An escape target gaussian process regression trajectory prediction method

Abstract

A Gaussian process regression method for predicting the trajectory of an escaping target belongs to the field of target trajectory prediction and analysis. In the escape process of a non-cooperative ground target, this method uses the target's velocity and heading angle sequences as subsequent prediction inputs based on the target's historical trajectory information. The target's velocity during the escape process is modeled as a submartingale process, with the velocity at each moment modeled as a random variable. Based on the velocity range determined by the target's kinematic constraints, the feasible velocity range within the prediction time domain is quantitatively narrowed using given confidence probabilities and submartingale inequalities. Then, Gaussian process regression is used to predict the velocity and heading angle respectively, and the velocity prediction results are corrected according to the feasible velocity range. Finally, based on the target's discrete state equation and the prediction results, a reliable target trajectory prediction result that satisfies the target's kinematic constraints is obtained. This invention is applicable to fields such as traffic scheduling and criminal pursuit, improving the accuracy of ground target tracking.

Description

Technical Field

[0001] This invention relates to a method for predicting the regression trajectory of an escape target's Gaussian process, belonging to the field of target trajectory prediction and analysis. Background Technology

[0002] With the increasing complexity of future battlefield environments and the diversification of combat missions, when using UAVs to track ground targets, simply considering the target's current position often results in poor tracking accuracy. To better track maneuvering targets, introducing target trajectory prediction is more reasonable. Moreover, during the escape of non-cooperative targets, their maneuvers are more complex due to their aim to evade tracking, exhibiting characteristics of speed uncertainty and frequent turning. Therefore, trajectory prediction for such non-cooperative targets during their escape is particularly important in tracking control applications. Currently, the mainstream target trajectory prediction methods are divided into three types: (1) using Kalman filtering to predict the position of the ground moving target at the next moment based on the target's state equation; (2) using Long Short-Term Memory networks to provide prediction results over a relatively long period of time with the support of a sufficiently large dataset; and (3) using regression methods such as Gaussian process regression for prediction.

[0003] Directly applying Gaussian process regression (referred to as the "direct method") essentially predicts the time series of a target trajectory without considering the actual target type and kinematic constraints. When the predicted target motion is complex, the direct method suffers from distortion due to excessively large or small gaps between adjacent predicted positions. Excessively large gaps imply a high target velocity requirement, which may exceed the upper limit of the ground target's velocity at the corresponding prediction time. Conversely, excessively small gaps imply a low target velocity, where the difference between the current prediction time and the previous prediction time may exceed the maximum deceleration. In these cases, the prediction results do not meet the kinematic constraints of the ground target and are unattainable for the target, constituting invalid predictions. While Gaussian process regression does not require a training dataset and has a long prediction time domain, for complex target motions, the trajectory prediction results may fail to meet the target's kinematic constraints, leading to invalid predictions and adversely affecting subsequent tracking and control. Summary of the Invention

[0004] To address the shortcomings of existing technologies in predicting complex trajectories of ground targets that do not meet kinematic constraints, the main objective of this invention is to provide a Gaussian process regression trajectory prediction method for escape targets. This method takes into account both the upper and lower limits of the allowable velocity at the corresponding prediction time, and further quantitatively narrows the feasible prediction velocity range based on a given confidence probability. This yields trajectory prediction results for complex ground target motion conditions that satisfy the target's kinematic constraints and are reasonably reliable, thereby improving the tracking accuracy of ground targets.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] This invention discloses a Gaussian process regression trajectory prediction method for escaping targets. During the escape of a non-cooperative ground target, the method uses the target's velocity and heading angle sequences as subsequent prediction inputs based on the target's historical trajectory information. The target's velocity during the escape process is modeled as a submartingale process, with the target velocity at each moment modeled as a random variable. Based on the velocity range determined by the target's kinematic constraints, the feasible velocity range within the prediction time domain is quantitatively narrowed using given confidence probabilities and submartingale inequalities. Then, Gaussian process regression is used to predict the velocity and heading angle respectively, and the velocity prediction results are corrected according to the feasible velocity range. Finally, based on the target's discrete state equation and the prediction results, a reliable target trajectory prediction result that satisfies the target's kinematic constraints is obtained, improving the tracking accuracy of ground targets.

