A fast regression identification method for cooperative guidance law of aircraft based on artificial intelligence

Abstract

The present invention discloses a method for rapid regression identification of aircraft cooperative guidance law based on artificial intelligence, comprising the following steps: establishing a cooperative guidance model, wherein the cooperative guidance model is a model capable of characterizing the motion state between our fixed target and the enemy aircraft; obtaining training samples according to the cooperative guidance model; establishing a neural network, training the neural network through the training samples to obtain an identification model; and obtaining the guidance parameters of the enemy aircraft through the trained identification model. The method for rapid regression identification of aircraft cooperative guidance law based on artificial intelligence provided by the present invention can more quickly and accurately identify the time-varying guidance parameters of the enemy aircraft.

Description

Technical Field

[0001] The invention relates to a rapid regression identification method of an aircraft cooperative guidance law based on artificial intelligence, and belongs to the field of guidance control. Background Art

[0002] Coordinated attack means that multiple missiles attack a target at the same time to increase the probability of killing. In order to effectively defend against enemy aircraft attacks, it is necessary to predict and estimate the trajectory and state of the enemy aircraft, and then implement high-precision interception. The important prerequisite for achieving trajectory prediction and state estimation is to identify the guidance parameters of the enemy aircraft.

[0003] Aircraft guidance law identification is a complex dynamic problem. If the aircraft guidance law identification only relies on kinematic information at a certain moment, the identification result will be one-sided. The traditional identification method is based on the Kalman filter. By comparing the measured enemy aircraft motion information with the predicted information of the Kalman filter, the Kalman filter output value is continuously adjusted until the measured value is close to the true value. This type of method has the following disadvantages:

[0004] a. The transition process usually takes more than 1 second, which places a relatively strict requirement on the continuous acquisition of missile information, which may limit the maneuverability of the aircraft and increase the risk of being hit;

[0005] b. Since the update of the Kalman filter is derived from the difference between the measured data and the Kalman filter output, the guidance law parameter identification is usually solved as a classification problem, under the premise that the system is in a finite set of possible outcomes known in advance to the aircraft. If the assumption is not true, the performance of the model may degrade.

[0006] Therefore, it is necessary to further study the traditional proportional guidance method to solve the above problems. Summary of the invention

[0007] In order to overcome the above problems, the inventors have conducted in-depth research and designed a method for rapid regression identification of aircraft collaborative guidance law based on artificial intelligence, which is characterized by comprising the following steps:

[0008] S1. Establishing a collaborative guidance model, wherein the collaborative guidance model is a model capable of characterizing the motion state between our fixed target and the enemy aircraft;

[0009] S2. Obtain training samples according to the collaborative guidance model;

[0010] S3, establish a neural network, train the neural network through training samples, and obtain a recognition model;

[0011] S4. Obtain the guidance parameters of the enemy aircraft through the trained recognition model.

[0012] In a preferred embodiment, in S1, in the collaborative guidance model, there are multiple enemy aircraft, and the CPN guidance law is adopted so that multiple enemy aircraft can collide with our fixed target at the same time.

[0013] In a preferred embodiment, in S2, multiple groups of information are extracted from the collaborative guidance model, each group of information includes the kinematic information of our fixed target and the enemy aircraft within a period of time, and the time-varying guidance law parameters of the enemy aircraft during the period of time, thereby constructing a training sample.

[0014] In a preferred embodiment, in S2, different initial states are set for our fixed targets and enemy aircraft, and different guidance law parameters and system guidance law parameters are set for the enemy aircraft, so as to diversify the training samples.

[0015] In a preferred embodiment, in S2, a relative motion model is established, and kinematic information of our fixed target and multiple enemy aircraft within a period of time is extracted through the relative motion model.

[0016] The relative motion model is expressed as:

[0017]

[0018]

[0019]

[0020]

[0021] Among them, ρ i represents the relative distance between the ith enemy aircraft and our fixed target, λ i represents the relative angle between the ith enemy aircraft and our fixed target, Represents ρ i The derivative of Represents λ i The derivative of i represents the acceleration of the ith enemy aircraft, Indicates a i The derivative of γ i represents the velocity angle of the i-th aircraft, Represents γ i The derivative of V i represents the flight speed of the i-th aircraft, σ i represents the error angle of the ith aircraft, u i represents the acceleration command of the ith aircraft, and τ represents the first-order lag coefficient of the control system.

