Moving target trajectory prediction method based on MLP network

Abstract

The invention provides a method for predicting the trajectory of a moving target based on a multi-layer perceptron (MLP) network, which is assisted by a direct position difference (DPD) algorithm, and relates to a method for predicting the trajectory of the moving target based on the multi-layer perceptron (MLP) network, in particular to a method for predicting the trajectory of the moving target based on the multi-layer perceptron (MLP) network. After a received signal is input, the method firstly samples the received signal, then estimates each observation moment position of a target by using an improved sub-space fusion (ISDF) criterion, and finally puts an estimation result into a trained MLP prediction network to obtain a detected trajectory and a trajectory prediction result in a future period of time. According to the method, the high-precision positioning advantage of a direct positioning algorithm and the powerful nonlinear modeling capability of an MLP network in deep learning are combined, and a feasible scheme is provided for reference of a direct positioning technology in the field of trajectory prediction.

Description

Technical Field

[0001] This invention discloses a method for predicting the trajectory of a moving target based on a multilayer perceptron (MLP) network, combining direct localization technology and deep learning methods, and involves fields such as passive localization and deep learning. Technical Background

[0002] Passive positioning method [1] Research began during World War II and continues to this day in radar, timing, navigation, and wireless sensors. [2] It has been widely applied in both military and civilian fields. Traditional passive positioning technology uses a two-step method: the first step estimates the target's Direction of Arrival (DOA) and Time Difference of Arrival (TDOA). [3,4] The first step involves obtaining parameters such as Frequency Difference of Arrival (FDOA). The second step uses the information obtained in the first step to establish mathematical equations to solve for the target's position. Although the traditional two-step method is simple to implement due to its computational simplicity, it suffers from information loss during the process and ignores the implicit constraint that all measurements come from the same target. Therefore, its positioning performance is poor under low signal-to-noise ratio (SNR) conditions.

[0003] In contrast, Direct Position Determination (DPD) technology... [5] The DPD technique can directly determine the target's location information from the original signal samples. Because it eliminates the need to estimate intermediate parameters, it avoids the information loss inherent in two-step methods and also satisfies the constraint that all received signals originate from the same source. The DPD technique has attracted widespread attention from scholars both domestically and internationally due to its higher positioning accuracy at low signal-to-noise ratios (SNR).

[0004] For unknown target radiation sources, estimating the target's trajectory over a future period helps observers gather more information about the target and make informed decisions. Target trajectory prediction requires one or more sets of position prediction results; traditional prediction methods include Kalman filtering (KF). [6]For direct localization techniques, the nonlinearity of the received signal model is very high. Directly processing the received signal using traditional prediction methods will significantly reduce the prediction accuracy. Deep learning, as a powerful paradigm in machine learning, has made significant progress in many fields. In trajectory fitting, it accurately reconstructs the motion path of an object through the analysis of time-series data. Multilayer Perceptron (MLP) [7] As one of the basic structures of deep learning, neural networks, with their hierarchical neuron organization, can effectively capture nonlinear features, thus providing strong support for complex trajectory fitting tasks and are widely used in the field of trajectory fitting and prediction. Summary of the Invention

[0005] This invention fully leverages the high-precision positioning advantage of direct localization algorithms and the powerful nonlinear modeling capabilities of MLP networks in deep learning to propose a moving target trajectory prediction method based on MLP networks. This invention first samples the received signal and then utilizes an improved subspace data fusion (ISDF) criterion. [8] The position of the target is estimated at each observation time, and the estimation results are then fed into a trained MLP prediction network to obtain the trajectory prediction results for a future time period. This invention combines the high-precision positioning advantage of the direct localization algorithm with the powerful nonlinear modeling capability of the MLP network in deep learning, proposing a feasible solution for the application of direct localization technology in the field of trajectory prediction. The technical solution adopted to achieve the above objectives is as follows:

[0006] A method for predicting the trajectory of a moving target based on an MLP network includes the following steps:

[0007] S1: Input the received signal and establish the received signal model;

