A method for estimating the deviation angle of proportional guidance control in an inertial coordinate system

Abstract

A method for estimating a deviation angle of a proportional guidance control direction in an inertial coordinate system comprises: providing an inertial rectangular coordinate system, and providing a variable representation and a calculation method for relative motion; using a traditional proportional guidance algorithm; judging whether a line of sight angular velocity vector Ω(t) is parallel approaching or misaligned; determining a control direction deviation method; determining a lead angle; deriving a control direction and characteristics of an ideal proportional guidance; deriving a control direction and characteristics of a true proportional guidance; deriving a control direction and characteristics of a pure proportional guidance; establishing a coordinate system based on an instantaneous interception surface; and calculating a control direction deviation angle φ of an ideal proportional guidance. IPN ; Calculate the control direction deviation angle φ of the true proportional guidance TPN ; Calculate the control direction deviation angle φ of pure proportional guidance PPN The present invention proposes a method for calculating the control direction deviation angle of a proportional guidance type guidance system based on the true proportional guidance control direction and on the instantaneous interception surface, which is of great significance to perfecting the proportional guidance theory.

Description

Technical Field

[0001] The invention belongs to the technical field of precision guidance, and in particular relates to a method for estimating a deviation angle of a proportional guidance control direction in an inertial coordinate system. Background Art

[0002] The analytical solution or closed-loop solution of the closed-loop guidance system is very important for studying the inherent characteristics of the guidance system state, the control quantity requirements, the guidance algorithm improvement, etc. It is also a difficult theoretical problem faced by the field of precision guidance (Li Hongyan, Tao Hong, Wang Jiang, He Shaoming. Three-Dimensional Optimal Guidance Without Terminal Maneuverability Advantage. Journal of Guidance Control and Dynamics, APR 2023, DOI: 10.2514 / 1.G007483). Even for traditional proportional navigation (PN Proportional Navigation), augmented proportional navigation (APN Augmented PN), pure proportional navigation PPN (Pure PN), true proportional navigation TPN (True PN), guidance based on ZEM (Zero Miss Distance) error, etc., we currently only know the stability of the closed-loop system and the analytical solution under special circumstances. In general, we can only obtain an approximate solution in a certain sense (Koray S Ererand Raziye Tekin. Impact Vector Guidance. Journal of Guidance Control and Dynamics, Oct. 2021, pp. 1892-1901).

[0003] In fact, to solve the analytical solution problem of traditional guidance, the theoretical problem of parallel approach guidance must be solved first, because the concepts and theories related to parallel approach guidance play a very important guiding role in accurately describing the state of the guidance system. The main difficulty faced by parallel approach guidance is the lack of basic theoretical foundation. Although NA Shneydor's book "Missile Guidance and Pursuit: Kinematics, Dynamics and Control" (ISBN 1-898563-43-8, 1998, Horwood Publishing Limited, West Sussex, England) published in 1998 studied the problem of parallel approach guidance (see Chapter 4 "chapter 4.parallel navigation"), it did not give a guidance algorithm. Professor Yang Jun of Northwestern Polytechnical University pointed out in his book "Modern Air Defense Missile Guidance and Control Technology" (ISBN 9787561241943, 2014, Northwestern Polytechnical University Press) that the parallel approach method is difficult to apply in practice, and there are few examples of truly implementing the parallel approach method (see P50-P51). Professor Debasish Ghose of the Department of Aerospace Engineering of the Indian Institute of Science pointed out in his 2015 lecture "Guidance Theory and Applications" that proportional guidance is a reasonable way to implement the parallel approach method ("Proportional Navigation (PN) Guidance—Most logical way to implement constant bearing course", see Lecture 3, P14). Li-Chen, Wei-Der Chang, Dung-ming Chuang and others proposed a parallel approach guidance law (A Nonlinear Constant Bearing Guidance and Adaptive Autopilot Design for BTT Missiles[C]. Proceedings of the American Control Conference, Albuquerque, New Mexico June 1997, pp: 2774-2778) based on the convergence of the line of sight angular velocity exponent. However, it is theoretically impossible to prove that it meets the key guidance characteristics of the parallel approach method, and the simulation results do not match the parallel approach method and are only similar to proportional guidance.Zhigao Liu, an engineer at the Beijing Institute of Aerospace Microsystems, studied a parallel approach guidance law based on the algebraic equation with zero line-of-sight angular velocity (Constant Bearing Guidance Law for Homing Missiles[C]. 2017 10. th International Symposium on Computational Intelligence and Design (ISCID) IEEE, 2017, pp: 247-251), its simulation results are far from the parallel approach method.

[0004] This case uses the parallel approach guidance related theories to study proportional guidance, augmented proportional guidance, pure proportional guidance, true proportional guidance, ZEM guidance problems, etc. Solving the analytical solution problem of the closed-loop system state is of great significance to precision guidance technology.

[0005] Proportional guidance is the most in-depth and fruitful guidance method in modern guidance research, and the algorithm has appeared in many forms. A large category of improved proportional guidance is to adjust the control direction in the hope of obtaining the best performance. Up to now, proportional guidance still lacks the basis for direct comparative research, which brings many difficulties to the evaluation of guidance performance.

[0006] The deviation angle between the control direction determined by the guidance and the reference direction is the control direction deviation angle, which is an important part of the guidance optimality research. The estimation method of the proportional guidance control direction deviation angle has an important theoretical support role in the proportional guidance characteristic analysis and guidance system design. Summary of the invention

[0007] Purpose of the invention: In order to overcome the above shortcomings, the purpose of the present invention is to provide a method for estimating the deviation angle of the proportional guidance control direction in an inertial coordinate system, and to determine the estimation method of the deviation angle of the proportional guidance control direction based on the normalized mode expression of the guidance algorithm by utilizing the parallel approach misalignment error characteristics. According to the instruction form of the proportional guidance, by introducing the control error vector and the angular velocity error vector, the guidance algorithm can be expressed as a normalized mode. Based on the analysis of the control error vector and the angular velocity error vector, a reference control direction expression based on the parallel approach misalignment error and in the instantaneous interception plane is established. On this basis, the control direction characteristics of the ideal proportional guidance, true proportional guidance and pure proportional guidance are calculated and analyzed respectively, and the control direction deviation angle of the guidance method is established.

[0008] Technical solution: In order to achieve the above-mentioned purpose, the present invention provides a method for estimating the deviation angle of the proportional guidance control direction in an inertial coordinate system, comprising: firstly giving the prerequisites of the method for estimating the deviation angle of the proportional guidance control direction in an inertial coordinate system, and the specific estimation method is as follows:

[0009] S1: Give the inertial rectangular coordinate system, and give the variable representation and calculation method of relative motion;

[0010] That is, establish the inertial rectangular coordinate system F I , specifically expressed as F I (oxyz), that is, the origin of the coordinate system is o, and the three coordinate axes are ox, oy and oz. The position vector of the interceptor in this coordinate system is P m , the velocity vector is V m , the acceleration vector is a m ; Similarly, the position vector of the target in this coordinate system is P t The velocity vector is represented by V t The acceleration vector is represented by a t ; Define the relative position (distance) vector between the interceptor and the target as R(t) = P t -P m , the relative velocity vector is V(t)=V t -V m , the relative acceleration vector is a=a t -a m In the inertial rectangular coordinate system F I (oxyz), the relative position vector is specifically expressed as R = [xyz] T , the relative velocity vector is specifically expressed as The relative acceleration is specifically expressed as

[0011] remember:

[0012] R=R(t)=||R(t)||, V=V(t)=||V(t)||, (1)

[0013]

[0014] V m =V m (t)=||V m (t)|,V t =V t (t)=||V t (t)||, (3)

[0015] The relative position vector R(t) of the inertial coordinate system is the sight vector, and its rotation speed in the coordinate system, that is, the sight angular velocity vector Ω(t), satisfies:

[0016] Let Ω=||Ω(t)|| (4)

[0017] The unit vector along the direction of vectors R(t), V(t), Ω(t) is

[0018]

