A method for estimating the remaining average velocity and controlling the flight time of a variable-speed missile

Abstract

This invention discloses a method for estimating the remaining average velocity and controlling the flight time of a variable-speed missile, comprising the following steps: constructing a missile motion model and a differential geometry guidance model; predicting the remaining flight path of the missile under proportional guidance, and constructing a flight path error dynamic equation in the form of biased proportional guidance; designing a flight path control guidance law based on the optimal error dynamics method; predicting the missile velocity profile and estimating the remaining average velocity; converting the desired remaining flight time into the desired remaining flight path, and achieving flight time control through the flight path control guidance law. This invention relates to the field of aircraft dynamics, guidance, and control, and can effectively improve the accuracy of existing missile remaining average velocity estimation algorithms and reduce flight time control errors. It can provide an effective solution to the problem of time-varying multi-missile cooperative guidance.

Description

Technical Field

[0001] This invention relates to the fields of aircraft dynamics, guidance, and control technology, specifically a method for estimating the remaining average velocity and controlling the flight time of a variable-speed missile. This method can accurately estimate the remaining average velocity of the missile, enabling the variable-speed missile to hit the target at a specified time. Background Technology

[0002] Modern, complex warfare places higher demands on missiles. To fully utilize their combat effectiveness, improve penetration probability, and enhance destructive capabilities, missiles must attack targets with minimal miss distance while simultaneously or sequentially attacking targets within predetermined flight times. Unlike general guidance law design problems, time-of-flight control guidance methods require the remaining flight time as a feedback variable to control the flight time. However, the remaining flight time of a missile cannot be measured by sensors and must be estimated for a specific guidance law. Similarly, the remaining average velocity, the average velocity of the missile from the current moment to the moment of impact, can also only be estimated for a specific guidance law.

[0003] Most existing time-of-flight control guidance methods assume that the missile's velocity remains constant. For example, patent publication CN114384808A discloses a three-dimensional guidance method for arrival time control based on an adaptive neural network, and patent publication CN 113625745A discloses an attack time control guidance method based on switching fixed-time convergence theory. Both assume that the missile's velocity remains constant. However, the time-of-flight control guidance law designed based on this assumption is at risk of performance degradation or even failure in actual variable-speed missiles. The design of time-of-flight control guidance methods for variable-speed missiles usually requires first constructing a variable-speed missile model, and then designing a time-of-flight control guidance law to control flight time errors. However, this method requires estimating the missile's remaining average velocity, and the guidance performance is greatly affected by the accuracy of the average velocity estimation. For example, Sun Guoxin's paper "Impact time control using biased proportional navigation for missiles with varying velocity" published in the *Acta Aeronautica Sinica* (English Edition) uses the small-angle assumption when estimating the missile's remaining average velocity, and the resulting remaining average velocity estimation algorithm has a large error when the missile's leading angle (field of view) is large. Furthermore, the flight time control guidance method disclosed in the hypersonic vehicle reentry guidance method under terminal time constraints in patent publication number CN 112947573A has an overly complex terminal time prediction method. The missile's flight time is affected by the missile's trajectory in space and the velocity variation along that trajectory. Summary of the Invention

[0004] To address the performance degradation or even failure risks of existing time-of-flight control guidance methods in real-world scenarios with varying missile speeds, this invention provides a method for estimating the remaining average velocity of variable-speed missiles and for time-of-flight control guidance. This method improves the accuracy of existing missile remaining average velocity estimation algorithms and reduces time-of-flight control errors. It offers an effective solution to the problem of coordinated guidance of multiple missiles with time-varying speeds.

[0005] To achieve the above objectives, this invention, from the perspective of differential geometry, decomposes the flight time control problem of a variable-speed missile into a spatial trajectory determination problem and a residual average velocity estimation problem. The spatial trajectory determination problem is essentially the flight path control problem. By introducing the arc length differential to eliminate the influence of missile velocity variations, the performance of the designed flight path control guidance law is unaffected by the magnitude and variation of the missile's velocity. After determining the missile's flight trajectory, the velocity variation law along that trajectory is also determined, enabling accurate estimation of the residual average velocity. Therefore, this invention designs a residual average velocity estimation method and a flight time control method for variable-speed missiles, enabling precise flight time control of variable-speed missiles and ensuring that the missile hits the target at a specified time.