[0007] This invention discloses a method for predicting the regression trajectory of an escape target's Gaussian process, comprising the following steps:

[0008] Step 1: Calculate approximate values ​​for the velocity and heading angle of the ground target;

[0009] Let the current time be k. Based on the current position of the ground target (x(k), y(k)), where x and y are the horizontal and vertical coordinates of the ground target in the inertial coordinate system, and the previous position of the ground target (x(k-1), y(k-1)), i.e., the positions of the ground target between two adjacent times, we can obtain approximate values ​​for the velocity and heading angle of the ground target.

[0010]

[0011]

[0012]

[0013] Where T is the sampling time; v x (k) and v y (k) are the approximate values ​​of the X-direction velocity and Y-direction velocity of the ground target in the inertial frame at time k, respectively; v(k) is the approximate value of the ground target velocity; and ψ(k) is the approximate value of the ground target heading angle.

[0014] Step 2: Quantitatively narrow down the feasible prediction speed range based on the confidence probability;

[0015] Estimate the maximum acceleration / deceleration a of the ground target based on its type. max and a min .

[0016] When a ground target discovers it is being tracked, its maneuvering tendency is to accelerate and escape. To evade tracking, the ground target may suddenly decelerate at certain moments. Due to the target's high speed during escape, the ground target cannot make sharp turns to prevent rollover; therefore, the change in the ground target's course is generally gradual. However, over a long time span, the ground target will frequently turn. Combining the speed characteristics of the ground target, a submartingale can be applied to model the target's uncertain velocity. That is, the speed of the ground target during its escape at each moment can be considered as the value of a random variable of the submartingale at the corresponding moment.

[0017] Let the prediction time domain length be N, and the confidence probability be β, β∈(0,1). Then, based on the current time k, the sequence of the set of velocity ranges of ground targets with a confidence probability of β within the prediction time domain is defined as follows:

[0018]

[0019] Where V β (k+m|k) represents the set of velocity ranges with a confidence probability of β at time k+m, and k+m|k represents the prediction of time k+m based on the current time k, and has...

[0020] V β (k+m|k)=[max{v(k)-η m ,v min (k+m|k)},v max (k+m|k)] (5)

[0021]

[0022] M = max{T|a min |,Ta max} (7)

[0023] ρ=-ln(1-β) (8)

[0024] v min (k+m|k)=v(k)+mTa min (9)

[0025] v max (k+m|k)=v(k)+mTa max (10)

[0026] If the confidence probability β is close to 1, it means that the speed prediction result is not in the set. The probability within is extremely small, that is It is a sequence of speeds with a confidence probability close to 1 and a reasonable range.

[0027] Using the historical velocity sequence as input to Gaussian process regression, the target velocity prediction value is obtained. Using equation (4) for amplitude limiting correction, a feasible ground target velocity prediction result can be obtained. This velocity prediction result conforms to the kinematic constraints and maneuver characteristics of the ground target and the confidence probability is close to 1.

[0028] Step 3: Predict speed and heading angle, and correct the speed prediction results;

[0029] The number of time points required for Gaussian process regression input, including the location information of ground targets at the corresponding time, is N. b Based on step one, the historical velocity and heading angle sequences are obtained. These sequences are then used as inputs for Gaussian process regression prediction. The predicted velocity output is limited by the feasible velocity range obtained in step two.

[0030]

[0031] Where k+j|k represents the prediction of time k+j based on the current time k.

[0032] Taking into account the changes in heading angle during the escape of ground targets, the heading angle sequence is used as the input of Gaussian process regression to obtain the predicted heading angle value in the prediction time domain.

[0033] Step 4: Based on the discrete state equations, obtain a reliable target trajectory prediction result that satisfies the target kinematic constraints;

[0034] After obtaining the predicted values ​​of velocity and heading angle, the predicted target position at each time point in the prediction time domain is calculated according to equation (12).

[0035]

[0036] Where x(k+j|k) and y(k+j|k) are the X-direction and Y-direction positions of the ground target in the inertial frame at time k+j, respectively.

[0037] It also includes step five: based on the target trajectory predicted in step four, the direction of movement of the ground target and its potential location at future moments can be predicted more accurately, providing more accurate prediction results for subsequent tracking and control applications, improving the tracking accuracy of the ground target, and solving related engineering problems.

[0038] Beneficial effects

[0039] 1. The present invention discloses a method for predicting the trajectory of an escape target through Gaussian process regression. It utilizes first-order difference to convert the target's historical position sequence as prediction input into velocity and heading angle sequences as prediction input, thereby enabling the application of kinematic constraints on the trajectory prediction results.

