Inertial-line-of-sight coordinate system interaction maneuvering target dynamic estimator design method

Abstract

This invention discloses a design method for a dynamic estimator of a maneuvering target using an inertial-line-of-sight coordinate system. The method includes: establishing a transformation relationship between the inertial and line-of-sight coordinate systems; selecting the relative distance between the missile and the target, the line-of-sight tilt angle, and the line-of-sight deflection angle as system states in both coordinate systems, and establishing the dynamic equations of the missile interception system in the line-of-sight coordinate system; defining non-deterministic equivalent auxiliary variables for target acceleration interference using the transformation relationship between the inertial and line-of-sight coordinate systems; and constructing a Luenberger observer for these non-deterministic equivalent auxiliary variables to design a target acceleration estimator. This invention utilizes the transformation relationship between the inertial and line-of-sight coordinate systems to introduce non-deterministic equivalent auxiliary variables, estimates these variables, and thus obtains an estimate of the target acceleration, providing technical support and solutions for the aerospace engineering practice of interference observer methods.

Description

Technical Field

[0001] This invention relates to the field of automation control technology, and in particular to a design method for a dynamic estimator of a maneuvering target with inertial-line-of-sight coordinate system interaction. Background Technology

[0002] In certain specific situations, it is necessary to use missiles to intercept non-maneuvering or low-speed maneuvering targets. The missile's speed is much greater than the target's speed, and the miss distance only needs to be within the missile's kill radius. Therefore, proportional guidance can achieve satisfactory guidance accuracy. However, existing targets intercepted by missiles are usually highly maneuverable, and traditional proportional guidance will produce a large miss distance. Modern guidance laws require known target acceleration information during the design process, thus necessitating the estimation of target acceleration that cannot be directly measured. Currently, the jamming observer method is the most representative method for estimating unknown targets. The jamming observer can use measurement information such as relative distance, relative distance change rate, and line-of-sight angle provided by the missile seeker to estimate the target maneuverability, and use a feedforward system to reduce the impact of unknown target maneuverability on guidance accuracy.

[0003] Typically, jamming observers are designed to estimate unknowns caused by target maneuvers as composite interference. However, during missile interception, target maneuvers are strongly coupled with the system state. Clearly, conventional methods for handling composite interference are not conducive to accurately estimating unknown target maneuvers, thus affecting guidance accuracy. Therefore, a jamming observer with higher estimation accuracy for unknown target maneuvers is needed to effectively improve interception accuracy. Summary of the Invention

[0004] Purpose of the invention: To address the above problems, the purpose of this invention is to provide a design method for a dynamic estimator of a maneuvering target based on inertial-line-of-sight coordinate system interaction. This method utilizes the transformation relationship between the inertial coordinate system and the line-of-sight coordinate system to introduce non-deterministic equivalent auxiliary variables, and estimates these non-deterministic equivalent auxiliary variables to obtain an estimated value of the target acceleration.

[0005] Technical solution: The present invention provides a design method for a dynamic estimator of a maneuvering target with inertial-line-of-sight coordinate system interaction, comprising the following steps:

[0006] Step 1: Determine the missile coordinate system and establish the transformation relationship between the inertial coordinate system and the line-of-sight coordinate system;

[0007] Step 2: Select the relative distance between the missile and the target, the line-of-sight tilt angle, and the line-of-sight deflection angle in the inertial coordinate system and the line-of-sight coordinate system as the system states, and establish the dynamic equations of the missile interception system in the line-of-sight coordinate system;

[0008] Step 3: Using the transformation relationship between the inertial and line-of-sight coordinate systems, define the nondeterministic equivalent auxiliary variable for the target acceleration disturbance;

[0009] Step 4: Construct a Luenberger observer for the non-deterministic equivalent auxiliary variables and design a target acceleration estimator.

[0010] Furthermore, step 1 specifically includes the following processes:

[0011] Establishing an inertial coordinate system (OI) x I y I z The origin O of the inertial coordinate system is taken at the center of mass of the missile, OI x The axis is in the horizontal plane, OI z Perpendicular to the ground, OI y Axis and OI x and OI z The two coordinate axes are perpendicular and form a right-handed coordinate system;

[0012] Establish line-of-sight coordinate system OL l L χ L γ The origin O of the line-of-sight coordinate system is taken at the center of mass of the missile, OL. l The axis coincides with the missile-target line of sight, OL γ The axis is located in the OL area l In the longitudinal plane of the axis, with OL l Axis perpendicular, OL χ The axis is perpendicular to OL l and OL γ The axes form a right-handed coordinate system;

[0013] Then from the inertial coordinate system OI x I y I z To the line-of-sight coordinate system OL l L ω L γ The coordinate transformation matrix is ​​represented as:

[0014]

[0015] Where χ is the line of sight deflection angle and γ is the line of sight tilt angle.

