An aircraft position prediction method based on a hidden Markov model

Abstract

An aircraft position prediction method based on a hidden Markov model is proposed. It eliminates the need for extensive preprocessing and training with large sample sizes, enabling effective modeling even with limited data. It does not require prior knowledge of the enemy aircraft's model or maneuvering behavior; the prediction task can be effectively completed using existing training aircraft or simulation environments. By employing aircraft motion parameters with more observable features that follow a Markov distribution, the method transforms aircraft motion into a hidden Markov process related to its actions, significantly reducing modeling complexity and greatly improving prediction accuracy with small sample sizes. It also provides the model with interpretability, facilitating offline or online modifications. Measurements show that predicting the aircraft's position within 10 seconds using actual trajectories yields an error within 3 kilometers, while predicting it using observed trajectories results in an error within 3 kilometers.

Description

Technical Field

[0001] This invention belongs to the field of machine learning, specifically relating to an aircraft position prediction method based on a hidden Markov model. Background Technology

[0002] Aircraft position prediction is a crucial element in effectively improving the combat success rate of aircraft. In highly contested environments (such as when both aircraft are performing high-G maneuvers), the air combat situation information is often incomplete. Therefore, it is necessary to fully utilize time-series information to estimate and predict the current enemy position, guiding the radar to focus its search within the smallest possible boundaries and shortening the time required for the radar to relock onto the enemy aircraft.

[0003] Currently, the main methods for location prediction based on past trajectory sets include the generalized pseudo-Bayes algorithm, the interactive multi-model algorithm, and the time series network training method.

[0004] The generalized pseudo-Bayesian algorithm assumes that the action at the current moment is strongly correlated with the action at the previous moment or the actions at the beginning and end of a previous time period, corresponding to GPB1 and GPB2 respectively. GPB1 is only related to the action at the previous moment, without considering the influence of environmental factors on decision-making, nor the changes that may be caused by executing the same action over a long period of time, resulting in lower accuracy, especially when the aircraft is performing large maneuvers. GPB2 can fully consider the influence of the previous time period on the current motion, but as the dimension of the action space increases, the computational time complexity and space complexity increase quadratically, which is not conducive to real-time calculation and judgment.

[0005] Interactive multiple model (EMB) methods, based on the generalized pseudo-Bayesian algorithm, utilize hypothesis management techniques for effective mixture estimation. They combine the performance advantages of GPB2 with computational complexity approaching that of GPB1, making them a mainstream method for aircraft position prediction. However, EMB methods require accurate modeling of parameters such as aircraft motion and current speed, making them difficult to handle unknown aircraft types or models. During large maneuvers, estimation errors are significant due to model accuracy limitations. Furthermore, maneuvering outside the model set can easily lead to filter divergence and tracking failure. Therefore, high modeling accuracy is crucial, as it significantly impacts prediction accuracy.

[0006] Time series network training methods include RNNs, LSTMs, and Transformers. These methods, through the design of specific network structures, focus on and process past time series information, which is well-suited to the requirements of aircraft position prediction tasks. However, the time series of aircraft performing large maneuvers only occupies a small segment of the entire aircraft action sequence, placing high demands on sample acquisition and processing. Furthermore, the input space simultaneously includes enemy aircraft heading angles, enemy aircraft speed information, relative positions of friendly and enemy aircraft, and relative positions of friendly missiles and enemy aircraft, resulting in high input dimensionality and significant model training difficulty. Additionally, time series network training lacks interpretability for some strongly correlated features, making it difficult to adjust and retrain the network structure and parameters according to specific tasks. Summary of the Invention

[0007] This invention proposes an aircraft position prediction method based on a hidden Markov model, which solves the problems of effective modeling in the case of small samples, motion calculation independent of the aircraft maneuver white-box model, construction of an interpretable and easily modifiable algorithm model, and low computational complexity.

[0008] An aircraft position prediction method based on a hidden Markov model is presented, with the following algorithm flow:

[0009] (1) Obtain test data through simulation software or real combat data to predict the aircraft position.

[0010] (2) Using the aircraft’s current position, speed and direction, calculate the estimated position matrix of different actions after interpolation in the motion position database, and correct the actions that cross the boundary according to the flight limit boundary.

[0011] (3) Obtain the action category probability matrix based on the current speed and direction of the aircraft and the action discrimination algorithm.