[0022] In a preferred embodiment, the kinematic information of the friendly fixed target and the enemy aircraft includes: the relative distance of each enemy aircraft relative to the friendly fixed target and the relative angle of each enemy aircraft relative to the friendly fixed target.

[0023] In a preferred embodiment, in S3, the recognition model includes an input layer, multiple hidden layers, an output layer and a multi-model layer, and each hidden layer includes one or more GRU neurons.

[0024] In a preferred embodiment, the multi-model layer has multiple model groups, and each model group has multiple models, wherein the model group is used to characterize the possible sets of time-varying guidance parameters of different enemy aircraft, and the model is used to characterize the different possible values ​​of the time-varying guidance parameters of the enemy aircraft.

[0025] In a preferred embodiment, the output layer is used to obtain the weight of each model in the multi-model layer, and the weights G of different model groups are i It can be expressed as:

[0026]

[0027] Among them, i represents different model groups, j represents the number of models in the model group, and G i,j represents the weight of the jth model in the i-th group of models, softmax() is the activation function, and w out is the weight of the output layer, h last is the output of the last hidden layer, b out is the bias of the output layer, and the superscript T represents transpose.

[0028] In a preferred embodiment, the multi-model layer is represented as:

[0029]

[0030] in, represents the time-varying guidance parameter of the ith enemy aircraft at the current moment, p i represents the number of models in the i-th model group, R i,j Represents the value of the jth model in the i-th model group.

[0031] The beneficial effects of the present invention include:

[0032] (1) According to the method for rapid regression identification of aircraft collaborative guidance law based on artificial intelligence provided by the present invention, the guidance law identification is regarded as a regression problem rather than a classification problem, thereby improving the identification accuracy;

[0033] (2) According to the rapid regression identification method of the aircraft cooperative guidance law based on artificial intelligence provided by the present invention, the transition time is short and the time-varying guidance parameters of the enemy aircraft can be identified more quickly;

[0034] (3) According to the artificial intelligence-based rapid regression identification method for aircraft collaborative guidance laws provided by the present invention, a small number of relative kinematic information types need to be collected, the identification speed is fast, and the accuracy of the identification results is guaranteed through a neural network with multiple model layers. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 A schematic flow chart of a method for rapid regression identification of an aircraft cooperative guidance law based on artificial intelligence according to a preferred embodiment of the present invention is shown;

[0036] Figure 2 A schematic diagram of a neural network structure in a method for rapid regression identification of an aircraft cooperative guidance law based on artificial intelligence according to a preferred embodiment of the present invention is shown;

[0037] Figure 3 The true value of the time-varying guidance parameter of the enemy aircraft in Embodiment 1 of the present invention is shown;

[0038] Figure 4 The identification process of the model output in Embodiment 1 of the present invention is shown. DETAILED DESCRIPTION

[0039] The present invention will be further described in detail below through the accompanying drawings and embodiments. Through these descriptions, the characteristics and advantages of the present invention will become more clear and distinct.

[0040] The word "exemplary" is used exclusively herein to mean "serving as an example, embodiment, or illustration." Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings are not necessarily drawn to scale unless otherwise noted.

[0041] According to the invention, a method for rapid regression identification of aircraft cooperative guidance law based on artificial intelligence is provided. Figure 1 As shown, the following steps are included:

[0042] S1. Establishing a collaborative guidance model, wherein the collaborative guidance is a model capable of characterizing the motion state between our fixed target and the enemy aircraft;

[0043] S2. Obtain training samples according to the collaborative guidance model;

[0044] S3, establish a neural network, train the neural network through training samples, and obtain a recognition model;

[0045] S4. Obtain the guidance law of the enemy aircraft through the identification model.

[0046] Furthermore, in S1, in the collaborative guidance model, our fixed target maneuvers according to a certain rule, there are multiple enemy aircraft, multiple enemy aircraft can collide with our fixed target, and multiple enemy aircraft can collide with our fixed target at the same time.