[0019] S2: Use the traditional proportional guidance algorithm, that is, calculate the guidance instructions a of the ideal proportional guidance respectively IPN , guidance command for true proportional guidance a TPN and guidance command a for pure proportional guidance PPN , among which, the guidance algorithms (guidance laws) of ideal proportional guidance (IPN), true proportional guidance (TPN) and pure proportional guidance (PPN), which are the methods for calculating the desired acceleration command of the interceptor;

[0020] S3: Determine whether the line of sight angular velocity vector Ω(t) is parallel approach or guidance misalignment;

[0021] S4: Control direction deviation determination method, setting the control direction deviation angle to φ, the control direction deviation angle φ is the guidance instruction a mc (t) The minimum angle between the direction and the true proportional guidance control direction;

[0022] S5: Determine the lead angle. For pure proportional guidance, the guidance lead angle L is the sum of the line of sight direction vector R(t) and the interceptor velocity vector V m The angle between

[0023] S6: Guidance command a according to the ideal proportional guidance calculated in step S2 IPN Derive the control direction and characteristics of the ideal proportional guidance;

[0024] S7: According to the guidance command a of the true proportional guidance calculated in step S2 TPN Derive the control direction and characteristics of true proportional guidance;

[0025] S8: Guidance command a for pure proportional guidance calculated in step S2 PPN The control direction and characteristics of pure proportional guidance are derived, where the control direction determined by the guidance is perpendicular to the interceptor's speed.

[0026] S9: Establish a coordinate system based on the instantaneous interception surface, that is, set the (R, V) plane as the instantaneous interception surface, establish a rectangular coordinate system on the interception surface, the first axis of the coordinate system is selected to be in the line of sight, and the unit vector is I R ; The second coordinate axis is I LOS =I Ω ×I R, which is in the vertical direction of the line of sight, that is, the true proportional guidance angular velocity error vector K TPN are unidirectional; the third coordinate axis is along I Ω Direction is the unit vector of the angular velocity direction of the line of sight and is also the normal vector of the instantaneous interception surface (R, V);

[0027] S10: Calculate the control direction deviation angle φ of the ideal proportional guidance IPN , that is, first define that the control direction deviation angle is the angle between the control method determined by the guidance algorithm and the vertical direction of the line of sight, that is, the control direction of the true proportional guidance is used as the reference; the control direction deviation angle of the ideal proportional guidance is φ IPN , then it is D m-IPN with I LOS S11: Calculate the control direction deviation angle φ of the true proportional guidance TPN ;

[0028] S12: Calculate the control direction deviation angle φ for pure proportional guidance PPN .

[0029] The method for estimating the deviation angle of the proportional guidance control direction in the inertial coordinate system of the present invention provides the guidance algorithms (guidance laws) of the ideal proportional guidance (IPN), true proportional guidance (TPN) and pure proportional guidance (PPN) in step S2, which are methods for calculating the expected acceleration command of the interceptor, as follows:

[0030] Guidance command for ideal proportional guidance a IPN Expressed as

[0031]

[0032] Guidance command for true proportional guidance a TPN Expressed as

[0033]

[0034] Guidance command for pure proportional guidance a PPN The expression is

[0035]

[0036] Where N>0 is the navigation ratio, V ref is the reference speed, which can be selected according to the situation, such as V ref =V or

[0037] The method for estimating the deviation angle of the proportional guidance control direction in the inertial coordinate system described in the present invention, the judgment process of judging whether the line of sight angular velocity vector Ω(t) is parallel approach and guidance misalignment in step 3) is as follows:

[0038] When Ω(t) = 0, it is in a parallel approach state, which satisfies the following formula:

[0039]

[0040] When Ω(t)≠0, it is in the guidance misalignment state. The guidance misalignment angle at this time is μ, which satisfies the following formula:

[0041]

[0042]

[0043] The method for estimating the deviation angle of the proportional guidance control direction in the inertial coordinate system described in the present invention and the method for determining the control direction deviation in step S4 are specifically as follows:

[0044] Define the control direction deviation angle as φ, and the control direction deviation angle φ is the guidance instruction a mc The minimum angle between the direction of (t) and the true proportional guidance control direction;

[0045] The control direction of the true proportional guidance is the reference, which is perpendicular to the line of sight. The vector along its control direction is K. LOS ,but

[0046]

[0047] The method for estimating the deviation angle of the proportional guidance control direction in the inertial coordinate system described in the present invention, the control direction and characteristics of the ideal proportional guidance in step S6 are specifically as follows:

[0048] Since the guidance algorithm of ideal proportional guidance is:

[0049]

[0050] Define the control error vector of ideal proportional guidance as D IPN , and the relationship satisfies the following formula:

[0051]

[0052] The guidance algorithm can be expressed as:

[0053] a IPN =NV ref D IPN (15)

[0054] It can be seen that the control error vector D of the ideal proportional guidance IPN In fact, it is the acceleration required when the interceptor's unit speed rotates at an angular velocity equal to the line-of-sight angular velocity. It represents the required intensity of acceleration and is also a kind of guidance error vector.

[0055] (1) The basic characteristics of ideal proportional guidance are as follows:

[0056] For ideal proportional guidance, the following relationship must be satisfied:

[0057]

[0058]

[0059] K IPN =I R +cosμI v , define R·V=-RV cosμ (18)

[0060] K IPN ⊥I v (19)

[0061] ||K IPN ||=|sinμ| (20) The present invention refers to K IPN =I R +cosμI v is the angular velocity error vector of ideal proportional guidance, K IPN dimensionless;

[0062] (2) Characteristics of the ideal proportional guidance angular velocity error vector;

[0063] Apparently

[0064] K IPN I v =I R I v +cosμI v I v =0 (21)

[0065] K IPN I R =I R I R +cosμI v I R =1-cos 2 μ=sin 2 μ (22)

[0066] therefore

[0067] K IPN ⊥I v (twenty three)

[0068] ||K IPN ||=|sinμ| (24)

[0069] (3) Control the characteristics of the error vector;

[0070] The control error vector D IPN ,because

[0071]

[0072] Define R·V=-RV cosμ, μ is the guidance misalignment angle, then the above formula gives

[0073]

[0074] Therefore

[0075]

[0076] That is

[0077]

[0078] Considering K IPN =I R +cosμI v , so the control error vector of the ideal proportional guidance satisfies the following formula:

[0079]

[0080] (4) The ideal proportional guidance control direction vector is defined as follows:

[0081] Define the angular velocity error vector K along the ideal proportional guidance IPN The unit vector of the direction is D m-IPN , called the control direction vector of the ideal proportional guidance, satisfies the following formula:

[0082]

[0083] The method for estimating the deviation angle of the proportional guidance control direction in the inertial coordinate system described in the present invention, the control direction and characteristics of the true proportional guidance in step S7, are specifically as follows:

[0084] The true proportional guidance expression is:

[0085]

[0086] The control error direction vector of true proportional guidance is defined to satisfy:

[0087] D TPN =-I R (32)

[0088] Then the following relationship holds for true proportional guidance:

[0089] a TPN =NV ref D TPN(33)

[0090]

[0091]

[0092] K TPN = cosμI R +I v , K TPN ⊥I R (36)

[0093] K TPN = cosμI R +I v is the angular velocity error vector of true proportional guidance, K TPN dimensionless;

[0094] It can be seen that the control error vector D of the true proportional guidance TPN In fact, it is the acceleration required when the interceptor's unit speed rotates at an angular velocity equal to the line-of-sight angular velocity. It represents the required intensity of acceleration and is also a kind of guidance error vector.

