A trajectory prediction method based on deleted and merged deep echo state network

Abstract

The application discloses a trajectory prediction method based on a node deletion and merging deep echo state network, optimizes the deep echo state network by using a node deletion and merging method, selects two most similar nodes according to node similarity evaluation, and merges similar nodes in the same reserve pool; similar nodes in different reserve pools at higher layers are deleted, the reserve pool structure can be adaptively optimized, redundant nodes in the network are deleted, the network optimized by using the method can be used for completing a target trajectory prediction task in an optoelectronic tracking system, and prediction precision and prediction speed can be improved, so that the performance of the optoelectronic tracking system is improved.

Description

Technical Field

[0001] The present invention belongs to the field of target trajectory prediction of optoelectronic tracking systems, and specifically relates to a trajectory prediction method based on a deleted and merged deep echo state network. The method is a technology that predicts the future trajectory of a tracking target based on signals collected by optoelectronic system sensors. The predicted trajectory can be used for feedforward control of optoelectronic tracking systems. Background Art

[0002] As a simple recurrent neural network (RNN), the echo state network (ESN) does not require backpropagation for training compared to other forms of recurrent neural networks. Instead, it randomly constructs a large hidden layer reservoir and can be trained using only simple linear regression. It performs well in many prediction tasks.

[0003] The performance of an ESN depends primarily on the structure of its hidden layer (reservoir). Numerous optimization methods have been proposed to improve this structure. The deep Echo State Network (ESN), first proposed and extensively studied by (Gallicchio, 2017), is an improved form of ESN constructed by stacking multiple single ESNs. Compared to single-layer ESNs, deep ESNs have greater reservoir information richness and the ability to represent nonlinear information.

[0004] The principle of feedforward control technology in optoelectronic tracking systems is to introduce the target miss distance signal and its various differential signals as feedforward into the control loop. Because control systems have various measurement delays caused by sensors, calculation delays caused by processors, and response delays caused by actuators, achieving ideal tracking control requires accurate prediction of the feedforward signal. Specifically, accurate predictions must be made of the target trajectory's lead position signal and its various differential signals. Target trajectory prediction technology is the core of feedforward control technology for optoelectronic tracking systems.

[0005] The target trajectory prediction technology currently commonly used by optoelectronic tracking systems includes a model-driven prediction method based on Kalman filtering. This method has poor prediction effect on randomly maneuvering non-orbital targets.

[0006] As an emerging and reliable prediction technology, deep ESN can address the uncertainty and model mismatch issues associated with target maneuvering patterns in feedforward predictive control of electro-optical systems. Electro-optical systems are low-latency, real-time control systems that place high demands on the time performance of trajectory prediction algorithms. Existing deep ESN cannot directly meet the application requirements of electro-optical tracking systems and requires further improvement. Summary of the Invention

[0007] The purpose of the present invention is to disclose a trajectory prediction method based on a deep echo state network (DESN) with pruning and merging, and to improve the traditional DESN structure. A similarity-based node pruning-merging (NPM-S) optimization method is proposed, which balances the computational complexity and error performance of the DESN. By reducing the network scale of the DESN, the computational complexity is reduced while ensuring accuracy. The DESN's advantage in predicting nonlinear objects is leveraged and applied to the target trajectory prediction feedforward of an optoelectronic tracking system, providing real-time and accurate target trajectory prediction for the optoelectronic tracking system, thereby improving the control bandwidth and tracking accuracy of the optoelectronic system.

[0008] The technical solution adopted by the present invention is: a trajectory prediction method based on a deleted and merged deep echo state network, which is implemented in the following steps:

[0009] Step (1): Initialize and construct a deep echo state network with redundant nodes;

[0010] Step (2): Iteratively use the node deletion-merging (NPM-S) optimization method based on similarity evaluation to optimize the degeneracy of each reserve pool node, reduce the network size, and keep the prediction error within a reasonable range;

[0011] Step (3): Use the optimized deep echo state network to perform real-time target trajectory prediction.

[0012] Furthermore, the steps for implementing the NPM-S optimization method in step (2) are as follows:

[0013] Step (21): Evaluate the similarity of two nodes using the node similarity evaluation method and find the two most similar nodes;

[0014] Step (22): Determine whether the two nodes selected in step (21) are in the same reserve pool. If so, go to step (31); otherwise, go to step (32).

[0015] Step (31): The two nodes selected in step (21) are merged as parent nodes into a new child node, a merging coefficient β is selected, the input weight coefficients of the original parent nodes are weighted and summed according to β:(1-β), and the output weight coefficients of the original parent nodes are weighted and summed according to 1:1;

[0016] Step (32): Discard the node at the higher level of the two nodes selected in step (21).