[0047] Further preferably, the enemy aircraft adopts a proportional guidance law. The proportional guidance (PN) guidance law is the most widely used guidance law at present. The current cooperative guidance laws are all implemented based on the PN guidance law. More preferably, in the present invention, the enemy aircraft adopts a cooperative proportional guidance (CPN) guidance law based on the PN guidance law. For a specific introduction to the CPN guidance law, see the article I.-S.Jeon, J.-I.Lee, and M.-J.Tahk, "Homing guidance law for cooperative attack of multiple missiles," Journal of guidance, control, and dynamics, vol.33, no.1, pp.275–280, 2010.

[0048] In S2, multiple groups of information are extracted from the collaborative guidance model. Each group of information contains the kinematic information of our fixed targets and enemy aircraft within a period of time, as well as the time-varying guidance law parameters of the enemy aircraft during that period of time, thereby constructing training samples.

[0049] More preferably, the period of time is 0.5 to 2 seconds, and the specific value can be freely selected by those skilled in the art according to actual conditions.

[0050] The samples used for training are crucial to the optimization effect of the recognition model. In order to cover the sample space as much as possible, in the present invention, different initial states are set for our fixed targets and enemy aircraft, and different guidance law parameters and system guidance law parameters are set for enemy aircraft to diversify the training samples.

[0051] According to a preferred embodiment of the present invention, in the cooperative guidance model, the range of different guidance rate parameters set for the enemy aircraft is N∈[2.5,5.5], and the range of different cooperative guidance parameters is K∈[50,120].

[0052] Preferably, the time-varying guidance law parameters of the aircraft at different times and places are obtained through simulation.

[0053] Further preferably, in S2, a relative motion model is established, and kinematic information of our fixed target and multiple enemy aircraft within a period of time is extracted through the relative motion model.

[0054] The relative motion model is expressed as:

[0055]

[0056]

[0057]

[0058]

[0059] Among them, ρ i represents the relative distance between the ith enemy aircraft and our fixed target, λ i Represents the relative angle between the ith enemy aircraft and our fixed target Represents ρ i The derivative of Represents λ i The derivative of i represents the acceleration of the ith enemy aircraft, Indicates a i The derivative of γ i represents the velocity angle of the i-th aircraft, Represents γ i The derivative of V i represents the flight speed of the i-th aircraft, σ i represents the error angle of the ith aircraft, u i represents the acceleration command of the ith aircraft, and τ represents the first-order lag coefficient of the control system.

[0060] Furthermore, in the relative motion model, since the enemy aircraft is in the terminal guidance stage, it is assumed that the enemy aircraft speed remains unchanged, that is,

[0061]

[0062] According to a preferred embodiment of the present invention, in S2, in the training sample, the kinematic information of our fixed target and the enemy aircraft within a period of time is used as the input information of the sample, and the time-varying guidance parameters corresponding to each enemy aircraft during the period of time are used as the output information of the sample.

[0063] The kinematic information of the fixed target and the enemy aircraft includes:

[0064] The relative distance and relative angle between our fixed target and the enemy aircraft (i.e., the error angle of the enemy aircraft) can be measured in real time by our sensors during the subsequent identification process.

[0065] Generally speaking, more relative kinematic information is needed to identify the guidance law through a neural network. In the present invention, through a large number of experimental analyses, the input items of the neural network are reduced, and only relative distance and relative angle are used as input items. Under the condition that the computing power of the onboard computer allows, the best identification result is obtained.

[0066] In a preferred embodiment, data processing is also performed on the kinematic information of our fixed targets and enemy aircraft, and the data processing includes normalization processing to accelerate model convergence, convert the original data into dimensionless values ​​with the same interval, and eliminate the impact of different attributes between different indicators.

[0067] In the present invention, the specific method of normalization processing is not particularly limited, and the maximum and minimum linear changes, Logistics / Softmax changes, inverse tangent function changes, Z-score normalization and logarithmic transformation, etc. can be used.

[0068] Preferably, the maximum and minimum linear changes are adopted to scale the data to the interval [0,1], which is expressed as:

[0069]

[0070] Among them, min A x is the minimum value of the x-th attribute, max A x is the maximum value of the attribute; a xi is the original data before processing, a' xi is the processed data used for training.