[0012] (4) By inputting the current position, speed and direction of the aircraft, the current position and speed of the opponent's aircraft, and the current position and speed of the opponent's missile into the environment discrimination algorithm, the current environment category is obtained, and the action transition matrix under the current environment conditions is extracted from the transition matrix database.

[0013] (5) The predicted position of the aircraft can be calculated by multiplying the action category probability matrix, the action transition matrix, and the action prediction position matrix together.

[0014] Furthermore, the methods for constructing each algorithm model in the algorithm flow are as follows:

[0015] (1) The maneuvering strategies performed by aircraft vary greatly under different combat environments. By comprehensively considering various environmental parameters and classifying the combat environment of enemy aircraft based on experience, the accuracy of predicting specific maneuvering actions under specific conditions (such as high maneuvering conditions) can be improved.

[0016] (2) Directly predicting the future position of an aircraft based on its current motion parameters and environmental parameters is an end-to-end regression task. This places high demands on the distribution characteristics and quantity of the dataset, making it difficult to meet the needs of effective modeling with small samples and the construction of interpretable and easily modifiable algorithm models. Therefore, obtaining a widely distributed sample and using an improved KNN clustering algorithm to transform the three-dimensional velocity features into a motion feature category matrix facilitates model construction and the interpretability of the prediction process.

[0017] (3) In a simulation environment, aircraft of the same type are set to perform corresponding actions along the nearest center and within a certain range around it, according to a certain degree of separation. The flight trajectory is recorded, and a database of action positions is established. The motion boundaries of the aircraft under different altitudes and speeds are tested and measured to further improve the prediction accuracy during the prediction process.

[0018] (4) Based on experience, the action transition matrices under various environmental conditions are initially set, and a transition matrix database is established. At the same time, a certain number of simulation samples are collected, classified into different environmental conditions, and the corresponding action transition matrices are corrected. A real-time learning interface is also provided, allowing the algorithm to correct the action transition matrix values ​​based on the label values ​​while calculating the corresponding action transition matrices, so as to better fit the actual combat strategy.

[0019] Beneficial effects: This invention eliminates the need for large-scale preprocessing and training, enabling effective modeling even with small sample sizes. It eliminates the need for prior knowledge of enemy aircraft models and maneuvers, effectively completing motion prediction tasks using existing training aircraft or simulation environments. Since end-to-end prediction directly from aircraft motion and environmental parameters is difficult in practice, this invention utilizes aircraft motion parameters to provide more observable features, and these features follow a P(action) property. t-1 ,state t-1 → P(action) t The Markov distribution of the model makes the aircraft motion a hidden Markov process related to the aircraft's actions, greatly reducing the modeling difficulty and significantly improving prediction accuracy in small sample cases. It also gives the model some interpretability, allowing for better offline or online modifications. Measurements show that the error in predicting the aircraft's position in the next 10 seconds using the actual trajectory is within 1 km, and the error in predicting the aircraft's position in the next 10 seconds using the observed trajectory is within 3 km. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the algorithm flow of the present invention.

[0021] Figure 2 This is a schematic diagram of the environment discrimination algorithm of the present invention.

[0022] Figure 3 This is a schematic diagram of the action discrimination algorithm model construction process of the present invention.

[0023] Figure 4 This is a schematic diagram of the application process of the action discrimination algorithm model of the present invention.

[0024] Figure 5 This is a schematic diagram of the action transition matrix construction process of the present invention.

[0025] Figure 6 This is a schematic diagram of the coordinate transformation of the present invention.

[0026] Figure 7 This is a schematic diagram of the aircraft position prediction results of the present invention. Detailed Implementation

[0027] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0028] This invention receives a certain number of battle data sessions provided by an air combat game to train relevant algorithms and construct a corresponding database. Then, this invention receives real-time information about our aircraft, enemy aircraft observation information, and situational observation information provided by the air combat game, processes them accordingly, outputs position prediction results, and compares them with the real-time enemy aircraft information. This embodiment is only tested with this air combat game.

[0029] like Figure 2 As shown, an environment discrimination algorithm for aircraft position prediction based on a hidden Markov model is presented:

[0030] (1) Extract enemy aircraft movement information, aircraft movement information, and missile movement information from the test data.

[0031] (2) Calculate the distance between the aircraft and the missile. If it is less than the threshold, it is considered to be in a high-maneuver evasion state (state1).