[0017] The principle of the present invention is that: since the reserve pool of the echo state network is constructed using random weight coefficients, it is difficult to ensure the compatibility of the reserve pool with the trajectory prediction task. The reserve pool contains a large number of neuron nodes, not all of which are helpful in obtaining the correct output. These unhelpful nodes are called "redundant nodes". Topology optimization is a practical reserve pool optimization technology that can adjust the size of the reserve pool by deleting "redundant nodes" and improve the richness of the reserve pool, so that it can obtain faster computing speed in time series prediction tasks and maintain good performance. The present invention provides a new deep echo state network optimization method. During optimization, the two most similar nodes are selected based on the node similarity evaluation, and similar nodes in the same reserve pool are merged (such as Figure 2 ); similar nodes at higher levels in different pools are deleted. This method optimizes the deep echo state network, adaptively optimizing the pool structure and removing / removing redundant nodes in the network, thereby reducing the network size without significantly increasing the network error. This method can reduce the computational efficiency of the deep echo state network, thereby meeting the trajectory prediction requirements of the electro-optical tracking system.

[0018] Compared with the prior art, the present invention has the following advantages:

[0019] (1) Compared with the general deep echo state network for target trajectory prediction, the present invention uses optimization methods to reduce the network size and the amount of calculation to meet the real-time online prediction needs of the optoelectronic tracking system.

[0020] (2) Compared with deep echo state network-inspired optimization methods, such as particle swarm optimization and genetic algorithm optimization, the present invention is simpler to implement, requires less additional computational effort, and is more robust.

[0021] (3) Compared with the feedforward prediction of the Kalman filter extrapolation method used in the photoelectric tracking system, the prediction accuracy of the present invention is higher and the scope of application is wider. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 This is a schematic diagram of the Deep ESN structure;

[0023] Figure 2 Schematic diagram of node merging connection weight coefficients, where (a) is before merging and (b) is after merging. DETAILED DESCRIPTION

[0024] The present invention is further described below with reference to the accompanying drawings and specific embodiments.

[0025] For the feedforward predictive control of optoelectronic systems, a deep echo state network is used to obtain accurate predictions of the feedforward control signal. In order to meet the low-latency requirements of the optoelectronic system for fast response, certain improvements need to be made to the deep echo state network prediction method.

[0026] The computational complexity of the deep echo state network algorithm increases with the increase in the number of nodes in the network, so we hope to keep the total number of nodes in the network as small as possible. However, the reduction in the number of nodes will also lead to poor network performance. We hope to find "redundant" nodes in the network through certain means. We propose a node deletion-merge based on similarity evaluation (NPM-S, Neuron prune merge based on similarity) optimization method to delete "redundant nodes" in the network. This method can ensure network performance while deleting redundant nodes. In order to achieve the purpose of this invention, we first briefly introduce deep ESN and clarify some parameters in the network:

[0027] like Figure 1 As shown, use represents the input signal in the network at time t, N u is the input signal dimension, Represents the hidden layer signal of the l-th layer reservoir at time t, and the number of nodes in the l-th layer is The entire network has L layers. is the output signal of the network at time t, N y is the output signal dimension. represents the first hidden layer input weight coefficient matrix, represents the echo coefficient matrix of the lth hidden layer, Represents the transfer coefficient matrix from layer l-1 to layer l. The total number of nodes in all hidden layers is is the output weight coefficient matrix of the network.

[0028] At each moment, the update equation for the reserve pool in layers 1 to L is:

[0029]

[0030] Among them, α l is the leak factor of the l-th layer reservoir, which is usually a number between 0 and 1; is the activation function of the lth layer. Represents the union of all hidden layer signals, and the network output equation is:

[0031]

[0032] Among them, f out (·) is the output layer activation function.

[0033] For a continuous set of training samples U of length T train = [u(1), u(2)…u(T)] According to formula (1), input them sequentially into deep ESN to obtain a set of training reserve pool signals The training reserve pool signal can be represented as M row vectors, where each row represents the historical state of a node from time 0 to time T.

[0034]

[0035] Define the node similarity matrix:

[0036]

[0037] Among them, the element s ij The similarity between the historical states of the i-th node and the j-th node can be calculated in the following ways:

[0038] Euclidean distance similarity:

[0039]

[0040] Pearson correlation similarity:

[0041]

[0042] Spearman correlation similarity:

[0043]

[0044] Kendall Correlation Similarity:

[0045]

[0046] in, Indicates n i and n j The mutual correlation coefficient of and Indicates n i and n j Respective autocorrelation coefficients; d t Indicates n i With n j The rank difference of the tth element, c and d represent n i and n j Corresponding to the positive and negative logarithms of the elements.

[0047] The NPM-S optimization method can be implemented through the following steps:

[0048] Step (1): Calculate the node similarity matrix S by one of the methods in equations (5)-(8), find the largest element in the non-diagonal elements of S, and obtain the two most similar node pair.

[0049] Step (2): Determine whether the most similar node pair is in the same reserve pool. If yes, go to step (31), otherwise go to step (32).