[0040] 2. The present invention discloses a Gaussian process regression trajectory prediction method for an escape target, which models the velocity of the target during the escape process as a submartingale process, which facilitates the quantitative description of the uncertainty behavior of the target velocity; based on the velocity range that satisfies the kinematic constraints, the feasible velocity range in the prediction time domain is further quantitatively narrowed with a given confidence probability, and the Gaussian process regression prediction result of the target velocity is corrected with the feasible range, which can improve the accuracy of subsequent trajectory prediction.

[0041] 3. The present invention discloses a Gaussian process regression trajectory prediction method for an escape target. Based on the discrete state equation of the target and the prediction results of velocity and heading angle, it can obtain a reliable target trajectory prediction result that satisfies the kinematic constraints of the target, thereby improving the tracking accuracy of ground targets. Attached Figure Description

[0042] Figure 1 This is a flowchart of a method for predicting the regression trajectory of an escape target Gaussian process, as disclosed in this invention.

[0043] Figure 2 This is a schematic diagram of the ground target velocity in an example of the present invention.

[0044] Figure 3 This is a schematic diagram of the heading angle of a ground target in an embodiment of the present invention.

[0045] Figure 4 This is a schematic diagram of the ground target trajectory in an example of the present invention.

[0046] Figure 5 This is a schematic diagram of the predicted velocity boundary with a confidence probability of 80% at t=60s, as shown in the example of this invention.

[0047] Figure 6 is a comparison of the prediction effects of the method of the present invention and the direct method.

[0048] Figure 6(a) is a comparison of trajectory prediction results at t=4s; Figure 6(b) is a comparison of trajectory prediction results at t=20s; Figure 6(c) is a comparison of trajectory prediction results at t=40s; and Figure 6(d) is a comparison of trajectory prediction results at t=80s. Detailed Implementation

[0049] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. The technical problems solved by the present invention and its beneficial effects are also described. It should be noted that the described embodiments are only intended to facilitate understanding of the present invention and do not constitute any limitation thereof.

[0050] This invention employs Matlab simulation to collect velocity, heading angle, and position information of a ground target during its escape process, and then predicts the target's trajectory over a future period. This example discloses a Gaussian process regression trajectory prediction method for an escape target, with the following specific implementation steps:

[0051] Step 1: Calculate approximate values ​​for the velocity and heading angle of the ground target;

[0052] Based on the current time k, the ground target's position (x(k), y(k)), where x and y are the ground target's horizontal and vertical coordinates in the inertial coordinate system, and the previous time k-1, the ground target's position (x(k-1), y(k-1)), i.e., the ground target's position between two adjacent times, we can obtain approximate values ​​for the ground target's velocity and heading angle.

[0053]

[0054]

[0055]

[0056] Taking T = 0.5s, the approximate values ​​of the transverse and longitudinal velocity components in the inertial coordinate system can be obtained from equation (1), the approximate value of the ground target velocity v(k) can be obtained from equation (3), and the approximate value of the ground target heading angle ψ(k) can be obtained from equation (2).

[0057] Step 2: Quantitatively narrow down the feasible prediction speed range based on the confidence probability;

[0058] Based on the type of ground target, the maximum acceleration / deceleration a of the ground target can be estimated. max and a min In the example a max =|a min |=2ms 2 .

[0059] We apply submartingale to model the uncertain velocity of a target during its escape process, treating the target's velocity at each moment as the value of a random variable in a submartingale stochastic process at the corresponding moment, and introduce the relevant submartingale inequalities.

[0060] make For the set of non-negative integers, And q < s, let Ω represents the sample space. Let Pr represent the set of events, E represent the expected value, and Var represent the variance.

[0061] Consider a discrete-time martingale Sequence of child events and Then for all There exists a positive number σ m And M, satisfy and X m -E[X m |X m-1 If ]≤M, then for all η≥0

[0062]

[0063] Equation (13) shows that there is a stochastic process. If it is a martingale, then Pr[X] m There is an upper limit to ≤X0-η.