[0095] (1) The control error characteristics of true proportional guidance are as follows:

[0096] because

[0097]

[0098] According to the relationship between the three vector cross products, we can get

[0099]

[0100] That is

[0101]

[0102] therefore

[0103]

[0104] According to the definition of guidance misalignment angle, I R I v = -cosμ, and (I R I R )=1, so we have

[0105]

[0106] Define K TPN = cosμI R +I v is the angular velocity error vector of true proportional guidance, so

[0107]

[0108]

[0109] (2) Characteristics of the true proportional guidance angular velocity error vector;

[0110] because

[0111]

[0112] therefore

[0113] K TPN ⊥I R (45)

[0114] In addition, because

[0115]

[0116] therefore

[0117]

[0118] Therefore

[0119] ||K TPN ||=|sinμ| (48)

[0120] The above formula shows that the angular velocity error vector K of true proportional guidance is TPN The angular velocity error vector K compared to the ideal proportional guidance IPN Although the expressions of are different, the magnitudes are equal;

[0121] (3) The true proportional guidance control direction vector is defined as follows:

[0122] Define the angular velocity error vector K for true proportional guidance TPN The unit vector of the direction is D m-TPN , called the control direction vector of true proportional guidance, satisfies

[0123]

[0124] The method for estimating the deviation angle of the proportional guidance control direction in the inertial coordinate system described in the present invention, the control direction and characteristics of the pure proportional guidance are given in the step S8, wherein the control direction determined by the guidance of the pure proportional guidance is along the vertical direction of the interceptor's speed;

[0125] The guidance algorithm expression is:

[0126]

[0127] Define the control error vector of pure proportional guidance as D PPN satisfy

[0128]

[0129] Then the guidance algorithm can be expressed as:

[0130] a PPN =NV ref D PPN (52)

[0131]

[0132] and

[0133]

[0134]

[0135] Here K PPN It is called the angular velocity error vector of pure proportional guidance, wherein the present invention defines L as the velocity lead angle of the interceptor (the angle at which the interceptor velocity vector direction deviates from the line of sight); definition is the interceptor's velocity deviation angle, which is the angle between the interceptor's velocity direction and the total relative velocity vector direction in the opposite direction, satisfying

[0136]

[0137]

[0138] here represents the unit vector along the interceptor's velocity direction;

[0139] (1) Control error vector characteristics;

[0140] because

[0141]

[0142] Previous definition therefore

[0143]

[0144] Since the present invention also defines is the angular velocity error vector of pure proportional guidance, so

[0145]

[0146] Therefore, the guidance algorithm of pure proportional guidance can be expressed as

[0147] a PPN =NV ref D PPN (61)

[0148]

[0149] (2) Characteristics of the angular velocity error vector of pure proportional guidance:

[0150] because therefore

[0151]

[0152] therefore

[0153]

[0154] in addition

[0155]

[0156] Right now

[0157]

[0158] so

[0159]

[0160] Finally got

[0161]

[0162] Apparently

[0163]

[0164] The above shows that the error angular velocity vector amplitude of pure proportional guidance changes dynamically with multiple guidance variables and cannot be described by a clear parameter.

[0165] In the method for estimating the deviation angle of the proportional guidance control direction in an inertial coordinate system described in the present invention, in step S9, the specific method for establishing a rectangular coordinate system based on the instantaneous interception surface is as follows:

[0166] Set the (R, V) plane as the instantaneous interception plane, establish a rectangular coordinate system on the interception plane, the first axis of the coordinate system is selected in the line of sight direction, and the unit vector is I R ; The second coordinate axis is I LOS =I Ω ×I R , which is in the vertical direction of the line of sight, that is, the true proportional guidance angular velocity error vector K TPN are unidirectional; the third coordinate axis is along I Ω Direction is the unit vector of the angular velocity direction of the line of sight and is also the normal vector of the instantaneous interception surface (R, V);

[0167] In vector order, the unit vector of the coordinate system based on the instantaneous interception surface is: I R , I LOS and I Ω and:

[0168] I R ⊥I LOS , I R ⊥I Ω , I LOS ⊥I Ω (70)

[0169] The method for estimating the deviation angle of the control direction of the proportional guidance in the inertial coordinate system described in the present invention is as follows: in step S10, the control direction deviation angle φ of the ideal proportional guidance is calculated. IPN The specific process is as follows:

[0170] First, we define that the control direction deviation angle is the angle between the control method determined by the guidance algorithm and the vertical direction of the line of sight, that is, the control direction of the true proportional guidance is used as the reference;

[0171] The control direction deviation angle of the ideal proportional guidance is φ IPN , then it is D m-IPN with I LOS The angle of

[0172] because

[0173]

[0174] therefore

[0175]

[0176] From this we get

[0177]

[0178] Considering I v I R = -cosμ, so I v I LOS sinμ, we can get

[0179]

[0180] Since ||K TPN ||=|sinμ|, so

[0181] |cosφ IPN |=|cosμ| (75)

[0182] and

[0183] |φ IPN |=|μ| (76)

[0184] The present invention provides a method for estimating the deviation angle of the proportional guidance control direction in an inertial coordinate system. In step S11, the deviation angle φ of the control direction of the true proportional guidance is calculated. TPN The specific process is as follows:

[0185] The control direction deviation angle of the true proportional guidance is φ TPN , according to the definition:

[0186] φ TPN =0 (77)

[0187] In fact, the angular velocity error vector K of the true proportional guidance TPN =I R cosμ+I v ,,by As the benchmark,

[0188]

[0189] Because I v I LOS = sinμ, I R ⊥I LOS ,therefore

[0190]

[0191] At the same time, because ||K TPN ||=sinμ, so

[0192] cosφ TPN =1,φ TPN =0 (80)

[0193] This also shows that I LOS

[0194]

[0195] The method for estimating the deviation angle of the proportional guidance control direction in an inertial coordinate system described in the present invention is as follows: in step 12, the deviation angle φ of the control direction of the pure proportional guidance is calculated. PPN The specific process is as follows:

[0196] (1) Calculation of control direction deviation angle

[0197] Angular velocity error vector K of true proportional guidance TPN =I R cosμ+I v , the angular velocity error vector of pure proportional guidance is

[0198] First calculate

[0199]

[0200] so

[0201]

[0202] Finally got

[0203] K PPN ·K TPN = cos L-cos 2 μcosL (84)

[0204] Right now

[0205] K PPN ·K TPN =sin 2 μcos L (85)

[0206] Since ||K TPN ||=|sinμ|, so

[0207] |K PPN ·K TPN |=||K TPN || 2 |cos L| (86)

[0208] The control direction deviation angle of pure proportional guidance is φ PPN ,therefore

[0209]

[0210] From formula 69, we know Therefore, in principle φ PPN Solvable, φ PPN The range meets

[0211]

[0212]

[0213] (2) Approximate calculation of control direction deviation angle

[0214] According to the vector decomposition law, the interceptor velocity vector V m In the rectangular coordinate system based on the instantaneous interception surface, it can be expressed as

[0215] V m =V mR I R +V mLOS I LOS +V mΩ I Ω (90)

[0216] Where V mR 、V mLOS and V mΩ are the interceptor velocity vector V m The projection along the coordinate system satisfies

[0217] V mR =V m I R , V mR =V m I R , V mΩ =V m I Ω (91)

[0218] The amplitude identity is

[0219]

[0220] Since Ω×I Ω =0, so

[0221]

[0222] This shows that Ω×V m Always within the instantaneous interception plane (R, V), the amount outside the plane is useless for relative motion control. In addition, considering Ω×I R =I LOS ||Ω||,Ω×I LOS =-I R ||Ω||, so

[0223] Ω×V m =V mR I LOS ||Ω||-V mLOS I R ||Ω|| (94)

[0224] According to the definition of the control direction deviation angle (direction according to I LOS Benchmark calculation), obviously

[0225]

[0226]

[0227]

[0228] Interceptor velocity vector V m with I R The angle between the two is the leading angle L, which satisfies

[0229]

[0230] Vector Ω×V m with I LOS The angle between is the control direction deviation angle, that is

[0231]

[0232] Next, we calculate [Ω×V m ]·I LOS ;

[0233] Since Ω×V m =V mR I LOS ||Ω||-V mLOS I R ||Ω||, then

[0234]

[0235] [Ω×V m ]·I LOS Substituting into the deviation angle formula we get

[0236]

[0237] Substitute the above formula into V mR =V m cos L gives

[0238]

[0239] Since Ω×V m =V mR I LOS ||Ω||-V mLOS I R ||Ω||, therefore

[0240]

[0241] In addition: V m =V mR I R +V mLOS I LOS +V mΩ I Ω , Therefore

[0242]

[0243] Considering the decreasing property of the cosine function when the angle is small,

[0244] cosφ PPN ≥cos L (105)

[0245] |φ PPN |≤|L| (106).