[0006] The technical concept of this invention is as follows: First, a missile motion model for velocity prediction and a differential geometry guidance model for designing flight path control guidance laws are constructed; second, the remaining flight path of the missile guided by proportional guidance laws is predicted in the differential geometry guidance model, and the missile flight path error dynamics equation is constructed; third, the error dynamics method is applied to design the flight path control guidance law, the performance of which is independent of the missile's velocity magnitude and its changes; then, the missile velocity profile is predicted, and the remaining average velocity of the missile is estimated; finally, the estimated remaining average velocity is applied to convert the desired flight time constraint into a desired flight path constraint, and flight time control is achieved through the flight path control guidance law.

[0007] This invention provides a method for estimating the remaining average velocity and controlling the flight time of a variable-speed missile, comprising the following steps:

[0008] Step 1: Construct the missile motion model and differential geometry guidance model;

[0009] Step 2: Predict the remaining flight path of the missile under proportional navigation guidance (PNG) and construct the flight path error dynamic equation in the form of bias proportional guidance.

[0010] Step 3: Design the flight path control guidance law based on the optimal error dynamics method;

[0011] Step 4: Predict the missile velocity profile and estimate the remaining average velocity;

[0012] Step 5: Convert the expected remaining flight time into the expected remaining flight distance, and achieve flight time control through the flight distance control guidance law.

[0013] In one embodiment, step 1 uses an air rudder-controlled missile motion model, which is as follows:

[0014]

[0015] In the formula, x and y are the missile's position in the inertial frame, and v m For missile speed, θ and θ' are the velocity tilt angle and field of view angle, respectively; L and D are the lift and drag forces acting on the missile, respectively; and g is the acceleration due to gravity.

[0016] In one embodiment, in step 1, the missile differential geometry guidance model is:

[0017]

[0018] In the formula, κ m For guidance curvature commands, r' represents the derivative of the relative distance r between the missile and the target with respect to the missile's arc length s, and q' represents the derivative of the line-of-sight angle q with respect to the missile's arc length s. Indicates the velocity angle The derivative of the missile arc length s, where θ is the field of view angle.

[0019] In one embodiment, step 2 specifically includes:

[0020] The remaining flight path of the missile under proportional guidance can be approximated as:

[0021]

[0022] In the formula, s go θ represents the remaining flight path, r represents the relative distance between the missile and the target, N represents the guidance gain of the proportional guidance system, and θ represents the field of view.

[0023] Guidance curvature command κ of flight path control guidance law m This can be expressed as a proportional guidance term used to control the zero-control miss distance, plus an offset proportional guidance term used to control the flight path error, i.e.:

[0024] κ m =κ PN +κ FR

[0025] In the formula, κ PN =Nq' is the guidance command for proportional guidance law, κ FR These are the guidance commands to be designed to control flight path errors.

[0026] Let the desired total flight distance be s d If the distance traveled from the start of guidance to the current time is s, then the expected remaining distance traveled can be expressed as s. go,d =s d -s, the flight distance error can be defined as:

[0027] ε s =s go,d -s go

[0028] Differentiating with the missile arc length as the differential component yields the flight path error dynamic equation, which is independent of the missile velocity:

[0029]

[0030] In the formula, ε s ' represents the flight path error ε s The derivative with respect to the missile arc length s.

[0031] In one embodiment, step 3 specifically includes:

[0032] The optimal error dynamics method, which takes flight path error as a variable and includes field-of-view constraints, is as follows:

[0033]

[0034] In the formula, K is the coefficient of the flight time control term, and θ max For the field of view constraint, φ(θ / θ) max ) is an auxiliary function used to process θ→θ max Field of view constraints.

[0035] The auxiliary function φ(x) in the designed guidance law is selected as:

[0036]

[0037] Where x is the independent variable of the auxiliary function, which is represented by θ / θ in this invention. max It means that n is the parameter for adjusting the change of the auxiliary function, which satisfies n>0, and the larger n is, the closer φ(x) is to 1, and the faster φ(x) converges to 0 as x→1.

[0038] Substituting the above equation into the flight path error dynamics equation, we obtain the optimal flight path control term expressed in terms of curvature as follows:

[0039]

[0040] Substituting this optimal flight path control term into the flight path control guidance law in the form of bias proportional guidance, we can obtain the flight path control guidance law expressed in curvature as follows:

[0041]

[0042] Without altering any properties of the guidance law, the curvature-form flight path control guidance law can be converted into an acceleration-form flight path control guidance law by applying the relationship between guidance curvature and guidance acceleration, as follows:

[0043]

[0044] In the formula, For missile line-of-sight rotation rate.