[0032] (3) Calculate the angle between the missile direction and the aircraft position. If it is less than the threshold, it is considered to be in a state of about to perform a large maneuver to avoid the enemy (state2).

[0033] (4) Calculate the distance between enemy and friendly aircraft. If it is greater than the threshold, it is considered to be in the reconnaissance state (state3).

[0034] (5) Calculate the angle between enemy and friendly aircraft. If it is less than the threshold, it is considered to be in the dominant scanning state (state4).

[0035] (6) Otherwise, it is considered to be in a disadvantageous scanning state (state5).

[0036] like Figure 3 The following is a flowchart illustrating the model construction process of an action discrimination algorithm for aircraft position prediction based on a hidden Markov model:

[0037] a) Based on experience, 11 motion centers are pre-defined.

[0038] Action Number Action description Action1 Slow ascent Action2 Take off quickly Action3 Slow descent Action4 Rapid descent Action5 Slow left flight Action6 Quick left flight Action7 Slow right flight Action8 Quick right flight Action9 Accelerate forward flight Action10 Decelerate before flying Action11 fly forward at a constant speed

[0039] b) Extract the aircraft's current velocity V2(x,y,z) and direction from the test data, and calculate the motion distance matrix between the current action and each motion center.

[0040] c) Apply boundary constraints to the action distance matrix to remove cases with excessively long distances.

[0041] d) Normalize the action distance matrix to obtain the action category matrix.

[0042] e) Interpolate the one-hot vectors corresponding to the test labels to obtain the action category error matrix.

[0043] f) Through the action category error matrix The center value of each action is adjusted. Actions of the same type (e.g., action1, action2) have a larger adjustment parameter, while actions of different types (e.g., action1, action3) have a smaller adjustment parameter. The adjustment parameter γ = γe -n It decreases as the number of test samples n increases.

[0044] g) After all test data has been tested, the corrected action center set is validated. If the accuracy is less than the threshold, samples are reselected for adjustment. If the accuracy is greater than the threshold, then the action center set is the action discrimination algorithm model.

[0045] like Figure 5 As shown, the process of constructing the action transition matrix for an aircraft position prediction method based on a hidden Markov model is as follows:

[0046] a) Extract time series data from the test data.

[0047] b) Obtain the environmental category of the current time series using an environmental discrimination algorithm.

[0048] c) Obtain the probability matrix of the current action using an action discrimination algorithm.

[0049] d) Accumulate the current action probability matrix into the transition matrix database.

[0050] e) After processing all the test data, normalize the transition matrix database.

[0051] like Figure 1 The following is an algorithm implementation flow for an aircraft position prediction method based on a hidden Markov model:

[0052] a) Obtain the real information S1 of the enemy aircraft (our aircraft), the observation information S2 of the aircraft (enemy aircraft), and the situation observation information M of the aircraft at a certain time period through simulation software, and predict the aircraft position.

[0053] b) Using the aircraft's current position X2(x,y,z), velocity V2(x,y,z), and predicted time t estim The system determines the nearest coordinates of the aircraft in the motion position database and calculates the predicted position matrix for different motions using interpolation.

[0054]

[0055] In the formula, The coordinates in the database correspond to the normalized weights. These are the coordinates corresponding to the values ​​in the database.

[0056] The interpolated estimated position matrix is ​​loaded onto the aircraft velocity direction, such as... Figure 6 The diagram shows how to transform Point3 in the Point1 coordinate system to its corresponding position in Point2:

[0057]

[0058]

[0059]

[0060]

[0061] And corrective actions that cross the flight limit boundaries are taken based on the flight limit boundaries, specifically including:

[0062] (1) The lower limit of flight that prevents normal flight

[0063] (2) Flight limits affected by aircraft speed

[0064] (3) Turning limits affected by aircraft speed

[0065] The predicted position of the aircraft under different maneuvers is obtained:

[0066]

[0067]

[0068] In the formula, γ represents the flight limit boundary, and γ is the bias parameter.

[0069] c) Based on the aircraft's current speed V2(x,y,z) and direction, according to Figure 4 Application flow of the action discrimination algorithm, obtaining the action category probability matrix:

[0070]

[0071] d) Using the aircraft's current position X2(x,y,z), velocity V2(x,y,z) and direction, the opponent's current position X1(x,y,z) and velocity V1(x,y,z), and the opponent's missile's current position X M (x,y,z) and velocity V M The input environment discrimination algorithm (x, y, z) is used to obtain the current environment category, and the action transition matrix under the current environment condition is extracted from the transition matrix database.