[0008] Assume the initial position of the moving target is The target moves at a constant linear velocity or follows a continuous white noise acceleration (CWNA) model. The location of the stationary receiving station is The target is emitting a narrowband radio signal with an unknown waveform, which can be simultaneously detected by... A static receiving station intercepted The observation time slot is T (the observation time slot is usually very short; it is assumed that the object's position and velocity remain constant during this time period). Let the time interval between two adjacent observation time slots be... Then the object on the th The position and velocity of each observation time slot are respectively represented as: and Assume the observation station is composed of... It consists of a uniform linear array of elements, with an element spacing of [missing information]. (in (where the carrier wave is half its wavelength), then the... The first observation station at the first The signal received in each observation time slot, after down-conversion, can be expressed as:

[0009] (1)

[0010] in and For the signal at the 1st The observation time slot reached the [number]th [time slot]. The complex propagation coefficient and signal complex envelope of each receiving station, The noise power is 0 with a mean of zero. Gaussian white noise.

[0011] The array response vector can be represented as:

[0012] (2)

[0013] in, For carrier wavelength, For the spacing between array elements, , It is DOA.

[0014] For time delay, it is represented as follows:

[0015] (3)

[0016] This is the Doppler frequency shift, expressed as follows:

[0017] (4)

[0018] S2: Sample the received signal model;

[0019] Assuming the sampling period is , then the first The sampled signal at each time point can be represented as:

[0020] (5)

[0021] The whole The sampled signals within are fused into a single vector:

[0022] (6)

[0023] in

[0024] (7)

[0025] Based on the Discrete Fourier Transform (DFT). and The relationship is:

[0026] (8)

[0027] in , which represents the phase deviation in the frequency domain caused by the time delay in the time domain. Represents the DFT matrix. Substituting equation (8) into equation (6) yields:

[0028] (9)

[0029] in , and It contains information about the parameters to be determined.

[0030] S3: Use the ISDF criterion to estimate the position of the moving target at the sampling time;

[0031] make Representing the The first observation station at the first All sampled signals within each observation time slot, ( ).

[0032] So covariance matrix The estimated value It can be represented as:

[0033] (10)

[0034] Perform eigenvalue decomposition on it:

[0035] (11)

[0036] in For signal subspace; It is a diagonal matrix, and the diagonal elements are the eigenvalues ​​arranged in descending order; It is the noise subspace.

[0037] The cost function for objective estimation based on the ISDF criterion can be expressed as:

[0038] (12)

[0039] The cost function is searched in a gridded manner within the planned region, and the location corresponding to the maximum value is the estimated location of the target at each time step.

[0040] S4: Use the trained MLP network to predict the trajectory of the target over a future period of time;

[0041] MLP neural networks mainly consist of three parts: an input layer, hidden layers, and an output layer. After obtaining the target output layer in the previous step... The bit at time t, therefore the input can be represented as The output is the target value before... Position estimation at a given moment and future Position prediction results at each time point ( The target number (Estimation results at each time point).

[0042] During the training phase, the training set is the set estimated in the previous step. Target trajectory estimation results at time 1 , tag as target That moment and the future The actual trajectory at that moment . ( The target number (The actual location at any given moment).

[0043] choose and The mean squared error (MSE) function is used as the loss function to optimize the output of the MLP network. Wireless Approach The expression for the loss function is:

[0044] (13)

[0045] in It's the loss rate.

[0046] The training process of MLP networks is derived as follows:

[0047] (14)

[0048] in, , It is the activation function pair from the hidden layer to the output layer. The derivative of .

[0049] (15)

[0050] (16)

[0051] (17)

[0052] (18)

[0053] The above is The derivatives of each adjustable parameter are used to update the weights and biases of each neuron.

[0054] (19)

[0055] , and The update method is similar, among which, The learning rate affects the speed of gradient descent.