[0016] Furthermore, step 2 specifically includes the following processes:

[0017] Define R L V L and ω L Let the relative position vector, relative velocity vector, and rotational angular velocity of the line-of-sight coordinate system relative to the inertial coordinate system be respectively. Then, the Coriolis equation can be expressed as:

[0018]

[0019] Where t represents time;

[0020] Based on the transformation relationship between the line-of-sight coordinate system and the inertial coordinate system, the rotational angular velocity of the line-of-sight coordinate system relative to the inertial coordinate system can be expressed as:

[0021]

[0022] Therefore, the Coriolis equation is expressed in the line-of-sight coordinate system as:

[0023]

[0024] Where l is the distance between the missile and the target;

[0025] According to Coriolis theorem, the derivative of the relative velocity vector in the line-of-sight coordinate system can be expressed as:

[0026]

[0027] The expression for establishing the relative motion dynamics model of the missile and the target in the line-of-sight coordinate system is as follows:

[0028]

[0029] Among them, let a L =[a l ,a χ ,a γ ] T Let a be the relative acceleration between the missile and the target in the line-of-sight coordinate system. l a χ a γ Representing the line-of-sight coordinate system OL l L χ L γ The component of relative acceleration, a L It is calculated from the following expression:

[0030]

[0031] in, These are the accelerations of the target and the missile in the inertial coordinate system, respectively.

[0032] Define the state vector x1 = [l, χ, γ] T , Therefore, the dynamic equations of the missile interception system in the line-of-sight coordinate system can be obtained as follows:

[0033]

[0034] in, and y c =x1 are the measurable and controllable output vectors, respectively. and Given function matrices, in the following forms:

[0035]

[0036]

[0037] Furthermore, the target's acceleration command is implemented by the autopilot, which tracks the target command by adjusting aerodynamic control surfaces or thrusters; therefore, the unknown acceleration command... Compared with actual acceleration a t There is a lag between them, and their relationship can be represented using the following nth-order linear system:

[0038]

[0039] in, The target autopilot status, and Given a known constant matrix (A, C) satisfying the observability condition, and an unknown time-varying vector Δ. u Bounded, that is:

[0040] ||Δ u || 2 ≤λ

[0041] Where λ is a constant vector, and λ>0.

[0042] Furthermore, step 3 specifically includes the following processes:

[0043] The expression for the nondeterministic equivalent auxiliary variable s is defined as follows:

[0044] s = a t -L(y m )

[0045] in, For the nonlinear function vector that needs to be designed;

[0046] The derivative form of the non-deterministic equivalent auxiliary variable is as follows:

[0047]

[0048] Substituting the expression for s into the derivative From the expression, we can obtain:

[0049]

[0050] in, Given a known function vector;

[0051] vector of nonlinear function Designed in the form of a linear equation, let the nonlinear function vector L(y) m The representation is as follows:

[0052] L(y m )=κG -1 x2

[0053] in, For the constant matrix that needs to be designed;

[0054] The dynamic induction of the final nondeterministic equivalent auxiliary variable is then expressed as follows:

[0055]

[0056] Where W = CAC -1 -k.

[0057] Furthermore, step 4 specifically includes the following processes:

[0058] For the defined nondeterministic equivalent auxiliary variable s, the observer expression is designed as follows:

[0059]

[0060] in, This is an estimate of the non-deterministic equivalent auxiliary variable s, where the estimated variable s is simply the unknown state a. t The partial estimate is combined with the designed auxiliary nonlinear function L to obtain a. t A complete estimate.

[0061] Beneficial Effects: Compared with existing technologies, the significant advantages of this invention are as follows: This invention proposes a design method for a maneuvering target dynamic estimator based on inertial-line-of-sight coordinate system interaction, addressing the general target dynamics in engineering. This method utilizes the transformation relationship between the inertial and line-of-sight coordinate systems to introduce non-deterministic equivalent auxiliary variables, estimating these variables to obtain an estimate of the target acceleration. This provides technical support and solutions for the aerospace engineering practice of interference observer methods. Furthermore, the design method of this invention decouples target acceleration from system state, improving the estimation accuracy of target maneuvers during terminal guidance interception. Attached Figure Description

[0062] Figure 1 A flowchart illustrating the design method for a dynamic estimator for a maneuvering target with inertial-line-of-sight coordinate system interaction, provided for an embodiment.