[0071] According to a preferred embodiment of the present invention, in S3, the identification model includes an input layer, multiple hidden layers, an output layer and a multi-model layer.

[0072] Different from the traditional neural network, in the present invention, multiple model layers are provided to smoothly map the values ​​of the unknown output range into the required range, thereby obtaining the time-varying guidance law of the enemy aircraft.

[0073] In the present invention, through multiple model layers, weight learning and smooth mapping, the problem of low recognition accuracy caused by the small amount of input relative kinematic information can be greatly compensated. While improving the recognition speed, the accuracy of recognition is guaranteed, and the training speed of the neural network in the regression problem can be greatly accelerated.

[0074] According to the present invention, the multi-model layer has multiple model groups, each model group has multiple models, wherein the model group is used to characterize the possible set of time-varying guidance parameters of different enemy aircraft, and the model is used to characterize the different possible values ​​of the time-varying guidance parameters of the enemy aircraft. The number of model groups is the same as the number of enemy aircraft in the training sample. For example, if there are 3 enemy drones in the training sample, then there are 3 model groups in total.

[0075] Specifically, according to the present invention, the input of the input layer is the kinematic information of our fixed targets and enemy aircraft over a period of time.

[0076] Preferably, the input of the input layer is a two-dimensional array, in which the rows represent the operational information between different enemy aircraft and our fixed targets at the same time, and the columns represent the data at different times, for example:

[0077]

[0078] Preferably, the number of hidden layers is 3.

[0079] Each hidden layer contains one or more GRU neural units for extracting information. Each neural unit takes one of the data in the input layer as input. Multiple GRU neural units are connected in sequence, so that each hidden layer can extract time series information.

[0080] Further, the GRU neural unit includes one or more neurons, each of which includes:

[0081] Two inputs: the output of the neuron at the previous moment and the output of the neuron in the previous layer, which are used to inherit the output of the neuron at the previous moment and receive the output of the neuron in the previous layer;

[0082] Two gates: the reset gate, which is used to calculate how much of the previous memory needs to be retained; the update gate, which is used to calculate the update content at the current moment, expressed as:

[0083] A state: a candidate hidden layer state, used to calculate the internal state of the neuron at the current moment;

[0084] One output: the final output, calculated based on the current input and internal state.

[0085] In a preferred embodiment, the activation function of the input layer is set to a Tanh function, which is used to compress the data input to the input layer into the range of [-1, 1].

[0086] Furthermore, the output layer is used to obtain the weight of each model in the multi-model layer. For example, when there are three model groups, the weights of the three model groups are recorded as G i , i=1,2,3,

[0087] Furthermore, the weights G of different model groups i It can be expressed as:

[0088]

[0089] Among them, i represents different model groups, j represents the number of models in the model group, and G i,j represents the weight of the jth model in the i-th group of models, softmax() is the activation function, and w out is the weight of the output layer, h last is the output of the last hidden layer, b out is the bias of the output layer.

[0090] Preferably, the multi-model layer is represented as:

[0091]

[0092] in, represents the time-varying guidance parameter of the ith enemy aircraft at the current moment, p i represents the number of models in the i-th model group, R i,j Represents the value of the jth model in the i-th model group.

[0093] In a preferred embodiment, in S3, the recognition model is trained by supervised learning.

[0094] More preferably, in S3, the identification model is trained based on the Adam method. More preferably, the parameter θ update formula based on the Adam algorithm is expressed as:

[0095]

[0096]

[0097] Among them, θ t is the parameter before updating; θ t+1 is the updated parameter; η is the learning rate; ε is the smoothing term to prevent division by zero; m' t is the first-order moment estimate, v' t is the second-order moment estimate; m t is the first-order moment of gradient, v t is the second-order moment of the gradient.

[0098] The Adam method combines the Momentum algorithm with the RMSprop algorithm, adds momentum and enables adaptive parameter training. Compared with the BP algorithm, the Adam method can effectively prevent the network from falling into the local optimal point, accelerate network convergence, and improve algorithm robustness.