[0056] S5: Output object before The target estimation results at each moment and the future The trajectory prediction results at each time point. Attached Figure Description

[0057] Figure 1 This is a flowchart illustrating a method for predicting the trajectory of a moving target based on an MLP network.

[0058] Figure 2 Schematic diagram of a scenario for locating a moving target;

[0059] Figure 3 This is a system block diagram of a moving target trajectory prediction method based on MLP networks;

[0060] Figure 4 Here is a diagram of the MLP neural network structure;

[0061] Figure 5 A trend chart of the ReLU function loss value of an MLP network;

[0062] Figure 6 Real-time performance diagram of target detection and trajectory prediction;

[0063] Figure 7 This is a comparison chart of the effects of different prediction schemes. Specific implementation methods

[0064] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent.

[0065] This invention can be implemented in different ways and is not limited to the specific embodiments described herein;

[0066] It will be understood by those skilled in the art that certain well-known structures and their descriptions may be omitted in the accompanying drawings.

[0067] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0068] Example 1

[0069] This embodiment provides a method for predicting the trajectory of a moving target based on an MLP network, such as... Figure 1 The flowchart shown includes the following steps:

[0070] S1: Input the received signal and establish the received signal model. Figure 2 Schematic diagram of a scenario for locating a moving target;

[0071] (20)

[0072] S2: Sample the received signal and use the discrete Fourier transform to improve the model;

[0073] (twenty one)

[0074] S3: Estimate the position of the moving target at the sampling time using the ISDF criterion; the cost function for target estimation based on the ISDF criterion can be expressed as:

[0075] (twenty two)

[0076] The cost function is searched in a gridded manner within the planned region, and the location corresponding to the maximum value is the estimated location of the target at each time step.

[0077] S4: Use the trained MLP network to predict the trajectory of the target over a future period of time;

[0078] Figure 4 For the MLP neural network architecture diagram, select and The MSE function between them is used as the loss function, which makes the output of the MLP network... Wireless Approach The expression for the loss function is:

[0079] (twenty three)

[0080] in It's the loss rate.

[0081] S5: Output object before The target estimation results at each moment and the future The trajectory prediction results at each time point.

[0082] In the specific implementation process, the simulation parameters are set as follows: With a signal-to-noise ratio of 0dB, four 4-element uniform linear arrays (ULAs) are considered, with the element spacing equal to half the wavelength. The positions of the four observation stations are (0,0)m, (0,4000)m, (4000, 0)m, and (4000,4000)m, respectively. It is assumed that the radiated signal from the moving target is a pulse sequence with a bandwidth of 0.4 MHz and a sampling rate of... (Hz), carrier frequency is (Hz). Each station collects data within each observation time slot. 1 sample, speed of light is (m / s). The initial position, velocity, and acceleration distribution of the target are shown in Table 1, where... Representing variables satisfy and The uniform distribution between them.

[0083] Table 1: Distribution of Target Initial Position, Velocity, and Acceleration

[0084]

[0085] Figure 3 This is a system block diagram for a moving target trajectory prediction method based on MLP networks. In this example, the total number of observation time slots is... Therefore, by inputting the observed signals from the first 8 time points, sampling the received signal, and estimating the observed signals, the signal is obtained. The position at each moment, and then the detected results (previous) The estimation results at each time step are fed into the trained MLP network to give the future... The trajectory prediction results at each time point.

[0086] Figure 5 The graph shows the trend of the ReLU function loss value of the MLP network. The loss value gradually decreases as the number of iterations increases.

[0087] Figure 6 The image shows the real-time performance of target detection and trajectory prediction. The green curve represents the target's true trajectory. The estimation results for the current moment are shown as the black dots in the figure, and the trajectory prediction results for the future period are shown as the red dashed lines in the figure. Specific numerical comparison results are given in Tables 2 and 3.

[0088] Table 2 Trajectory Detection Table (Unit: m)

[0089]

[0090] Table 3 Trajectory Prediction Table (Unit: m) )

[0091] Example 1 shows that, under low signal-to-noise ratio conditions, the method of the present invention can predict the trajectory for a future period of time after detecting the existing trajectory of the target, and the accuracy is high.