[0063] Figure 2This represents the coordinate transformation relationship between the inertial coordinate system and the line-of-sight coordinate system. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments.

[0065] Figure 1 The diagram shown is a flowchart of a design method for a maneuvering target dynamic estimator with inertial-line-of-sight coordinate system interaction as described in this embodiment. The method specifically includes the following steps:

[0066] Step 1: Determine the missile coordinate system and establish the transformation relationship between the inertial coordinate system and the line-of-sight coordinate system.

[0067] In one example, step 1 above specifically includes the following process:

[0068] like Figure 2 As shown, an inertial coordinate system OI is established. x I y I z The origin O of the inertial coordinate system is taken at the center of mass of the missile, OI x The axis lies in the horizontal plane, and is typically taken as positive in the direction the missile is pointing towards the target at the moment of launch; OI z Perpendicular to the ground, upward is positive; OI y Axis and OI x and OI z The two coordinate axes are perpendicular and form a right-handed coordinate system, and the inertial coordinate system OI. x I y I z It is fixedly connected to the missile body.

[0069] Establish line-of-sight coordinate system OL l L χ L γ The origin O of the line-of-sight coordinate system is taken at the center of mass of the missile, OL. l The axis coincides with the missile-target line of sight, and the direction from the missile to the target is positive; OL γ The axis is located in the OL area l In the longitudinal plane of the axis, with OL l An axis that is perpendicular and points downwards is considered positive; OL χ The axis is perpendicular to OL l and OL γ The axes form a right-handed coordinate system.

[0070] Then we obtain the coordinates from the inertial coordinate system OI. x I y I z To the line-of-sight coordinate system OL l L χ L γThe coordinate transformation matrix is:

[0071]

[0072] Where χ is the line of sight deflection angle and γ is the line of sight tilt angle.

[0073] The aforementioned line-of-sight angle χ is OL l The projection of the axis onto the horizontal plane and the OI x The angle between axes, such as Figure 2 As shown, along OI z When viewed from above the axis, if OI x Rotate the axis to OL l If the projection of the axis onto the horizontal plane is counterclockwise, then the line-of-sight deflection angle χ is positive; otherwise, it is negative. This can be expressed using the components of an inertial coordinate system. The line of sight tilt γ is OL l Axis and horizontal plane OI x I y The angle between them. If OL l The axis is in the horizontal plane OI x I y When the line of sight is above the reference inertial coordinate system, the tilt angle γ is positive; otherwise, it is negative. Expressed in terms of the components of the reference inertial coordinate system, γ = arctan(y mt / x mt ), where x mt y mt z mt These represent the components of the relative coordinates between the missile and the target in the inertial coordinate system.

[0074] Step 2: Select the relative distance between the missile and the target, the line-of-sight tilt angle, and the line-of-sight deflection angle in the inertial coordinate system and the line-of-sight coordinate system as the system states, and establish the dynamic equations of the missile interception system in the line-of-sight coordinate system.

[0075] In one example, step 2 above specifically includes the following process:

[0076] Define R L V L and ω L Let the relative position vector, relative velocity vector, and rotational angular velocity of the line-of-sight coordinate system relative to the inertial coordinate system be respectively. Then, the Coriolis equation can be expressed as:

[0077]

[0078] Where t represents time;

[0079] Based on the transformation relationship between the line-of-sight coordinate system and the inertial coordinate system, the rotational angular velocity of the line-of-sight coordinate system relative to the inertial coordinate system is expressed as:

[0080]

[0081] Therefore, the Coriolis equation is expressed in the line-of-sight coordinate system as:

[0082]

[0083] Where l is the distance between the missile and the target;

[0084] According to Coriolis theorem, the derivative of the relative velocity vector in the line-of-sight coordinate system can be expressed as:

[0085]

[0086] The expression for establishing the relative motion dynamics model of the missile and the target in the line-of-sight coordinate system is as follows:

[0087]

[0088] Among them, let a L =[a l ,a χ ,a γ ] T Let a be the relative acceleration between the missile and the target in the line-of-sight coordinate system. l a χ a γ Representing the line-of-sight coordinate system OL l L χ L γ The component of relative acceleration, a L It can be calculated using the following expression:

[0089]

[0090] in, These are the accelerations of the target and the missile in the inertial coordinate system, respectively.