[0099] In S4, the trained identification model is set on our aircraft, the kinematic information of our aircraft and the enemy aircraft is obtained through the sensors on the aircraft, the kinematic information of our aircraft and the enemy aircraft is input into the identification model, and the identification model outputs the collaborative guidance law of the enemy aircraft.

[0100] Example

[0101] Example 1

[0102] Conducting a model experiment includes the following steps:

[0103] S1. Establishing a collaborative guidance model, wherein the collaborative guidance model is a model capable of characterizing the motion state between our fixed target and the enemy aircraft;

[0104] S2. Obtain training samples according to the collaborative guidance model;

[0105] S3, establish a neural network, train the neural network through training samples, and obtain a recognition model;

[0106] S4. Obtain the guidance parameters of the enemy aircraft through the trained recognition model.

[0107] In S1, in the collaborative guidance model, there are multiple enemy aircraft, and the CPN guidance law is adopted, so that multiple enemy aircraft can collide with our fixed target at the same time.

[0108] In S2, multiple groups of information are extracted from the collaborative guidance model. Each group of information contains the kinematic information of our fixed targets and enemy aircraft within a period of time, as well as the time-varying guidance law parameters of the enemy aircraft during that period of time, thereby constructing training samples.

[0109] In S2, different initial states are set for our fixed targets and enemy aircraft, and different guidance law parameters and system guidance law parameters are set for enemy aircraft to diversify the training samples.

[0110] In S2, a relative motion model is established to extract the kinematic information of our fixed target and multiple enemy aircraft within a period of time.

[0111] The relative motion model is expressed as:

[0112]

[0113]

[0114]

[0115]

[0116] Among them, ρ i represents the relative distance between the ith enemy aircraft and our fixed target, λ i represents the relative angle between the ith enemy aircraft and our fixed target, Represents ρ i The derivative of Represents λ i The derivative of i represents the acceleration of the ith enemy aircraft, Indicates a i The derivative of γ i represents the velocity angle of the i-th aircraft, Represents γ i The derivative of V i represents the flight speed of the i-th aircraft, σ i represents the error angle of the ith aircraft, u i represents the acceleration command of the ith aircraft, and τ represents the first-order lag coefficient of the control system.

[0117] The kinematic information of our fixed target and the enemy aircraft includes: the relative distance of each enemy aircraft relative to our fixed target and the relative angle of each enemy aircraft relative to our fixed target.

[0118] In S3, the recognition model includes an input layer, multiple hidden layers, an output layer and a multi-model layer, and each hidden layer includes one or more GRU neurons.

[0119] The multi-model layer has multiple model groups, each model group has multiple models, wherein the model group is used to characterize the possible sets of time-varying guidance parameters of different enemy aircraft, and the model is used to characterize the different possible values ​​of the time-varying guidance parameters of the enemy aircraft.

[0120] The output layer is used to obtain the weight of each model in the multi-model layer, and the weights of different model groups G i It can be expressed as:

[0121]

[0122] Among them, G i,j represents the weight of the jth model in the i-th group of models, softmax() is the activation function, and w out is the weight of the output layer, h last is the output of the last hidden layer, b out is the bias of the output layer, and the superscript T represents transpose.

[0123] The multi-model layer is represented as:

[0124]

[0125] in, represents the time-varying guidance parameter of the ith enemy aircraft at the current moment, p i represents the number of models in the i-th model group, R i,j Indicates the value of the jth model in the i-th model group. During the simulation experiment, three enemy aircraft were set to carry out coordinated attacks on our fixed targets. The guidance law parameters used by the enemy aircraft were N = 4.0, and the coordinated guidance parameters were K = 120. Through the simulation software, the true value of the time-varying guidance parameters of the enemy aircraft was obtained. The flight trajectory of the enemy aircraft is shown in Figure 3 As shown in Figure 4 As shown, it can be seen that after about 0.5s, the enemy's time-varying guidance parameter results obtained by the model output identification converge to near the true value, proving the reliability of the model.