[0045] In one embodiment, step 4 specifically includes:

[0046] Using the analytical properties of the proportional guidance law, the differential relationship between the rate of change of missile velocity and the relative distance between the missile and the target can be obtained as follows:

[0047]

[0048] In the formula, ρ(r) is the atmospheric density with relative distance r as the independent variable, and v m (r) represents the missile velocity with r as the independent variable. Let r be the missile velocity tilt angle, θ(r) be the missile velocity lead angle with r as the independent variable, and m be the missile mass. For the aerodynamic lift derivative, The induced drag coefficient, It is a zero-lift drag coefficient.

[0049] The velocity profile is obtained through numerical integration, with the relative distance r between the missile and the target as the independent variable. When the integration interval dr is sufficiently small, the missile velocity can be considered constant within each integration interval. Therefore, the missile velocity profile is transformed into a form with time as the independent variable, and the average value is calculated to obtain the residual average velocity, which is:

[0050]

[0051] in, v is the remaining average velocity. m (t) represents the missile velocity profile with time as the independent variable, where t0 is the guidance start time, and t f The moment the missile hits its target.

[0052] In one embodiment, step 5 specifically includes:

[0053] Let the total expected flight time be t. d If the flight time already taken is t, then the expected remaining flight time is t. go,d =t d-t, using the remaining average velocity estimate, converts the expected remaining flight time into the expected remaining flight distance, as follows:

[0054]

[0055] Introducing a gravity compensation term, we obtain the flight path control guidance law used to control flight time, which is:

[0056]

[0057] Finally, flight time control is achieved through a flight path control guidance law.

[0058] This invention provides a method for estimating the remaining average velocity and controlling the flight time of a variable-speed missile. Under the guidance of the designed guidance law, the missile, whose velocity varies with time, can hit the target at a specified time. Compared with traditional flight time control guidance laws based on the assumption of constant-speed missiles, the performance of the flight time control guidance law disclosed in this invention is not affected by changes in missile velocity. Compared with the flight time control guidance law of variable-speed missiles, the design method disclosed in this invention decouples the flight time control problem into a spatial trajectory determination problem (the flight path control guidance law design problem) and a remaining average velocity estimation problem on that trajectory, achieving high-precision remaining average velocity estimation. Compared with general flight time control guidance laws, the flight time control guidance law disclosed in this invention can satisfy the missile's field of view constraint. Attached Figure Description

[0059] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0060] Figure 1 This is a flowchart of the variable-speed missile residual average velocity estimation and flight time control guidance method in this embodiment;

[0061] Figure 2 This is a schematic diagram of the missile motion model in this embodiment;

[0062] Figure 3 This is a schematic diagram of the missile trajectory provided by the embodiment of the present invention;

[0063] Figure 4 This is a schematic diagram of the missile guidance acceleration curve provided by the embodiment of the present invention;

[0064] Figure 5 This is a schematic diagram of the field of view curve of the method provided in the embodiments of the present invention;

[0065] Figure 6 This is a schematic diagram of the time-of-flight error curve of the method provided in the embodiments of the present invention;

[0066] Figure 7 This is a schematic diagram of the missile energy consumption curve provided by the embodiment of the present invention.

[0067] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. 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 a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0069] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indication will also change accordingly.

[0070] Furthermore, in this invention, descriptions involving "first," "second," etc., are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0071] In this invention, unless otherwise explicitly specified and limited, the terms "connection," "fixed," etc., should be interpreted broadly. For example, "fixed" can mean a fixed connection, a detachable connection, or an integral part; it can mean a mechanical connection, an electrical connection, a physical connection, or a wireless communication connection; it can mean a direct connection or an indirect connection through an intermediate medium; it can mean the internal communication of two elements or the interaction between two elements, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0072] Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are feasible for those skilled in the art. If the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0073] This embodiment uses simulation software to verify the correctness of the designed flight path control guidance method for controlling flight time. The initial simulation scenario and missile parameter settings are shown in Table 1. The simulation time interval is 10ms, the missile saturation overload is 10g, and the blind zone is 50m. After the missile enters the blind zone, the remaining average velocity is taken as the value at the moment before entering the blind zone, and the guidance command only has a gravity compensation term.

[0074] Table 1

[0075]

[0076]

[0077] refer to Figure 1 The variable-speed missile residual average velocity estimation and flight time control guidance method in this embodiment specifically includes the following steps:

[0078] Step 1: Construct the missile motion model and differential geometry guidance model.