[0246] It can be seen from the above technical solution that the present invention has the following beneficial effects:

[0247] 1. The present invention shows a method for estimating the deviation angle of the proportional guidance control direction in an inertial coordinate system. The method for estimating the deviation angle of the proportional guidance control direction is determined based on the normalized mode expression of the guidance algorithm by utilizing the parallel approach misalignment error characteristics. According to the instruction form of the proportional guidance, the guidance algorithm can be expressed as a normalized mode by introducing the control error vector and the angular velocity error vector. Based on the analysis of the control error vector and the angular velocity error vector, a reference control direction expression based on the parallel approach misalignment error and in the instantaneous interception plane is established. On this basis, the control direction characteristics of the ideal proportional guidance, the true proportional guidance and the pure proportional guidance are calculated and analyzed respectively, and the control direction deviation angle of the guidance method is established.

[0248] 2. The present invention proposes a method for calculating the deviation angle of the control direction of the proportional guidance type guidance based on the true proportional guidance control direction and in the instantaneous interception plane, which is of great significance to the improvement of the proportional guidance theory. The determination of the guidance instruction includes two aspects: the instruction direction and the size. It is the core of the precision guidance technology. For precision guidance, choosing a reasonable control direction is far more important than choosing the control size.

[0249] 3. The present invention standardizes ideal proportional guidance, true proportional guidance and pure proportional guidance into a unified expression mode by introducing control error vector and angular velocity error vector, laying a foundation for theoretical research on proportional guidance performance.

[0250] 4. The present invention provides a control direction calculation method based on the parallel approach misalignment error, establishes an angular velocity error vector calculation method for true proportional guidance, and uses this as a basis for calculating the control direction deviation angle of the guidance method. BRIEF DESCRIPTION OF THE DRAWINGS

[0251] Figure 1 It is a flow chart of the method for estimating the deviation angle of the proportional guidance control direction in the inertial coordinate system of the present invention;

[0252] Figure 2 Schematic diagram of the inertial coordinate system in the present invention;

[0253] Figure 3 It is a schematic diagram of the relative positions of the inertial coordinate system of the present invention;

[0254] Figure 4 It is a schematic diagram of relative velocity of the inertial coordinate system of the present invention;

[0255] Figure 5It is a schematic diagram of relative acceleration of the inertial coordinate system of the present invention;

[0256] Figure 6 It is a schematic diagram of the inertial coordinate system based on the instantaneous interception surface of the present invention;

[0257] Figure 7 It is a schematic diagram of the ideal proportional guidance control direction and its deviation angle of the present invention;

[0258] Figure 8 It is a schematic diagram of the true proportional guidance control direction and its deviation angle of the present invention;

[0259] Fig. 9 It is a schematic diagram of the pure proportional guidance control direction and its deviation angle of the present invention. DETAILED DESCRIPTION

[0260] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments.

[0261] Example

[0262] like Figures 1 to 9 A method for estimating a deviation angle of a proportional guidance control direction in an inertial coordinate system is shown, which is characterized by comprising: firstly providing a prerequisite for the method for estimating a deviation angle of a proportional guidance control direction in an inertial coordinate system, and the specific estimation method is as follows:

[0263] S1: Give the inertial rectangular coordinate system, and give the variable representation and calculation method of relative motion;

[0264] like Figure 2 As shown, the inertial rectangular coordinate system F is established. I , specifically expressed as F I (oxyz), that is, the origin of the coordinate system is o, and the three coordinate axes are ox, oy and oz. The position vector of the interceptor in this coordinate system is P m , the velocity vector is V m , the acceleration vector is a m ; Similarly, the position vector of the target in this coordinate system is P t The velocity vector is represented by V t The acceleration vector is represented by a t ; Define the relative position (distance) vector between the interceptor and the target as R(t) = P t -P m like Figure 3 As shown, the relative velocity vector is V(t)=V t -V m like Figure 4 As shown, the relative acceleration vector is a=a t -a m like Figure 5 As shown. In the inertial rectangular coordinate system FI (oxyz), the relative position vector is specifically expressed as R = [xyz] T , the relative velocity vector is specifically expressed as The relative acceleration is specifically expressed as

[0265] remember:

[0266] R=R(t)=||R(t)||, V=V(t)=||V(t)||, (107)

[0267]

[0268] V m =V m (t)=||V m (t)||,V t =V t (t)=||V t (t)||, (109)

[0269] The relative position vector R(t) of the inertial coordinate system is the sight vector, and its rotation speed in the coordinate system, that is, the sight angular velocity vector Ω(t), satisfies:

[0270] Let Ω=||Ω(t)|| (110)

[0271] The unit vector along the direction of vectors R(t), V(t), Ω(t) is

[0272]

[0273] S2: Use the traditional proportional guidance algorithm, that is, calculate the guidance instructions a of the ideal proportional guidance respectively IPN , guidance command for true proportional guidance a TPN and guidance command a for pure proportional guidance PPN , among which, the guidance algorithms (guidance laws) of ideal proportional guidance (IPN), true proportional guidance (TPN) and pure proportional guidance (PPN), which are the methods for calculating the desired acceleration command of the interceptor;

[0274] S3: Determine whether the line of sight angular velocity vector Ω(t) is parallel approach or guidance misalignment;

[0275] S4: Control direction deviation determination method, setting the control direction deviation angle to φ, the control direction deviation angle φ is the guidance instruction a mc (t) The minimum angle between the direction and the true proportional guidance control direction;

[0276] S5: Determine the lead angle. For pure proportional guidance, the guidance lead angle L is the sum of the line of sight direction vector R(t) and the interceptor velocity vector V m The angle between

[0277] S6: Guidance command a according to the ideal proportional guidance calculated in step S2 IPN Derive the control direction and characteristics of the ideal proportional guidance;

[0278] S7: According to the guidance command a of the true proportional guidance calculated in step S2 TPN Derive the control direction and characteristics of true proportional guidance;

[0279] S8: Guidance command a for pure proportional guidance calculated in step S2 PPN The control direction and characteristics of pure proportional guidance are derived, where the control direction determined by the guidance is perpendicular to the interceptor's speed.

[0280] S9: Establish a coordinate system based on the instantaneous interception surface, that is, set the (R, V) plane as the instantaneous interception surface, establish a rectangular coordinate system on the interception surface, the first axis of the coordinate system is selected to be in the line of sight, and the unit vector is I R ; The second coordinate axis is I LOS =I Ω ×I R , which is in the vertical direction of the line of sight, that is, the true proportional guidance angular velocity error vector K TPN are unidirectional; the third coordinate axis is along I Ω Direction is the unit vector of the angular velocity direction of the line of sight and is also the normal vector of the instantaneous interception surface (R, V);

[0281] S10: Calculate the control direction deviation angle φ of the ideal proportional guidance IPN , that is, first define that the control direction deviation angle is the angle between the control method determined by the guidance algorithm and the vertical direction of the line of sight, that is, the control direction of the true proportional guidance is used as the reference; the control direction deviation angle of the ideal proportional guidance is φ IPN , then it is D m-IPN with I LOS The angle of

[0282] S11: Calculate the control direction deviation angle φ of the true proportional guidance TPN ;

[0283] S12: Calculate the control direction deviation angle φ for pure proportional guidance PPN .