[0064] When a ground target discovers it is being tracked, its maneuvering tendency is to accelerate and escape. To evade tracking, the ground target may suddenly decelerate at certain moments. Due to the target's high speed during escape, the ground target cannot make sharp turns to prevent rollover; therefore, the change in the ground target's course is generally gradual. However, over a long time span, the ground target will frequently turn. Combining the speed characteristics of the ground target, a submartingale can be applied to model the target's uncertain velocity. That is, the speed of the ground target during its escape at each moment can be considered as the value of a random variable of the submartingale at the corresponding moment.

[0065] In this example, the prediction time domain length is N = 10, and the confidence probability is β = 80%. Then, based on the current time k, the sequence of velocity ranges of ground targets within the prediction time domain with a confidence probability of β is defined as follows:

[0066]

[0067] Where V β (k+m|k) is the set of velocity ranges with a confidence probability of β at time k+m, and has

[0068] V β (k+m|k)=[max{v(k)-η m ,v min (k+m|k)},v max (k+m|k)] (5)

[0069]

[0070] M = max{T|a min |,Ta max} (7)

[0071] ρ=-ln(1-β) (8)

[0072] v min(k+m|k)=v(k)+mTa min (9)

[0073] v max (k+m|k)=v(k)+mTa max (10)

[0074] The velocity curves of ground targets acquired in the example are as follows: Figure 2 As shown, the target speed limit is 25 m / s, with minor fluctuations allowed. Figure 2 As can be seen, during the escape process, non-cooperative ground targets will suddenly decelerate and accelerate at certain moments to evade tracking. The overall change in the ground target's speed shows an upward trend. Due to the limitations of the ground target's own performance, the maximum escape speed fluctuates around the upper speed limit. The heading angle curve is as follows: Figure 3 As shown, by Figure 3 As can be seen, non-cooperative ground targets will continuously change their direction of travel to evade tracking, complicating their movement and inevitably increasing the difficulty of trajectory prediction. The actual trajectory curve of the ground target is shown below. Figure 4 As shown, Figure 4 The results verified Figure 2 and Figure 3 The analysis of ground target motion tends to be more complex. In the example, at time t=60s, the feasible velocity prediction range obtained based on the given confidence probability and the lower martingale inequality is as follows: Figure 5 As shown, by Figure 5 It is evident that the feasible range of predicted velocity is asymmetrical, limited by the confidence probability and the maximum velocity. Compared to the velocity range determined directly by target dynamics constraints, i.e., the maximum acceleration and deceleration, the method of this invention further narrows the feasible range of predicted velocity, making the trajectory prediction results more accurate.

[0075] Step 3: Predict speed and heading angle, and correct the speed prediction results;

[0076] Perform Gaussian process regression prediction on the velocity and heading angle of ground targets. Let N be... b =20, based on step one, the historical velocity sequence and heading angle sequence are obtained, N b =20 is insufficient in the initial stage of ground target trajectory prediction. The solution of this invention is to predict the target trajectory of future time points of equal length based on the number of existing historical time points. This applies when the number of existing historical time points is greater than N but less than N. b The same steps are used to predict the target trajectory at N future time points.

[0077] The obtained target velocity sequence and heading angle sequence are used as inputs for Gaussian process regression prediction. The velocity prediction output is limited by the feasible predictable velocity range obtained in step two based on the martingale.

[0078]

[0079] Where k+j|k represents the prediction of time k+j based on the current time k.

[0080] Considering that the target moves at a relatively high speed during the escape process and the trend of speed direction change is relatively gentle, the accuracy of direct prediction is high, and Gaussian process regression can be directly applied for prediction.

[0081] Step 4: Based on the discrete state equations, obtain a reliable target trajectory prediction result that satisfies the target kinematic constraints;

[0082] After obtaining the predicted values ​​of speed and heading angle, the predicted value of the target position at the corresponding prediction time can be obtained according to equation (12).

[0083]

[0084] Where x(k+j|k) and y(k+j|k) are the X-direction and Y-direction positions of the ground target in the inertial frame at time k+j, respectively.

