target acceleration estimation and line-of-sight angular rate extraction, for reentry strong maneuvering targets, the maneuvering frequency is 0.5 Hz and the maximum maneuvering acceleration is a max = ±20g spiral maneuver is 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 velocity 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[Q1 Q2 ... Q 12 ]

[0146] in,

[0147] Q1=10^(-14), Q2=10^(-14), Q3=10^(-12), Q4=10^(-14), Q5=10^(-12),

[0148] Q6=10^(-14), Q7=10^(2), Q8=10^(2), Q9=10^(2), Q 10 =1,Q 11 =1,Q 12 =1

[0149] Using the tracker and target information above, simulations were conducted, focusing on three key areas of analysis: line-of-sight angular rate estimation, acceleration estimation, and miss distance analysis. The simulations demonstrated that, at a maximum overload of 20g, the proposed model provided more accurate estimates of line-of-sight angular rate and target acceleration. Through 100 Monte Carlo simulations, the miss distances were consistently within 0.06m, demonstrating the ability to effectively intercept highly maneuverable targets. This model possesses significant engineering application value and lays the foundation for guidance law design.

[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 the large maneuvering target modeling and tracking method based on the 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. 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 synchronous DRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), and direct RAM bus RAM (DRRAM). It should be noted that the memory of the methods described herein is intended to include, but is not limited to, these and any other suitable types of memory.

[0153] In the above embodiments, all or part of the embodiments may be implemented by software, hardware, firmware, or any combination thereof. When implemented using software, all or part of the embodiments may be implemented 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, all or part of the processes or functions described in the embodiments of the present application are generated. 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 one website, computer, server, or data center to another website, computer, server, or data center via a wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) method. 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 therein. 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] During implementation, each step of the above method can be completed by an integrated logic circuit of the hardware in the processor or by instructions in the form of software. The steps of the method disclosed in conjunction with the embodiments of the present application can be directly embodied as being executed by a hardware processor, or can be executed by a combination of hardware and software modules in the processor. 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 the 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 will not be described in detail here.

[0155] It should be noted that the processor in the embodiments of the present application can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method embodiment can be completed by an integrated logic circuit of the hardware in the processor or by instructions 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 device, a discrete gate or transistor logic device, or a discrete hardware component. The various 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. The steps of the method disclosed in the embodiments of the present application can be directly embodied as being executed by a hardware decoding processor, or can be executed by a combination of hardware and software modules in the decoding processor. The software module can be located in a storage medium mature in the art, such as random access memory, flash memory, read-only memory, programmable read-only memory, or electrically erasable programmable memory, registers, etc. The storage medium is located in the 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 the large maneuvering target modeling and tracking method based on the improved Singer model proposed in the present invention. Specific examples are used in this article 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 ideas. At the same time, for those skilled in the art, according to the ideas of the present invention, there will be changes in the specific implementation methods and application scopes. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A large maneuvering target modeling and tracking method based on forecast information, 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 jerk as a state variable in the line-of-sight coordinate system to establish a 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. The extended Kalman filter is designed based on the relative distance, relative velocity 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; In step 1, the target-tracker sight line vector is expressed as (1) in, and Represent the position vectors of the target and tracker in the inertial coordinate system respectively; Differentiating Equation (1) with respect to time, we get (2) in, and Respectively represent the time derivative of the sight vector in the inertial coordinate system and the sight coordinate system, Represents the angular velocity of the sight coordinate system relative to the inertial coordinate system, and Represent the target and tracker velocity vectors respectively; the projection form of the above formula in the line of sight coordinate system is: (3) in, ， (4) Substituting formula (4) into formula (3), we can get (5) Taking the derivative of Equation (5) with respect to time, we get (6) Projected into the line of sight coordinate system, where , (7) Substituting (5) into the equation, we can simplify the equation of motion to: (8) in, 、 and is the component of the tracker acceleration on the three axes of the line of sight coordinate system, 、 and are the components of the target acceleration on the three axes of the line of sight coordinate system; In step 2, a twelve-order state model of the target is established, specifically: Substituting formula (5) into formula (8) yields (9) in, 、 and 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. The Singer model is used, and the state variable is selected as: (10) In summary, we can obtain the twelve-order state model shown in formula (11): (11) in 、 、 The variance is Q Gaussian white noise, 、 、 is the target maneuvering frequency; select the relative distance , relative speed , height and low angle and azimuth As a measurement quantity.

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, Represents the three coordinate axes of the sight coordinate system, R represents the relative distance between the tracker and the target, and They represent altitude and azimuth respectively.

3. The method according to claim 1, 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, specifically: Lemma 1 For the twelve-order state model, we have: The element is A finite linear combination of the form like If the dimension at any x is n, then Σ is said to satisfy the observability rank condition, that is, Σ is locally weakly observable. For the twelve-order state model, we can get From the above calculation results, we can get , the twelve-order state model satisfies the observability rank condition, that is, the twelve-order state model is locally weakly observable.

4. The method according to claim 3, characterized in that In step 4, we can know from formula (5) , according to the seeker measurement information, the relative distance can be measured , relative speed , height and low angle and azimuth , therefore, the measurement matrix is: Based on the above, the model of the tracking filter can be obtained as follows: (12) in, and is the measured output of the filter, and are system noise and measurement noise, and both are Gaussian white noise.

5. The method according to claim 4, characterized in that The steps for designing an extended Kalman filter based on the tracking filter model are as follows: The first step is to linearize the twelfth-order state model and obtain the Jacobian matrix : (13) The second step is to predict the prior estimate of the state : (14) The third step is to predict the prior estimate of the covariance matrix : (15) The fourth step is to calculate the state gain matrix based on the obtained prior estimate : (16) The fifth step is to obtain the state posterior estimate according to the state gain matrix correction : (17) The sixth step is to obtain the covariance posterior estimate based on the state gain matrix correction .

6. The method according to claim 5, characterized in that The posterior estimate of the covariance for: (18)。 7. 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 6 are implemented.

8. 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 6 are implemented.

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