[0284] It should be noted that in step 1

[0285] The method for estimating the deviation angle of the proportional guidance control direction in the inertial coordinate system described in this embodiment provides the following prerequisites for estimating the deviation angle of the proportional guidance control direction in the inertial coordinate system:

[0286] Condition 1: All calculation methods are established in the inertial rectangular coordinate system. The inertial rectangular coordinate system is referred to as the inertial coordinate system, and the direction of the coordinate system axis can be freely selected according to actual needs; the absolute position, absolute velocity vector and absolute acceleration vector of the interceptor and the target are all measured in the inertial coordinate system; Condition 2: The relative position vector, relative velocity vector and relative acceleration vector of the interceptor and the target are defined according to the absolute position vector, absolute velocity vector and absolute acceleration vector of the interceptor and the target in the inertial coordinate system; the relative position vector, relative velocity vector and relative acceleration vector between the interceptor and the target are calculated as follows: the relative position vector is the absolute position vector of the target minus the absolute position vector of the interceptor, the relative velocity vector is the absolute velocity vector of the target minus the absolute velocity vector of the interceptor, and the relative acceleration vector is the absolute acceleration vector of the target minus the absolute acceleration vector of the interceptor; the relative position, relative velocity and relative acceleration belong to instantaneous physical quantities; the line of sight refers to the line connecting the interceptor to the target, and the line of sight is consistent with the direction of the relative position vector between the interceptor and the target; the rotation speed of the line of sight in the inertial space is called the line of sight angular velocity;

[0287] Condition 3: The proportional navigation (PN) includes three types of guidance instruction formation methods: pure proportional navigation (PPN), ideal proportional navigation (IPN) and true proportional navigation (TPN);

[0288] Among them, the acceleration command of the ideal proportional guidance is perpendicular to the direction of the relative velocity vector;

[0289] The acceleration command of true proportional guidance is perpendicular to the direction of the relative position vector (i.e. the direction of sight);

[0290] The acceleration command of pure proportional guidance is perpendicular to the speed direction of the interceptor itself.

[0291] The direction of the command vector of the proportional guidance is perpendicular to the line of sight angular velocity vector, and the amplitude of the command vector is proportional to the line of sight angular velocity;

[0292] Condition 4: The parallel approach method, parallel approach method guidance or parallel approach guidance have the same meaning; during the guidance process, the guidance method that can quickly return the line of sight angular velocity to zero and always maintain it at zero is called parallel approach guidance; the error of the parallel approach guidance is the guidance misalignment angle; the state in which the line of sight angular velocity is not zero is called guidance misalignment;

[0293] Condition 5: The control direction deviation angle is defined as the minimum angle between the guidance command direction and the true proportional guidance control direction, that is, the control direction deviation angle is based on the true proportional guidance control direction;

[0294] Condition 6: The guidance lead angle is based on the line of sight direction vector. The angle between the interceptor velocity vector and the line of sight direction is positive when the interceptor points in the direction of target movement, and negative otherwise.

[0295] The method for estimating the deviation angle of the proportional guidance control direction in the inertial coordinate system described in this embodiment provides the guidance algorithms (guidance laws) of the ideal proportional guidance (IPN), true proportional guidance (TPN) and pure proportional guidance (PPN), which are methods for calculating the expected acceleration command of the interceptor, as follows:

[0296] Guidance command for ideal proportional guidance a IPN Expressed as

[0297]

[0298] Guidance command for true proportional guidance a TPN Expressed as

[0299]

[0300] Guidance command for pure proportional guidance a PPN The expression is

[0301]

[0302] Where N>0 is the navigation ratio, V ref is the reference speed, which can be selected according to the situation, such as V ref =V or

[0303] In the method for estimating the deviation angle of the proportional guidance control direction in the inertial coordinate system described in this embodiment, the judgment process of judging whether the line of sight angular velocity vector Ω(t) is parallel approach and guidance misalignment in step 3) is as follows:

[0304] When Ω(t) = 0, it is in a parallel approach state, which satisfies the following formula:

[0305]

[0306] When Ω(t)≠0, it is in the guidance misalignment state. The guidance misalignment angle at this time is μ, which satisfies the following formula:

[0307]

[0308]

[0309] The method for estimating the deviation angle of the proportional guidance control direction in the inertial coordinate system described in this embodiment, the method for determining the control direction deviation in step S4 is specifically as follows:

[0310] Define the control direction deviation angle as φ, and the control direction deviation angle φ is the guidance instruction a mc The minimum angle between the direction of (t) and the true proportional guidance control direction;

[0311] The control direction of the true proportional guidance is the reference, which is perpendicular to the line of sight. The vector along its control direction is K. LOS ,but

[0312]

[0313] In the method for estimating the deviation angle of the proportional guidance control direction in the inertial coordinate system described in this embodiment, the control direction and characteristics of the ideal proportional guidance in step S6 are specifically as follows:

[0314] Since the guidance algorithm of ideal proportional guidance is:

[0315]

[0316] Define the control error vector of ideal proportional guidance as D IPN , and the relationship satisfies the following formula:

[0317]

[0318] The guidance algorithm can be expressed as:

[0319] a IPN =NV ref D IPN (121) It can be seen that the control error vector D of the ideal proportional guidance IPN In fact, it is the acceleration required when the interceptor's unit speed rotates at an angular velocity equal to the line-of-sight angular velocity. It represents the required intensity of acceleration and is also a kind of guidance error vector.

[0320] (1) The basic characteristics of ideal proportional guidance are as follows:

[0321] For ideal proportional guidance, the following relationship must be satisfied:

[0322]

[0323]

[0324] K IPN =I R +cosμI v , define R·V=-RV cosμ (124)

[0325] K IPN ⊥I v (125)

[0326] ||K IPN ||=|sinμ| (126)

[0327] The present invention is called K IPN =I R +cosμI v is the angular velocity error vector of ideal proportional guidance, K IPN dimensionless;

[0328] (2) Characteristics of the ideal proportional guidance angular velocity error vector;

[0329] Apparently

[0330] K IPN I v =I R I v +cosμI v I v =0 (127)

[0331] K IPN I R =I R I R +cosμI v I R =1-cos 2 =sin 2 μ (128)

[0332] therefore

[0333] K IPN ⊥I v (129)

[0334] ||K IPN ||=|sinμ| (130)

[0335] (3) Control the characteristics of the error vector;

[0336] The control error vector D IPN ,because

[0337]

[0338] Define R·V=-RV cosμ, μ is the guidance misalignment angle, then the above formula gives

[0339]

[0340] Therefore

[0341]

[0342] That is

[0343]

[0344] Considering K IPN =I R +cosμI v , so the control error vector of the ideal proportional guidance satisfies the following formula:

[0345]

[0346] (4) The ideal proportional guidance control direction vector is defined as follows:

[0347] Define the angular velocity error vector K along the ideal proportional guidance IPN The unit vector of the direction is D m-IPN , called the control direction vector of the ideal proportional guidance, satisfies the following formula:

[0348]

[0349] The method for estimating the deviation angle of the proportional guidance control direction in the inertial coordinate system described in this embodiment, the control direction and characteristics of the true proportional guidance in step S7 are specifically as follows:

[0350] The true proportional guidance expression is:

[0351]

[0352] The control error direction vector of true proportional guidance is defined to satisfy:

[0353] D TPN =-I R ×Ω (138)

[0354] Then the following relationship holds for true proportional guidance:

[0355] a TPN =NV ref D TPN (139)

[0356]

[0357]

[0358] K TPN = cosμI R +I v , K TPN ⊥I R (142)

[0359] K TPN = cosμI R +I v is the angular velocity error vector of true proportional guidance, K TPN dimensionless;

[0360] It can be seen that the control error vector D of the true proportional guidance TPN In fact, it is the acceleration required when the interceptor's unit speed rotates at an angular velocity equal to the line-of-sight angular velocity. It represents the required intensity of acceleration and is also a kind of guidance error vector.