[0079] Missile motion model such as Figure 2 As shown, the missile motion model using aerodynamic control is as follows:

[0080]

[0081] Where x and y are the missile's position in the inertial frame, and v m For missile speed, θ and θ' are the velocity tilt angle and field of view angle, respectively; L and D are the lift and drag forces acting on the missile, respectively; and g is the acceleration due to gravity.

[0082] Velocity angle The field of view angle θ and the line of sight angle q satisfy the following geometric relationship:

[0083]

[0084] The lift and drag models are as follows:

[0085]

[0086] In the formula, ρ is the atmospheric density, and S ref For reference area, C L C is the lift coefficient. D This is the drag coefficient.

[0087] The lift coefficient and drag coefficient are:

[0088]

[0089] In the formula, For the lift aerodynamic derivative, Zero-lift drag coefficient, α is the induced drag coefficient, and α is the angle of attack.

[0090] The exponential form of the atmospheric density model is:

[0091] ρ=ρ0e -βy (4)

[0092] Where, ρ0 = 1.225 kg / m 2 The atmospheric density at altitude y = 0 is given by β = 1 / 7110m. -1 It is the atmospheric density variation coefficient in exponential form.

[0093] Because the missile uses aerodynamic control, its guidance acceleration a m The relationship with lift is as follows:

[0094]

[0095] Therefore, the missile differential geometry guidance model is:

[0096]

[0097] Among them, κ m For guidance curvature commands, r' represents the derivative of the relative distance r between the missile and the target with respect to the missile's arc length s, and q' represents the derivative of the line-of-sight angle q with respect to the missile's arc length s. Indicates the velocity angle The derivative with respect to the missile arc length s.

[0098] According to the relevant theories of differential geometry, the missile guidance curvature κ m and guidance acceleration a m The relationship is:

[0099]

[0100] By applying this relational equation, guidance curvature commands designed in the arc length domain can be directly converted into common guidance acceleration commands without changing any properties of the guidance commands.

[0101] Step 2: Predict the remaining flight path of the missile under proportional guidance and construct the flight path error dynamic equation in the form of bias proportional guidance.

[0102] The remaining flight path of a missile under proportional guidance can be approximated as:

[0103]

[0104] In the formula, s go denoted as , where r is the distance between the missile and the target, and N is the guidance gain of the proportional guidance law.

[0105] Guidance curvature command κ of flight path control guidance law m This can be expressed as a proportional guidance term for controlling the zero-control miss distance, plus an offset term for controlling the flight path error, in the following bias proportional guidance form:

[0106] κ m =κ PN +κ FR (9)

[0107] Among them, κ PN =Nq' is the guidance command for proportional guidance law, κ FR These are guidance commands used to control flight path errors.

[0108] Let the desired total flight distance be s d Let the distance already flown be s, then the expected remaining distance flown can be expressed as s go,d =s d -s, the flight distance error can be defined as:

[0109] ε s =s go,d -s go (10)

[0110] Substituting equations (8)-(9) into equation (10) and differentiating equation (10) with respect to the missile arc length, we obtain the flight path error dynamic equation, which is independent of the missile speed:

[0111]

[0112] Step 3: Design the flight path control guidance law based on the optimal error dynamics method.

[0113] First, we present the optimal error dynamics method with flight path error as the variable and field of view constraints:

[0114]

[0115] Where, ε′ s To represent the flight path error ε s The derivative of the missile arc length s, where K is the coefficient of the flight time control term, θ max For the field of view constraint, φ(θ / θ) max ) is an auxiliary function used to process θ→θ maxThe field of view is constrained; the auxiliary function φ(x) in the designed guidance law is selected as:

[0116]

[0117] Where x is the independent variable of the auxiliary function, which is represented by θ / θ in this invention. max It means that n is the parameter for adjusting the change of the auxiliary function, which satisfies n>0, and the larger n is, the closer φ(x) is to 1, and the faster φ(x) converges to 0 as x→1.

[0118] Substituting equations (12)-(13) into the flight path error dynamics equation, the optimal flight path control term expressed in terms of curvature can be obtained as follows:

[0119]

[0120] Substituting this optimal flight path control term into the bias proportional guidance form of the flight path control guidance law, we can obtain the flight path control guidance law expressed in curvature:

[0121]

[0122] Without altering any properties of the guidance law, the curvature-form flight path control guidance law is converted into an acceleration-form flight path control guidance law by applying the relationship between guidance curvature and guidance acceleration (7), which is:

[0123]

[0124] in, For missile line-of-sight rotation rate.