[0091] Define the state vector x1 = [l, χ, γ] T , Therefore, the dynamic equations of the missile interception system in the line-of-sight coordinate system can be obtained as follows:

[0092]

[0093] in, and y c =x1 are the measurable and controllable output vectors, respectively. and Given function matrices, in the following forms:

[0094]

[0095]

[0096] The distance l mentioned above refers to the distance between the missile and the target, expressed in terms of components of the reference inertial coordinate system as l = ||L||, where L = [x mt y mt z mt ] T Line-of-sight variables l, χ, γ can be obtained from measuring devices such as radar or infrared seekers.

[0097] Step 3: Using the transformation relationship between the inertial and line-of-sight coordinate systems, define the nondeterministic equivalent auxiliary variable for the target acceleration disturbance.

[0098] In practical applications, the target's acceleration command is implemented by the autopilot. The autopilot tracks the target command by adjusting aerodynamic control surfaces or thrusters; therefore, the unknown acceleration command... Compared with actual acceleration a t There is a lag between them, and their relationship can be represented using the following nth-order linear system:

[0099]

[0100] in, The target autopilot status, and Given a known constant matrix (A, C) satisfying the observability condition, and an unknown time-varying vector Δ. u Bounded, that is:

[0101] ||Δ u || 2 ≤λ

[0102] Where λ is a constant vector, and λ>0.

[0103] In one example, step 3 specifically includes the following process:

[0104] The expression for the nondeterministic equivalent auxiliary variable s is defined as follows:

[0105] s = a t -L(y m )

[0106] in, For the nonlinear function vector that needs to be designed;

[0107] The derivative form of the non-deterministic equivalent auxiliary variable is as follows:

[0108]

[0109] Substituting the expression for s into the derivative From the expression, we can obtain:

[0110]

[0111] in, Given a known function vector;

[0112] vector of nonlinear function Designed in the form of a linear equation, let the nonlinear function vector L(y) m The representation is as follows:

[0113] L(y m )=κG -1 x2

[0114] in, For the constant matrix that needs to be designed;

[0115] The dynamic induction of the final nondeterministic equivalent auxiliary variable is then expressed as follows:

[0116]

[0117] Where W = CAC -1 -κ.

[0118] Step 4: Construct a Luenberger observer for the non-deterministic equivalent auxiliary variables and design a target acceleration estimator.

[0119] In one example, step 4 above specifically includes the following process:

[0120] For the defined nondeterministic equivalent auxiliary variable s, the observer expression is designed as follows:

[0121]

[0122] in, This is an estimate of the non-deterministic equivalent auxiliary variable s, where the estimated variable s is simply the unknown state a. t The partial estimate is combined with the designed auxiliary nonlinear function L to obtain a. t A complete estimate.

[0123] To further illustrate the effectiveness of the target acceleration estimator in this embodiment, the estimation error is defined. Its derivative satisfies the following form:

[0124]

[0125] Specify positive definite matrix Define alternative Lyapunov functions Its derivative satisfies the following inequality:

[0126]

[0127] Among them, Q s =PW+W T P+η s PCBB T C T P T η s These are adjustable parameters. By selecting appropriate parameters κ and P, Q can be optimized. s When the value is less than 0, the estimation error is bounded, and the target dynamic estimator can estimate the target acceleration.

[0128] In summary, regarding the missile interception problem, this invention first determines the missile coordinate system and its transformation relationship, establishes a dynamic model of the relative motion between the missile and the target in the line-of-sight coordinate system, selects a nonlinear function, defines an equivalent auxiliary variable for the nondeterministic target acceleration, and designs a target acceleration estimator. By selecting appropriate parameters κ and P, Q is made more stable. s When the value is less than 0, the estimation error is bounded, indicating that the target dynamic estimator can estimate the target acceleration.