[0361] (1) The control error characteristics of true proportional guidance are as follows:

[0362] because

[0363]

[0364] According to the relationship between the three vector cross products, we can get

[0365]

[0366] That is

[0367]

[0368] therefore

[0369]

[0370] According to the definition of guidance misalignment angle, I R I v = -cosμ, and (I R I R )=1, so we have

[0371]

[0372] Define K TPN = cosμI R +I v is the angular velocity error vector of true proportional guidance, so

[0373]

[0374]

[0375] (2) Characteristics of the true proportional guidance angular velocity error vector;

[0376] because

[0377]

[0378] therefore

[0379] K TPN ⊥I R (151)

[0380] In addition, because

[0381]

[0382] therefore

[0383]

[0384] Therefore

[0385] ||K TPN ||=|sinμ| (154)

[0386] The above formula shows that the angular velocity error vector K of true proportional guidance is TPN The angular velocity error vector K compared to the ideal proportional guidance IPN Although the expressions of are different, the magnitudes are equal;

[0387] (3) The true proportional guidance control direction vector is defined as follows:

[0388] Define the angular velocity error vector K for true proportional guidance TPN The unit vector of the direction is D m-TPN , called the control direction vector of true proportional guidance, satisfies

[0389]

[0390] The method for estimating the deviation angle of the proportional guidance control direction in the inertial coordinate system described in this embodiment, the control direction and characteristics of the pure proportional guidance are given in the step S8, wherein the control direction determined by the guidance of the pure proportional guidance is along the vertical direction of the interceptor's speed;

[0391] The guidance algorithm expression is:

[0392]

[0393] Define the control error vector of pure proportional guidance as D PPN satisfy

[0394]

[0395] Then the guidance algorithm can be expressed as:

[0396] a PPN =NV ref D PPN (158)

[0397]

[0398] and

[0399]

[0400]

[0401] Here K PPN It is called the angular velocity error vector of pure proportional guidance, wherein the present invention defines L as the velocity lead angle of the interceptor (the angle at which the interceptor velocity vector direction deviates from the line of sight); definition is the interceptor's velocity deviation angle, which is the angle between the interceptor's velocity direction and the total relative velocity vector direction in the opposite direction, satisfying

[0402]

[0403]

[0404] here represents the unit vector along the interceptor's velocity direction;

[0405] (1) Control error vector characteristics;

[0406] because

[0407]

[0408] Previous definition therefore

[0409]

[0410] Since the present invention also defines is the angular velocity error vector of pure proportional guidance, so

[0411]

[0412] Therefore, the guidance algorithm of pure proportional guidance can be expressed as

[0413] a PPN =NV ref D PPN (167)

[0414]

[0415] (2) Characteristics of the angular velocity error vector of pure proportional guidance:

[0416] because therefore

[0417]

[0418] therefore

[0419]

[0420] in addition

[0421]

[0422] Right now

[0423]

[0424] so

[0425]

[0426] Finally got

[0427]

[0428] Apparently

[0429]

[0430] The above shows that the error angular velocity vector amplitude of pure proportional guidance changes dynamically with multiple guidance variables and cannot be described by a clear parameter.

[0431] In the method for estimating the deviation angle of the proportional guidance control direction in an inertial coordinate system described in this embodiment, in step S9, the specific method for establishing a rectangular coordinate system based on the instantaneous interception surface is as follows:

[0432] Set the (R, V) plane as the instantaneous interception plane, establish a rectangular coordinate system on the interception plane, the first axis of the coordinate system is selected in the line of sight direction, and the unit vector is I R ; The second coordinate axis is I LOS =I Ω ×I R , which is in the vertical direction of the line of sight, that is, the true proportional guidance angular velocity error vector K TPN are unidirectional; the third coordinate axis is along I Ω Direction is the unit vector of the angular velocity direction of the line of sight and is also the normal vector of the instantaneous interception surface (R, V);

[0433] In vector order, the unit vector of the coordinate system based on the instantaneous interception surface is: I R , I LOS and I Ω and:

[0434] I R ⊥I LOS , I R ⊥I Ω , I LOS ⊥I Ω (176)

[0435] In the method for estimating the deviation angle of the control direction of the proportional guidance in the inertial coordinate system described in this embodiment, the control direction deviation angle φ of the ideal proportional guidance is calculated in step S10. IPN The specific process is as follows:

[0436] First, we define that the control direction deviation angle is the angle between the control method determined by the guidance algorithm and the vertical direction of the line of sight, that is, the control direction of the true proportional guidance is used as the reference;

[0437] The control direction deviation angle of the ideal proportional guidance is φ IPN , then it is D m-IPN with I LOS The angle of Figure 7 As shown,

[0438] because

[0439]

[0440] therefore

[0441]

[0442] From this we get

[0443]

[0444] Considering I v I R = -cosμ, so I v I LOS = sinμ, we can get

[0445]

[0446] Since ||K TPN ||=|sinμ|, so

[0447] |cosφ IPN |=|cosμ| (181)

[0448] and

[0449] |φ IPN |=|μ| (182)

[0450] like Figure 8 The method for estimating the deviation angle of the proportional guidance control direction in an inertial coordinate system described in this embodiment is as follows: in step S11, the deviation angle φ of the control direction of the true proportional guidance is calculated. TPN The specific process is as follows:

[0451] The control direction deviation angle of the true proportional guidance is φ TPN , according to the definition:

[0452] φ TPN =0 (183)

[0453] In fact, the angular velocity error vector K of the true proportional guidance TPN =I R cosμ+I v ,by As the benchmark,

[0454]

[0455] Because I v I LOS = sinμ, I R ⊥I LOS ,therefore

[0456]

[0457] At the same time, because ||K TPN ||=sinμ, so

[0458] cosφ TPN =1,φ TPN =0 (186)

[0459] This also shows that I LOS

[0460]

[0461] like Fig. 9 As shown, in the method for estimating the deviation angle of the proportional guidance control direction in the inertial coordinate system described in this embodiment, the control direction deviation angle φ of the pure proportional guidance is calculated in step 12. PPN The specific process is as follows:

[0462] (1) Calculation of control direction deviation angle

[0463] Angular velocity error vector K of true proportional guidance TPN =I R cosμ+I v , the angular velocity error vector of pure proportional guidance is

[0464] First calculate

[0465]

[0466] so

[0467]

[0468] Finally got

[0469] K PPN·K TPN = cos L-cos 2 μcos L (190)

[0470] Right now

[0471] K PPN ·K TPN =sin 2 μcos L (191)

[0472] Since ||K TPN ||=|sin|, so

[0473] |K PPN ·K TPN |=||K TPN || 2 |cos L| (192)

[0474] The control direction deviation angle of pure proportional guidance is φ PPN ,therefore

[0475]

[0476] From formula 69, we know Therefore, in principle PPN Solvable, φ PPN The range meets

[0477]

[0478]

[0479] (2) Approximate calculation of control direction deviation angle

[0480] like Figure 6 As shown, according to the vector decomposition law, the interceptor velocity vector V m In the rectangular coordinate system based on the instantaneous interception surface, it can be expressed as

[0481] V m =V mR I R +V mLOS I LOS +V mΩ I Ω (196)

[0482] Where V mR 、V mLOS and V mΩ are the interceptor velocity vector V m The projection along the coordinate system satisfies

[0483] V mR =Vm I R , V mR =V m I R , V mΩ =V m I Ω (197)

[0484] The amplitude identity is

[0485]

[0486] Since Ω×I Ω =0, so

[0487]

[0488] This shows that Ω×V m Always within the instantaneous interception plane (R, V), the amount outside the plane is useless for relative motion control. In addition, considering Ω×I R =I LOS ||Ω||,Ω×I LOS =-I R ||Ω||, so

[0489] Ω×V m =V mR I LOS ||Ω||-V mLOS I R ||Ω|| (200)

[0490] According to the definition of the control direction deviation angle (direction according to I LOS Benchmark calculation), obviously

[0491]

[0492]

[0493]

[0494] Interceptor velocity vector V m with I R The angle between the two is the leading angle L, which satisfies

[0495]

[0496] Vector Ω×V m with I LOS The angle between is the control direction deviation angle, that is

[0497]

[0498] Next, we calculate [Ω×Vm ]·I LOS ;

[0499] Since Ω×V m =V mR I LOS ||Ω||-V mLOS I R ||Ω||, then

[0500]

[0501] [Ω×V m ]·I LOS Substituting into the deviation angle formula we get

[0502]

[0503] Substitute the above formula into V mR =V m cos L gives

[0504]

[0505] Since Ω×V m =V mR I LOS ||Ω||-V mLOS I R ||Ω||, therefore

[0506]

[0507] In addition: V m =V mR I R +V mLOS I LOS +V mΩ I Ω , Therefore

[0508]

[0509] Considering the decreasing property of the cosine function when the angle is small,

[0510] cosφ PPN ≥cos L (211)

[0511] |φ PPN |≤|L| (212).