[0125] Step 4: Predict the missile velocity profile and estimate the remaining average velocity.

[0126] By fully utilizing the analytical properties of the proportional guidance law, the differential relationship between the rate of change of missile velocity and the relative distance between the missile and the target can be obtained:

[0127]

[0128] In the formula, ρ(r) is the atmospheric density with relative distance r as the independent variable, and v m (r) represents the missile velocity with r as the independent variable. Let r be the missile velocity tilt angle, θ(r) be the missile velocity lead angle with r as the independent variable, and m be the missile mass. For the aerodynamic lift derivative, The induced drag coefficient, It is a zero-lift drag coefficient.

[0129] Since there is no analytical solution to equation (17), the velocity profile can be solved by numerical integration. It should be noted that the velocity profile has the relative distance r as the independent variable. It should also be noted that the solution equation for the velocity profile is an exact differential equation in the range θ∈(-π / 2,π / 2), which eliminates the small angle assumption and has no linear approximation, thus further improving the calculation accuracy.

[0130] After obtaining the missile velocity profile, since the purpose of this invention is to unify the flight path control problem and the flight time control problem, that is, to use the flight path control guidance law to achieve the goal of controlling flight time, it is necessary to convert the missile velocity profile into a form with time as the independent variable and then calculate the average value, that is, to obtain the residual average velocity, which is:

[0131]

[0132] in, v is the remaining average velocity. m (t) represents the missile velocity profile with time as the independent variable, where t0 is the guidance start time, and t f The moment the missile hits its target.

[0133] Step 5: Convert the expected remaining flight time into the expected remaining flight distance, and achieve flight time control through the flight distance control guidance law.

[0134] Let the total expected flight time be t. d Let the flight time be t, then the expected remaining flight time is t. go,d =t d -t. Using the remaining average velocity estimate obtained in step 4, the expected remaining flight time is converted into the expected remaining flight distance:

[0135]

[0136] By further introducing a gravity compensation term, the flight path control guidance law used to control flight time can be obtained as follows:

[0137]

[0138] In this embodiment, the guidance coefficients are N=3, K=8, and n=5, respectively; the desired flight times are set to 35s, 40s, and 45s, respectively; and the field of view constraint is set to θ. max =40°.

[0139] Simulation results are as follows Figures 3-7 As shown, overall, the missiles were able to hit the target within the expected flight time, the flight time error converged to 0, and the field of view angle satisfied the constraints throughout the entire guidance process. Figure 3 and Figure 4The figures show the missile's flight trajectory and guidance acceleration variation curves, respectively. Under the guidance of the flight time control guidance law with proportional guidance law as the benchmark strategy, the longer the expected flight time, the more curved the missile's trajectory, and the greater the required guidance acceleration. This is because achieving flight time constraints requires increasing the field of view to extend the missile's trajectory. In contrast, the missile's trajectory is the shortest and smoothest under proportional guidance law guidance without flight time constraints. This is because proportional guidance law only needs to reduce the zero-control miss by decreasing the field of view. Figure 5 and Figure 6 The figures show the field of view angle change curve and the flight time change curve, respectively. As can be seen from the figures, for missiles guided by proportional guidance law, the field of view angle is the largest at the initial moment and decreases with time, and there is no field of view angle saturation. For missiles guided by the flight time control guidance method disclosed in this invention, the longer the expected flight time, the slower the convergence speed of the flight time error, and the longer the duration of the field of view angle approaching saturation. Figure 7 The curve shows the change in missile energy consumption. It is clear that the proportional guidance law without flight time constraints requires the least energy consumption. For the flight time control guidance method disclosed in this invention, it is expected that the shorter the flight time, the less energy the missile consumes.