[0092] Example 2

[0093] This embodiment, based on Embodiment 1, further discloses the following: Currently, the most classic and commonly used data-based trajectory prediction algorithms include traditional trajectory prediction algorithms based on data fitting and dynamic trajectory prediction algorithms based on KF. Before estimating the target using the direct positioning method, this invention... After obtaining the trajectory at each time point, the results are fed into both algorithms to predict the trajectory on the same simulation platform and compared with the results output by the MLP network.

[0094] To obtain stable results, this paper sets the number of Monte Carlo trials to 100. The root mean square error (RMSE) is used to calculate the geometrical spatial error between the predicted trajectory points and the actual trajectory points.

[0095] (twenty four)

[0096] In the formula To predict the system for the first The target's true location at any given moment The predicted value. When trajectory prediction is complete, Compared with a given threshold, if If the value is less than the threshold, it is considered a hit; otherwise, it is considered a miss. Finally, the overall hit rate is calculated to measure the predictive performance of the system.

[0097] The mean distance between the target and each observation station at each time step is R. The threshold for determining whether the target has been hit is 0.05R. When the root mean square error (RMSE) of the prediction point is less than 0.05R, it is considered a hit. The simulation parameters are the same as the previous two sets of experiments, and the online prediction results are as follows: Figure 7 As shown in Table 4, after estimating the target location information, the data was fed into three different methods, and target trajectory prediction results were obtained in all of them.

[0098] Table 4. Trajectory prediction results of different algorithms (unit: seconds)

[0099] Example 2 shows that under low signal-to-noise ratio, the prediction method based on MLP described in this invention has the least total running time and the least complexity, making it most suitable for real-time prediction.

[0100] Finally, it should be noted that the above-described embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above examples, those skilled in the art should understand that different modifications or equivalent substitutions can still be made to the specific implementation scenarios or methods of the present invention. It is neither necessary nor possible to exhaustively list all implementation methods here. Any modifications, equivalent substitutions, and improvements that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

[0101] [1] Guo Fucheng, Li Jinzhou, Zhang Min. Principles and methods of passive positioning [M]. Beijing: National Defense Industry Press, 2021.

[0102] [2]Wax M, Kailath T. Optimum localization of multiple sources bypassive arrays[J]. IEEE Transactions on Acoustics, Speech, and SignalProcessing, 1983, 31(5): 1210 – 1217.

[0103] [3]Gholami M R. Improved position estimation using hybrid TW-TOA andTDOA in cooperative networks[J]. IEEE Transactions on Signal Processing, 2012, 60(7): 3770 – 3785.

[0104] [4]Chan YT, Ho K C. A simple and efficient estimator for hyperboliclocation[J]. IEEE Transactions on Signal Processing, 1994, 42(8): 1905 –1915.

[0105] [5]Amar A, Weiss A J. Direct position determination of multiple radiosignals[C] / / IEEE International Conference on Acoustics. Montreal, Quebec,Canada : IEEE, 2004 : 81 – 84.

[0106] [6]Simon D. Kalman filtering[J]. Embedded systems programming, 2001,14(6) : 72 – 79.

[0107] [7]Yilmaz I, Kaynar O. Multiple regression, ANN (RBF, MLP) and ANFISmodels for prediction of swell potential of clayey soils[J]. Expert Systemswith Applications, 2011, 38(5) : 5958 – 5966.

[0108] [8]He, S, Jiang Y, Zhao L et al. Direct position determination ofmoving targets based on DOA[J]. Electronics Letters, 2024, 60(15):1-4.

Claims

1. A method for predicting the trajectory of a moving target based on an MLP network. Its characteristics include the following steps: S1: Input the received signal and establish the received signal model; S2: Sample the received signal and use the discrete Fourier transform to improve the model; S3: Use the ISDF criterion to estimate the position of the moving target at the sampling time; S4: Use the trained MLP network to predict the trajectory of the target over a future period of time; S5: Output object before The target estimation results at each moment and the future The trajectory prediction results at each time point.