[0085] Figure 6 compares the method of this invention with the direct method. As shown in Figure 6(a), in the initial prediction stage, due to the limited number of historical time points, neither method can accurately predict the target trajectory. However, the method proposed in this invention is more accurate in predicting the heading of the ground target and can better infer the direction of movement of the ground target. As shown in Figures 6(b) and (d), the direct prediction method has the problem of excessively large or small spacing between adjacent predicted trajectory points at the end of the prediction time domain. As can be seen from the velocity curve of the ground target, the velocity of the ground target is near the upper limit of velocity at this time. Excessively large or small spacing between adjacent predicted trajectory points at the end of the prediction time domain does not satisfy the kinematic constraints of the ground target. The trajectory prediction result of the original method is an invalid prediction, and the target will not actually reach the predicted position. As shown in Figure 6(c), both trajectory prediction methods satisfy the kinematic constraints regarding the velocity of the ground target and have similar judgments on the target's motion trend, which can be judged as a hyperbolic motion. However, the improved method proposed in this invention considers a smaller range of feasible target velocities, thus it can more accurately infer the potential position of the ground target in the future, which provides a more accurate basis for subsequent tracking and control applications. Based on the comparison of trajectory prediction results between the improved method and the direct method in the examples of this invention, it is shown that this invention can correct the invalid trajectory prediction of the original Gaussian process regression method in complex motion scenarios of target escape, and improve the accuracy of prediction by narrowing the feasible speed range.

[0086] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is merely a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting the regression trajectory of an escape target's Gaussian process, characterized in that: Includes the following steps, Step 1: Calculate approximate values ​​for the velocity and heading angle of the ground target; Step 2: Quantitatively narrow down the feasible prediction speed range based on confidence probabilities; When a ground target discovers it is being tracked, its maneuvering tendency is to accelerate and escape. To evade tracking, the ground target may suddenly decelerate at certain times. Due to the high speed of the target during the escape, the ground target cannot make sharp turns to prevent rollover. Therefore, the change in the ground target's course is relatively gradual, but over a long time span, the ground target will frequently turn. Combining the speed characteristics of the ground target, a submartingale can be applied to model the uncertain speed of the target, that is, the speed of the ground target during the escape process at each moment can be regarded as the value of the submartingale random variable at the corresponding moment. Take the prediction time domain length as The confidence probability is , Based on the current time The ground target has an embedded probability of being in the prediction time domain. The speed range set sequence is defined as (4) in for The confidence probability at time step is The set of speed ranges, Indicates based on the current time predict At any time, and have (5) (6) (7) (8) (9) (10) Confidence probability A value close to 1 indicates that the predicted velocity is not in the set. The probability within is extremely small, that is It is a sequence of speeds with a confidence probability close to 1 and a reasonable range. Using the historical velocity sequence as input to Gaussian process regression, the target velocity prediction value is obtained. Using equation (4) for amplitude limiting correction, a feasible ground target velocity prediction result can be obtained. The velocity prediction result conforms to the kinematic constraints and maneuver characteristics of the ground target and the confidence probability is close to 1. Step 3: Predict speed and heading angle, and correct the speed prediction results; Step 4: Based on the discrete state equations, obtain a reliable target trajectory prediction result that satisfies the target kinematic constraints.

2. The method for predicting the regression trajectory of an escape target's Gaussian process as described in claim 1, characterized in that: The implementation method for step one is as follows: Define the current time as Based on the current position of the ground target , and These represent the horizontal and vertical coordinates of the ground target in the inertial coordinate system, and the position of the ground target at the previous moment. This means taking the ground target's position at two adjacent moments, and obtaining approximate values ​​for its velocity and heading angle. (1) (2) (3) in Sampling time; and They are time points Ground targets in inertial frame Directional velocity and Approximate value of directional velocity, This is an approximation of the velocity of the ground target. This is an approximation of the heading angle of the ground target.

3. The method for predicting the regression trajectory of an escape target's Gaussian process as described in claim 2, characterized in that: The implementation method for step three is as follows: Estimate the maximum acceleration / deceleration of the ground target based on its type. and The number of time points required for Gaussian process regression input, including the location information of ground targets at the corresponding time, is: Based on step one, the historical velocity and heading angle sequences are obtained. These sequences are then used as inputs for Gaussian process regression prediction. The predicted velocity output is limited by the feasible velocity range obtained in step two. (11) in Indicates based on the current time predict time; Taking into account the changes in heading angle during the escape of ground targets, the heading angle sequence is used as the input of Gaussian process regression to obtain the predicted heading angle value in the prediction time domain.

4. The method for predicting the regression trajectory of an escape target's Gaussian process as described in claim 3, characterized in that: The implementation method for step four is as follows: After obtaining the predicted values ​​of velocity and heading angle, the predicted target position at each time in the prediction time domain is calculated according to equation (12). (12) in and They are respectively Ground targets at any given time in an inertial frame Direction and position Direction and position.

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