[0072] e) The action category probability matrix Action transition matrix Motion prediction position matrix The predicted position of the aircraft can be calculated by multiplying the results:

[0073]

[0074] The experimental results are as follows Figure 7 As shown in the figure, the blue dots represent the actual trajectory, the orange dots represent the current position, the green dots represent the weighted position, and the red dots represent the aircraft's future actual position. This demonstrates that the invention can effectively predict the future position of an aircraft even with a small sample size.

Claims

1. A method for predicting aircraft position based on a hidden Markov model, characterized in that, a) Obtain the aircraft's real information S1, aircraft observation information S2, and situational observation information M at a certain time period through simulation software, and predict the aircraft's position. b) Using the aircraft's current position X2(x,y,z), velocity V2(x,y,z), and predicted time t estim The system determines the nearest coordinates of the aircraft in the motion position database and calculates the predicted position matrix for different motions using interpolation. In the formula, The coordinates in the database correspond to the normalized weights. The coordinates correspond to the values ​​in the database; The interpolated estimated position matrix is ​​loaded onto the aircraft velocity direction, and Point3 in the Point1 coordinate system is transformed to the corresponding position in Point2: And correct actions that cross the flight limit boundaries based on the flight limit boundaries, including: (1) The lower limit of flight that cannot fly normally; (2) The upper limit of flight speed affected by aircraft speed; (3) Turning limits affected by aircraft speed; The predicted position of the aircraft under different maneuvers is obtained: In the formula, The flight limit boundary is γ, which is the bias parameter. c) Using the aircraft's current speed V2(x,y,z) and direction, determine the algorithm's application process and obtain the action category probability matrix: d) Using the aircraft's current position X2(x,y,z), velocity V2(x,y,z) and direction, the opponent's current position X1(x,y,z) and velocity V1(x,y,z), and the opponent's missile's current position X M (x,y,z) and velocity V M The input environment discrimination algorithm (x, y, z) is used to obtain the current environment category, and the action transition matrix under the current environment condition is extracted from the transition matrix database. The process of constructing the action transition matrix is ​​as follows: (1) Extract time series data from the test data; (2) Obtain the environmental category of the current time series through an environmental discrimination algorithm; (3) Obtain the probability matrix of the action category of the current action through the action discrimination algorithm; (4) Accumulate the current action category probability matrix into the transition matrix database; (5) After processing all the test data, normalize the transition matrix database; e) The action category probability matrix Action transition matrix Motion prediction position matrix The predicted aircraft position is calculated by multiplying the results:

2. The aircraft position prediction method based on a hidden Markov model according to claim 1, characterized in that, The algorithm model construction method in the algorithm flow is as follows: (1) The maneuvering strategies performed by aircraft vary greatly under different combat environments. Taking into account various environmental parameters and classifying the combat environment in which the aircraft is located based on experience, we can improve the accuracy of predicting specific maneuvers under specific conditions. (2) Predicting the future position of an aircraft by using the current motion parameters and environmental parameters is an end-to-end regression task. It places high demands on the distribution characteristics and quantity of the dataset. It cannot meet the requirements of effective modeling and interpretable, easily modifiable algorithm model construction in the case of small samples. It is necessary to obtain a wide range of samples and use the improved KNN clustering algorithm to transform the three-dimensional velocity features into a motion feature category matrix, which facilitates the construction of the model and the interpretability of the prediction process. (3) In the simulation environment, set up the aircraft of the same type along the features of the nearest center and a certain range around it, and perform corresponding actions according to a certain degree of separation. Record the flight trajectory and establish an action position database. Test and measure the motion boundary of the aircraft under different altitude and speed conditions to further improve the prediction accuracy in the prediction process. (4) Based on experience, the motion transfer matrix is ​​initially set for various environmental conditions, and a transfer matrix database is established; Collect simulation samples, classify them into different environmental conditions, and correct the corresponding action transition matrices; It provides a real-time learning interface, allowing the algorithm to correct the action transition matrix values ​​based on the label values ​​while calculating the corresponding action transition matrix, so as to better fit the actual combat strategy.

Images