[0126] The traditional Kalman filter-based method generally takes more than 1 second to identify the guidance law parameters and collaborative guidance parameters of enemy aircraft. Compared with the traditional Kalman filter-based method, this method can reduce the guidance law identification time to 0.5 seconds, shortening it by more than 50%, and greatly reduces our aircraft's measurement requirements on enemy aircraft, thereby improving our aircraft's survivability.

[0127] In the description of the present invention, it should be noted that the terms "upper", "lower", "inner", "outer", "front", "rear", etc. indicate positions or positional relationships based on the working state of the present invention, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", "third", and "fourth" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0128] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected" and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0129] The present invention has been described above in conjunction with preferred embodiments, but these embodiments are only exemplary and serve only as an illustration. On this basis, the present invention may be subjected to a variety of substitutions and improvements, all of which fall within the scope of protection of the present invention.

Claims

1. A method for rapid regression identification of aircraft cooperative guidance law based on artificial intelligence, characterized in that: The following steps are involved: S1. Establishing a collaborative guidance model, wherein the collaborative guidance model is a model capable of characterizing the motion state between our fixed target and the enemy aircraft; S2. Obtain training samples according to the collaborative guidance model; S3, establish a neural network, train the neural network through training samples, and obtain a recognition model; S4, obtaining the guidance law of the enemy aircraft through the trained recognition model; In S2, multiple sets of information are extracted from the collaborative guidance model, each set of information contains the kinematic information of our fixed target and the enemy aircraft within a period of time, as well as the time-varying guidance parameters of the enemy aircraft during the period of time, so as to construct a training sample; In S2, a relative motion model is established to extract the kinematic information of our fixed target and multiple enemy aircraft within a period of time. The relative motion model is expressed as: Among them, ρ i represents the relative distance between the ith enemy aircraft and our fixed target, λ i represents the relative angle between the ith enemy aircraft and our fixed target, Represents ρ i The derivative of Represents λ i The derivative of i represents the acceleration of the ith enemy aircraft, Indicates a i The derivative of γ i represents the velocity angle of the i-th aircraft, Represents γ i The derivative of V i represents the flight speed of the i-th aircraft, σ i represents the error angle of the ith aircraft, u i represents the acceleration command of the ith aircraft, τ represents the first-order lag coefficient of the control system; The kinematic information of the fixed target and the enemy aircraft is only: the relative distance of each enemy aircraft relative to the fixed target and the relative angle of each enemy aircraft relative to the fixed target; In S3, the recognition model includes an input layer, multiple hidden layers, an output layer and a multi-model layer, and each hidden layer includes one or more GRU neurons; The multi-model layer has multiple model groups, each model group has multiple models, wherein the model group is used to characterize the possible sets of time-varying guidance parameters of different enemy aircraft, and the model is used to characterize the different possible values ​​of the time-varying guidance parameters of the enemy aircraft.

2. The method for rapid regression identification of aircraft cooperative guidance law based on artificial intelligence according to claim 1 is characterized in that: In S1, in the collaborative guidance model, there are multiple enemy aircraft, and the CPN guidance law is adopted, so that multiple enemy aircraft can collide with our fixed target at the same time.

3. The method for rapid regression identification of aircraft cooperative guidance law based on artificial intelligence according to claim 1 is characterized in that: In S2, different initial states are set for our fixed targets and enemy aircraft, and different time-varying guidance parameters and system guidance parameters are set for enemy aircraft to diversify the training samples.

4. The method for rapid regression identification of aircraft cooperative guidance law based on artificial intelligence according to claim 1 is characterized in that: The output layer is used to obtain the weight of each model in the multi-model layer, and the weights of different model groups G i It can be expressed as: Among them, i represents different model groups, j represents the number of models in the model group, G i,j represents the weight of the jth model in the i-th group of models, softmax() is the activation function, and w out is the weight of the output layer, h last is the output of the last hidden layer, b out is the bias of the output layer, the superscript T represents transposition, and p i Represents the number of models in the i-th model group.

5. The method for rapid regression identification of aircraft cooperative guidance law based on artificial intelligence according to claim 4 is characterized in that: The multi-model layer is represented as: in, represents the time-varying guidance parameter of the ith enemy aircraft at the current moment, R i,j Represents the value of the jth model in the i-th model group.

Images