Claims

1. A design method for a dynamic estimator of a maneuvering target using an inertial-line-of-sight coordinate system, characterized in that, Includes the following steps: Step 1: Determine the missile coordinate system and establish the transformation relationship between the inertial coordinate system and the line-of-sight coordinate system; Step 2: Select the relative distance between the missile and the target, the line-of-sight tilt angle, and the line-of-sight deflection angle in the inertial coordinate system and the line-of-sight coordinate system as the system states, and establish the dynamic equations of the missile interception system in the line-of-sight coordinate system; Step 3: Using the transformation relationship between the inertial and line-of-sight coordinate systems, define the nondeterministic equivalent auxiliary variable for the target acceleration disturbance; Step 4: Construct a Luenberger observer for the non-deterministic equivalent auxiliary variables and design a target acceleration estimator; Step 3 details The process includes the following: Define nondeterministic equivalent auxiliary variables The expression is as follows: ； in, , For the vector of nonlinear functions that need to be designed; , , , The distance between the missile and the target. For the angle of view, Angle of view; The derivative form of the non-deterministic equivalent auxiliary variable is as follows: ； in, Given a constant matrix, For an unknown time-varying vector, To assist nonlinear functions, and Given a function matrix, These are the accelerations of the target and the missile in the inertial coordinate system, respectively. Will Substituting the expression into the derivative From the expression, we can obtain: ； in, Given a known function vector; nonlinear function vectors Designed in the form of linear equations, let the nonlinear function vectors The representation is as follows: ； in, For the constant matrix that needs to be designed; The dynamic induction of the final nondeterministic equivalent auxiliary variable is then expressed as follows: ； in, ; Step 4 specifically includes the following processes: For the defined nondeterministic equivalent auxiliary variables The observer expression is designed as follows: ； in, Non-deterministic equivalent auxiliary variables The estimated value, the estimated variable It's just an unknown state. Partial estimation, combining partial estimation with the designed auxiliary nonlinear function Combined, we obtain A complete estimate.

2. The design method for a dynamic estimator of a maneuvering target according to claim 1, characterized in that, Step 1 in detail The process includes the following: Establish an inertial coordinate system The origin of the inertial coordinate system Take it at the missile's center of mass. The axis is in the horizontal plane. Perpendicular to the ground shaft and and The two coordinate axes are perpendicular and form a right-handed coordinate system; Establish line-of-sight coordinate system The origin of the line-of-sight coordinate system Take it at the missile's center of mass. The axis coincides with the missile-target line of sight. The axis is located in the area containing In the longitudinal plane of the axis, with The axis is perpendicular. Axis perpendicular to and The axes form a right-handed coordinate system; From the inertial coordinate system To the line-of-sight coordinate system The coordinate transformation matrix is ​​represented as: ； in, For the angle of view, The angle of view.

3. The design method for a dynamic estimator of a maneuvering target according to claim 2, characterized in that, Step 2 details The process includes the following: definition , and Let the relative position vector, relative velocity vector, and rotational angular velocity of the line-of-sight coordinate system relative to the inertial coordinate system be respectively. Then, the Coriolis equation can be expressed as: ； in, Indicates time; Based on the transformation relationship between the line-of-sight coordinate system and the inertial coordinate system, the rotational angular velocity of the line-of-sight coordinate system relative to the inertial coordinate system can be expressed as: ； Therefore, the Coriolis equation is expressed in the line-of-sight coordinate system as: ； in, The distance between the missile and the target; According to Coriolis theorem, the derivative of the relative velocity vector in the line-of-sight coordinate system can be expressed as: ； The expression for establishing the dynamic model of the relative motion between the missile and the target in the line-of-sight coordinate system is as follows: ； Among them, let Let be the relative acceleration between the missile and the target in the line-of-sight coordinate system. Representing the line-of-sight coordinate system The component of relative acceleration, It is calculated by the following formula: ； in, These are the accelerations of the target and the missile in the inertial coordinate system, respectively. Define state vector , Therefore, the dynamic equations of the missile interception system in the line-of-sight coordinate system can be obtained as follows: ； in, and These are the measurable and controllable output vectors, respectively. and Given function matrices, in the following forms: ； 。 4. The design method for a dynamic estimator of a maneuvering target according to claim 3, characterized in that, The target's acceleration command is executed by the autopilot, which tracks the target command by adjusting aerodynamic control surfaces or thrusters; therefore, the unknown acceleration command... With actual acceleration There is a lag between them, and their relationship can be explained using the following... Represented as a linear system of order: ； in, The target autopilot status, Given a constant matrix, and Satisfying the observability condition, an unknown time-varying vector Bounded, that is: ； in It is a constant vector, and .

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