[0140] The above description is only a preferred embodiment of the present invention and does not limit the patent scope of the present invention. All equivalent structural transformations made under the inventive concept of the present invention using the contents of the present invention specification and drawings, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. A variable speed missile residual average velocity estimation and time of flight control guidance method, characterized by, The method comprises the following steps: Step 1, constructing a missile motion model and a differential geometry guidance model; Step 2, predicting the remaining flight distance of the missile under the guidance of a proportional navigation law, and constructing a flight distance error dynamics equation in the form of biased proportional navigation; Step 3, designing a flight distance control guidance law based on an optimal error dynamics method; Step 4, predicting a missile speed profile and estimating a remaining average speed, specifically comprising: By using the analytical properties of the proportional navigation law, a differential relationship between the rate of change of the missile speed and the relative distance between the missile and the target is obtained, which is as follows: where p(r) is the atmospheric density as a function of the relative distance r, v m (r) is the missile velocity as a function of r, is the missile velocity angle as a function of r, θ(r) is the missile velocity pre-pendicular angle as a function of r, m is the missile mass, is the aerodynamic lift derivative, is the induced drag coefficient, is the zero-lift drag coefficient; The speed profile is obtained by numerical integration, and the form of the speed profile with respect to the relative distance r between the missile and the target is obtained; when the integral interval dr is small enough, the missile speed in each integral interval is considered to be constant, and then the missile speed profile is converted into a form with respect to time, and the average value is obtained, that is, the remaining average speed is obtained, which is as follows: wherein, v is the residual average velocity, m (t) is the missile velocity profile as a function of time, t0is the guidance start time, t f is the time of missile impact on the target; Step 5, converting the expected remaining flight time into expected remaining flight distance, and realizing flight time control through the flight distance control guidance law, specifically comprising: Let the total expected flight time be t d , the expected remaining flight time is t go,d = t d -t, convert this expected remaining flight time into an expected remaining flight distance using the remaining average velocity estimate, which is: A gravity compensation term is introduced to obtain a flight distance control guidance law for controlling flight time, which is as follows: Finally, flight time control is realized through the flight distance control guidance law.

2. The variable speed missile residual average velocity estimation and time of flight control guidance method of claim 1, wherein, In step 1, the motion model of the missile controlled by the air rudder is as follows: where x and y are the position of the missile in the inertial frame, v m is the velocity of the missile, and θ are the velocity inclination angle and the field of view angle, respectively, L and D are the lift and drag forces experienced by the missile, g is the gravitational acceleration, and m is the mass of the missile.

3. The variable speed missile residual average velocity estimation and time of flight control guidance method of claim 1, wherein, In step 1, the differential geometry guidance model of the missile is as follows: wherein κ m is the guidance curvature command, r' represents the derivative of the missile-target relative distance r with respect to the missile arc length s, q' represents the derivative of the line-of-sight angle q with respect to the missile arc length s, represents the velocity angle of attack with respect to the missile arc length s, and θ is the field of view angle.

4. The variable speed missile residual average velocity estimation and time of flight control guidance method according to claim 1 or 2 or 3, characterized in that, Step 2 specifically comprises: The remaining flight path s of the missile under the guidance of the proportional guidance law go Can be approximated as: In the formula, N is the guidance gain of the proportional navigation law; Guidance curvature command K of the flight-path control guidance law m may be expressed in the form of biased proportional guidance with a proportional guidance term for controlling the zero-control miss distance + a bias term for controlling the flight-path error, i.e.: Kappa m = kappa PN + kappa FR In the formula, κ PN = Nq' is the guidance command of the proportional guidance law, κ FR is the guidance command to be designed for controlling the flight path error, i.e., the flight time control term; Let the desired total flight distance be s d The desired remaining flight distance can be expressed as s go,d = s d The flight distance error can be defined as: e s = s go,d -s go By taking the differential of the arc length of the missile as a differential variable, a flight distance error dynamics equation independent of the speed of the missile is obtained, which is as follows: where ε s is the flight path error ε s Derivative of the missile arc length s.

5. The variable speed missile residual average velocity estimation and time of flight control guidance method of claim 4, wherein, Step 3 specifically comprises: An optimal error dynamics method with a flight distance error as a variable and containing a field of view angle constraint is obtained, which is as follows: where K is a coefficient of the time-of-flight control term, θ max is a field-of-view constraint, φ(θ / θ max ) is an auxiliary function for handling the field-of-view constraint θ→θ max . The auxiliary function φ(x) in the designed guidance law is selected as follows: wherein x is the argument of the auxiliary function, denoted by θ / θ max in the present application; n is a parameter for adjusting the variation of the auxiliary function, satisfying n>0, and the larger n is, the closer φ(x) is to 1, and the faster φ(x) converges to 0 as x→1. The above formula is substituted into the flight distance error dynamics equation to obtain an optimal flight distance control term expressed by curvature, which is as follows: The optimal flight distance control term is substituted into the flight distance control guidance law in the form of biased proportional navigation to obtain a flight distance control guidance law expressed by curvature, which is as follows: Without changing any properties of the guidance law, the flight distance control guidance law in the form of curvature is converted into a flight distance control guidance law in the form of acceleration by using the relationship between the guidance curvature and the guidance acceleration, which is as follows: In the formula, is the line-of-sight slew rate of the missile.

Images