2. The method for predicting the trajectory of a moving target based on an MLP network according to claim 1, characterized in that, In step S1, the received signal is input, and the received signal model is established, as follows: Assume the initial position of the moving target is The target moves at a constant linear velocity or follows a continuous white noise acceleration (CWNA) model. The location of the stationary receiving station is The target is emitting a narrowband radio signal with an unknown waveform, which can be simultaneously detected by... A static receiving station intercepted The observation time slot is T (the observation time slot is usually very short; it is assumed that the object's position and velocity remain constant during this time period). Let the time interval between two adjacent observation time slots be... Then the object on the th The position and velocity of each observation time slot are respectively represented as: and Assume the observation station is composed of... It consists of a uniform linear array of elements, with an element spacing of [missing information]. (in (where the carrier wave is half its wavelength), then the... The first observation station at the first The signal received in each observation time slot, after down-conversion, can be expressed as: (1) in The array response vector can be represented as: (2) in , For DOA, For time delay, it is represented as follows: (3) This is the Doppler frequency shift, expressed as follows: (4) and For the signal at the 1st The observation time slot reached the [number]th [time slot]. The complex propagation coefficient and signal complex envelope of each receiving station, The noise power is 0 with a mean of zero. Gaussian white noise.

3. The method for predicting the trajectory of a moving target based on an MLP network according to claim 1, characterized in that, In step S2, the received signal is sampled and the model is improved using the Discrete Fourier Transform, as detailed below: Assuming the sampling period is , then the first The sampled signal at each time point can be represented as: (5) The whole The sampled signals within are fused into a single vector, represented as: (6) in (7) Based on the Discrete Fourier Transform (DFT). and The relationship is: (8) in This indicates the phase deviation in the frequency domain caused by the time delay in the time domain. Representing the DFT matrix, substituting equation (8) into equation (6) yields: (9) in , and It contains information about the parameters to be determined.

4. The method for predicting the trajectory of a moving target based on an MLP network according to claim 1, characterized in that, Step S3 uses the ISDF criterion to estimate the position of the moving target at the sampling time, specifically as follows: make Representing the The first observation station at the first All sampled signals within each observation time slot, ( ). So covariance matrix The estimated value It can be represented as: (10) Eigenvalue decomposition yields: (11) in For signal subspace; It is a diagonal matrix, and the diagonal elements are the eigenvalues ​​arranged in descending order; Given a noisy subspace, the cost function for objective estimation based on the Improved Subspace Data Fusion (ISDF) criterion can be expressed as: (12) The cost function is searched in a gridded manner within the planned region, and the location corresponding to the maximum value is the estimated location of the target at each time step.

5. The method for predicting the trajectory of a moving target based on a multilayer perceptron (MLP) network according to claim 1, characterized in that, Step S4 uses the trained MLP network to predict the target's trajectory over a future period of time, specifically as follows: Target That moment and the future The actual trajectory at each moment is: ( Is the target number (actual location at any given moment), in front of the target Position estimation at a given moment and future The predicted position at each time point is: ( Is the target number (Estimation results at each time point), select and The mean squared error (MSE) function is used as the loss function to optimize the output of the MLP network. Wireless Approach The expression for the loss function is: (13) in The loss rate is the basis for the training process of an MLP network, which is derived as follows: (14) in, , It is the activation function pair from the hidden layer to the output layer. derivative (15) (16) (17) (18) The above is The derivatives of each adjustable parameter are used to update the weights and biases of each neuron. (19) , and The update method is similar, among which, The learning rate affects the speed of gradient descent.

6. The method for predicting the trajectory of a moving target based on an MLP network according to claim 1, characterized in that, Step S5 Output Object Before The target estimation results at each moment and the future The trajectory prediction results at each time point are as follows: In step S3 The position estimation results at each time point and the future in step S4 The predicted position at each time point is plotted as the trajectory of the object.

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