[0512] The above description is only a preferred embodiment of the present invention. It should be pointed out that a person skilled in the art can make several improvements without departing from the principle of the present invention, and these improvements should also be regarded as within the protection scope of the present invention.

Claims

1. A method for estimating a deviation angle of a proportional guidance control direction in an inertial coordinate system, characterized in that: include: First, the prerequisites for the estimation method of the deviation angle of the proportional guidance control direction in the inertial coordinate system are given. The specific estimation method is as follows: S1: Give the inertial rectangular coordinate system, and give the variable representation and calculation method of relative motion; That is, establish the inertial rectangular coordinate system F I , specifically expressed as F I (oxyz), that is, the origin of the coordinate system is o, and the three coordinate axes are ox, oy and oz; The position vector of the interceptor in this coordinate system is P m , the velocity vector is V m , the acceleration vector is a m ; Similarly, the position vector of the target in this coordinate system is P t The velocity vector is represented by V t The acceleration vector is represented by a t ; Define the relative position vector of the interceptor and the target as R(t)=P t -P m , the relative velocity vector is V(t)=V t -V m , the relative acceleration vector is a=a t -a m ; In the inertial rectangular coordinate system F I (oxyz), the relative position vector is specifically expressed as R = [xyz] T , the relative velocity vector is specifically expressed as The relative acceleration is specifically expressed as remember: R=R(t)=||R(t)||, V=V(t)=||V(t)||, (1) V m =V m (t)=||V m (t)||,V t =V t (t)=||V t (t)||, (3) Where R represents the magnitude of the relative position vector, represents the rate of change of the relative position vector, V represents the magnitude of the relative velocity vector, and V m and V t Respectively represent the speed of the interceptor and the target; The relative position vector R(t) of the inertial coordinate system is the sight vector, and its rotation speed in the coordinate system, that is, the sight angular velocity vector Ω(t), satisfies: The unit vector along the direction of vectors R(t), V(t), Ω(t) is S2: Use the traditional proportional guidance algorithm, that is, calculate the guidance instructions a of the ideal proportional guidance respectively IPN , guidance command for true proportional guidance a TPN and guidance command a for pure proportional guidance PPN , where the guidance algorithms of ideal proportional guidance, true proportional guidance and pure proportional guidance are the methods for calculating the desired acceleration command of the interceptor; S3: Determine whether the line of sight angular velocity vector Ω(t) is parallel approach or guidance misalignment; S4: Control direction deviation determination method, setting the control direction deviation angle to φ, the control direction deviation angle φ is the guidance instruction a mc (t) The minimum angle between the direction and the true proportional guidance control direction; S5: Determine the lead angle. For pure proportional guidance, the guidance lead angle L is the sum of the line of sight direction vector R(t) and the interceptor velocity vector V m The angle between S6: Guidance command a according to the ideal proportional guidance calculated in step S2 IPN Derive the control direction and characteristics of the ideal proportional guidance; S7: According to the guidance command a of the true proportional guidance calculated in step S2 TPN Derive the control direction and characteristics of true proportional guidance; S8: Guidance command a for pure proportional guidance calculated in step S2 PPN The control direction and characteristics of pure proportional guidance are derived, where the control direction determined by the guidance is perpendicular to the interceptor's speed. S9: Establish a coordinate system based on the instantaneous interception surface, that is, set the (R, V) plane as the instantaneous interception surface, establish a rectangular coordinate system on the interception surface, the first axis of the coordinate system is selected to be in the line of sight direction, and the unit vector is I R ; The second coordinate axis is I LOS =I Ω ×I R , which is in the vertical direction of the line of sight, that is, the true proportional guidance angular velocity error vector K TPN are unidirectional; The third coordinate axis is along I Ω Direction is the unit vector of the line of sight angular velocity direction, and is also the normal vector of the instantaneous interception surface (R, V); S10: Calculate the control direction deviation angle φ of the ideal proportional guidance IPN , that is, first define that the control direction deviation angle is the angle between the control method determined by the guidance algorithm and the vertical direction of the line of sight, that is, the control direction of the true proportional guidance is used as the reference; the control direction deviation angle of the ideal proportional guidance is φ IPN , then it is Dm -IPN with I LOS The angle of S11: Calculate the control direction deviation angle φ of the true proportional guidance TPN ; S12: Calculate the control direction deviation angle φ for pure proportional guidance PPN .

2. The method for estimating the deviation angle of proportional guidance control direction in an inertial coordinate system according to claim 1, characterized in that: The guidance algorithms of ideal proportional guidance, true proportional guidance and pure proportional guidance are given. They are the methods for calculating the expected acceleration command of the interceptor, as follows: Guidance command for ideal proportional guidance a IPN Expressed as Guidance command for true proportional guidance a TPN Expressed as Guidance command for pure proportional guidance a PPN The expression is Where N>0 is the navigation ratio, V ref is the reference speed, V ref =V or 3. The method for estimating the deviation angle of the proportional guidance control direction in the inertial coordinate system according to claim 2, characterized in that: The specific process of judging whether the line of sight angular velocity vector Ω(t) is parallel approaching and guidance misalignment in step S3 is as follows: When Ω(t) = 0, it is in a parallel approach state, which satisfies the following formula: When Ω(t)≠0, it is in the guidance misalignment state. The guidance misalignment angle at this time is μ, which satisfies the following formula:

4. The method for estimating the deviation angle of proportional guidance control direction in an inertial coordinate system according to claim 3 is characterized in that: The control direction deviation determination method in step S4 is specifically as follows: Define the control direction deviation angle as φ, and the control direction deviation angle φ is the guidance instruction a mc The direction of (t) is related to the true proportional guide The minimum angle between the guiding control directions; The control direction of the true proportional guidance is the reference, which is perpendicular to the line of sight. The vector along its control direction is K. LOS ,but 5. The method for estimating the deviation angle of proportional guidance control direction in an inertial coordinate system according to claim 4, characterized in that: The control direction and characteristics of the ideal proportional guidance in step S6 are as follows: Since the guidance algorithm of ideal proportional guidance is: Define the control error vector of ideal proportional guidance as D IPN , and the relationship satisfies the following formula: The guidance algorithm can be expressed as: a IPN =NV ref D IPN (15) It can be seen that the control error vector D of the ideal proportional guidance IPN In fact, it is the acceleration required when the interceptor's unit speed rotates at an angular velocity equal to the line-of-sight angular velocity. It represents the required intensity of acceleration and is also a kind of guidance error vector. (1) The basic characteristics of ideal proportional guidance are as follows: For ideal proportional guidance, the following relationship must be satisfied: K IPN =I R +cosμI v , define R·V=-RV cosμ (18) K IPN ⊥I v (19) ||K IPN ||=|sinμ| (20) K IPN =I R +cosμI v is the angular velocity error vector of ideal proportional guidance, K IPN Dimensionless, where μ is the angle between the relative position vector R and the relative velocity vector V; (2) Characteristics of the ideal proportional guidance angular velocity error vector; K IPN ·I v =I R ·I v +cosμI v ·I v =0 (21) K IPN ·I R =I R ·I R +cosμI v ·I R =1-cos 2 μ=sin 2 m (22) therefore K IPN ⊥I v (23) ||K IPN ||=|sinμ| (24) (3) Control the characteristics of the error vector; The control error vector D IPN ,because Define R·V=-RVcosμ, μ is the guidance misalignment angle, then the above formula gives Therefore That is Considering K IPN =I R +cosμI v , so the control error vector of the ideal proportional guidance satisfies the following formula: (4) The ideal proportional guidance control direction vector is defined as follows: Define the angular velocity error vector K along the ideal proportional guidance IPN The unit vector of the direction is D m-IPN , called the control direction vector of the ideal proportional guidance, satisfies the following formula:

6. The method for estimating the deviation angle of proportional guidance control direction in an inertial coordinate system according to claim 5, characterized in that: The control direction and characteristics of the true proportional guidance in step S7 are as follows: The true proportional guidance expression is: The control error direction vector of true proportional guidance is defined to satisfy: D TPN =-I R ×Ω (32) Then the following relationship holds for true proportional guidance: a TPN =NV ref D TPN (33) K TPN =cosμI R +I v ,K TPN ⊥I R (36) K TPN = cosμI R +I v is the angular velocity error vector of true proportional guidance, K TPN dimensionless; It can be seen that the control error vector D of the true proportional guidance TPN In fact, it is the acceleration required when the interceptor's unit speed rotates at an angular velocity equal to the line-of-sight angular velocity. It represents the required intensity of acceleration and is also a kind of guidance error vector. (1) The control error characteristics of true proportional guidance are as follows: because According to the relationship between the three vector cross products, we can get That is therefore According to the definition of guidance misalignment angle, I R I v = -cosμ, and (I R I R )=1, so we have Define K TPN = cosμI R +I v is the angular velocity error vector of true proportional guidance, so (2) Characteristics of the true proportional guidance angular velocity error vector; because therefore K TPN ⊥I R (45) In addition, therefore Therefore ||K TPN ||=|sinμ| (48) The above formula shows that the angular velocity error vector K of true proportional guidance is TPN The angular velocity error vector K compared to the ideal proportional guidance IPN Although the expressions of are different, the magnitudes are equal; (3) The true proportional guidance control direction vector is defined as follows: Define the angular velocity error vector K for true proportional guidance TPN The unit vector of the direction is D m-TPN , called the control direction vector of true proportional guidance, satisfies 7. The method for estimating the deviation angle of proportional guidance control direction in an inertial coordinate system according to claim 6, characterized in that: The control direction and characteristics of pure proportional guidance are given in step S8, wherein the control direction of pure proportional guidance determined by guidance is along the vertical direction of the interceptor's speed; The guidance algorithm expression is: Define the control error vector of pure proportional guidance as D PPN satisfy Then the guidance algorithm can be expressed as: a PPN =NV ref D PPN (52) and Here K PPN It is called the angular velocity error vector of pure proportional guidance, L is the velocity lead angle of the interceptor, that is, the angle at which the velocity direction deviates from the line of sight; definition is the interceptor's velocity deviation angle, which is the angle between the interceptor's velocity direction and the total relative velocity vector direction in the opposite direction, satisfying here represents the unit vector along the interceptor's velocity direction; (1) Control error vector characteristics; because Previous definition therefore Since we also define is the angular velocity error vector of pure proportional guidance, so Therefore, the guidance algorithm of pure proportional guidance can be expressed as a PPN =NV ref D PPN (61) (2) Characteristics of the angular velocity error vector of pure proportional guidance: because therefore therefore in addition Right now so Finally got Apparently The above shows that the error angular velocity vector amplitude of pure proportional guidance changes dynamically with multiple guidance variables and cannot be described by a clear parameter.

8. The method for estimating the deviation angle of proportional guidance control direction in an inertial coordinate system according to claim 7, characterized in that: In step S9, the specific method for establishing a rectangular coordinate system based on the instantaneous interception surface is as follows: Set the (R, V) plane as the instantaneous interception plane, establish a rectangular coordinate system on the interception plane, the first axis of the coordinate system is selected to be in the line of sight, and the unit vector is I R ; The second coordinate axis is I LOS =I Ω ×I R , which is in the vertical direction of the line of sight, that is, the true proportional guidance angular velocity error vector K TPN are unidirectional; The third coordinate axis is along I Ω Direction is the unit vector of the line of sight angular velocity direction, and is also the normal vector of the instantaneous interception surface (R, V); In vector order, the unit vector of the coordinate system based on the instantaneous interception surface is: I R , I LOS and I Ω and: I R ⊥I LOS ,I R ⊥I Ω ,I LOS ⊥I Ω (70)。 9. The method for estimating the deviation angle of proportional guidance control direction in an inertial coordinate system according to claim 8, characterized in that: In step S10, the control direction deviation angle φI of the ideal proportional guidance is calculated. PN The specific process is as follows: First, we define that the control direction deviation angle is the angle between the control method determined by the guidance algorithm and the vertical direction of the line of sight, that is, the control direction of the true proportional guidance is used as the reference; The control direction deviation angle of the ideal proportional guidance is φ IPN , then it is D m-IPN with I LOS The angle of because therefore From this we get Considering I v I R = -cosμ, so I v I LOS = sinμ, we can get Since ||K TPN ||=|sinμ|, so |cosφ IPN |=|cosμ| (75) and |f IPN |=|μ| (76).

10. The method for estimating the deviation angle of proportional guidance control direction in an inertial coordinate system according to claim 1, characterized in that: In step S11, the control direction deviation angle φ of the true proportional guidance is calculated. TPN The specific process is as follows: The control direction deviation angle of the true proportional guidance is φ TPN , according to the definition: f TPN =0 (77) In fact, the angular velocity error vector K of the true proportional guidance TPN =I R cosμ+I v , with I LOS As the benchmark, Because I v I LOS = sinμ, I R ⊥I LOS ,therefore At the same time, because ||K TPN ||=sinμ, so cosφ TPN =1,φ TPN =0 (80) This also shows that I LOS In step 12, the control direction deviation angle φ of the pure proportional guidance is calculated. PPN The specific process is as follows: (1) Calculation of control direction deviation angle Angular velocity error vector K of true proportional guidance TPN =I R cosμ+I v , the angular velocity error vector of pure proportional guidance is First calculate so Finally got K PPN ·K TPN =cosL-cos 2 μcosL (84) Right now K PPN ·K TPN =you 2 μcosL (85) Since ||K TPN ||=|sinμ|, so |K PPN ·K TPN |=||K TPN || 2 |cosL| (86) The control direction deviation angle of pure proportional guidance is φ PPN ,therefore From formula 69, we know Therefore, in principle PPN Solvable, φ PPN The range meets (2) Approximate calculation of control direction deviation angle According to the vector decomposition law, the interceptor velocity vector V can be expressed in the rectangular coordinate system based on the instantaneous interception surface as follows: V m =V mR I R +V mLOS I LOS +V mΩ I Ω (90) Where V mR 、V mLOS and V mΩ are the interceptor velocity vector V m The projection along the coordinate system satisfies V mR =V m .I R ,V mLOS =V m ·I LOS ,V mΩ =V m ·I Ω (91) The amplitude identity is Since Ω×IΩ=0, This shows that Ω×Vm is always within the instantaneous interception plane (R, V), and the amount outside the plane is useless for relative motion control; in addition, considering Ω×I R =I LOS ||Ω||,Ω×I LOS =-I R ||Ω||, so Ω×V m =V mR I LOS ||Ω||-V mLOS I R ||Ω|| (94) According to the definition of the control direction deviation angle, the direction is I LOS Benchmark calculations The interceptor velocity vector Vm and I R The angle between the two is the leading angle L, which satisfies Vector Ω×V m with I LOS The angle between is the control direction deviation angle, that is, Next, we calculate [Ω×V m ]·I LOS ; Since Ω×V m =V mR I LOS ||Ω||-V mLOS I R ||Ω||, then [Ω×V m ]·I LOS Substituting into the deviation angle formula we get Substitute V into the above formula mR =V m cosL Since Ω×V m =V mR I LOS ||Ω||-V mLOS I R ||Ω||, therefore In addition: V m =V mR I R +V mLOS I LOS +V mΩ I Ω , Therefore Considering the decreasing property of the cosine function when the angle is small, cosφ PPN ≥cosL (105) |f PPN |≤|L| (106).

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