[0050] Step (31): Merge the two selected nodes (denoted as and ) into a new node (as shown in Figure 2 ). Since before merging, and are two similar nodes, it is expected that after merging will replace the parent node. Select a merging coefficient β (β∈[0,1]). Merge the input coefficients of the parent nodes according to this coefficient:

[0051]

[0052] where represents the i-th row of the matrix , and the rest are similar. If l=1, replace with , and the rest are similar. It is recommended to select β=0.5. The output weight coefficient is the sum of the original parent node weight coefficients:

[0053]

[0054] If l=L, there is no output to the next layer, only is updated, and the rest are similar.

[0055] Step (32): Select the node in and that is in a higher level and delete it (assuming m

[0056] That is, set all the weight coefficients connected to to zero:

[0057]

[0058] Thus, the NPM-S method is introduced.

[0059] The NPM-S optimization method can be iterated repeatedly, and one redundant node is selected for deletion in each round, gradually reducing the network size. Similarity evaluation ensures that the deleted (or merged) node is a redundant node, and the merging method ensures the stability of high-level nodes during iteration. During iteration, only the diversity of all reserve pool nodes is guaranteed, and no node in any reserve pool is predetermined to be deleted (or merged), so the network structure presents adaptive characteristics during optimization.

[0060] The application provides a trajectory prediction method based on a delete-merge deep echo state network, and the implementation process is as follows:

[0061] Step (1): Set the number of layers of the deep echo state network, and determine the input and output signal dimensions N u and N y , according to the hardware structure of the optoelectronic tracking system and the needs of target trajectory prediction.

[0062] Step (2): Select a suitable number of reserve pools L, and determine the number of nodes in each layer of the reserve pool The initially selected number of nodes should be redundant, and will be optimized later.

[0063] Step (3): Reserve pool weight coefficient initialization.

[0064] Step (3.1): Initialize the input weight coefficient matrix The elements in the matrix can be randomly generated according to a certain probability distribution, for example, using a uniform distribution between -1 and 1.

[0065]

[0066] Step (3.2): Determine different reserve pool leakage factors 1 ,α 2 ,…,α l , and initialize the echo coefficient matrix of each layer of the reserve pool and the transfer coefficient matrix between reserve pool layers Like , and , the elements in the matrix can also be randomly generated. It should be noted that need to meet the following necessary conditions of the echo state property of the deep echo state network (Gallicchio, 2017, Echo State Property of Deep Reservoir Computing Networks)

[0067]

[0068] where p(·) denotes the spectral radius of a matrix, numerically equal to the largest absolute value of the eigenvalues of the matrix.

[0069] So far, the initial construction of the deep echo state network has been completed. This initial construction serves as the starting point for the NPM-S optimization method.

[0070] Step (4): NPM-S iterative optimization.

[0071] Step (4.1): Select one of the similarity criteria in the aforementioned formulas (5)-(8), and apply the NPM-S optimization described in the invention content in a loop. After each round of optimization, evaluate the network's error performance according to the method described in step (4.2) until the total number of network nodes is reduced to the desired preset value, or the network error increases to the preset tolerance.

[0072] Step (4.2): After applying the NPM-S optimization method to delete (or merge) one node in each round, the error performance of the network should be evaluated. The evaluation process is as follows:

[0073] Step (4.2.1): Training sample construction.

[0074] Construct data samples from the data collected by the sensors of the photoelectric system over a period of time.

[0075] Select a continuous set of training samples U train = [u(1), u(2)…u(T)] of length T from the data samples.

[0076] Step (4.2.2): Network initialization.

[0077] Take the previous set of inputs as the washout signal U train = [..., u(-1), u(0)], U wash of length T. The length of U wash may be freely selected, typically ranging from tens to hundreds. Input U wash sequentially into the deep ESN to form memories in the reservoir.

[0078] Step (4.2.3): Weight coefficient training.

[0079] Input U train sequentially into the deep ESN according to formula (1) to obtain a set of training reservoir signals Let the desired network output be Solve the output weight coefficient W o using linear regression methods (such as least squares regression, support vector regression, ridge regression, etc.). For example: when fout (·) When the unit activation function is taken, the output weight coefficient obtained by ridge regression is:

[0080]

[0081] Where (·) T represents the transpose of the matrix, λ is the regularization coefficient, and I is the identity matrix.

[0082] Step (4.2.4): Test set verification.

[0083] Select a continuous set of test samples U of length K from the data sample test =[u(1),u(2)…u(K)], and initialize in the same way as step (4.2.2).

[0084] At each moment t∈1:K, according to formula (1), U test (t) Input deep ESN to obtain the reserve pool signal According to formula (2), the network output y(t) at the current moment is obtained. The network output at all moments is recorded as Y validate =[y(1),y(2),...,y(K)], let the expected network output be The training root mean square error of the network is:

[0085]

[0086] In the formula Y validate The mean of .

[0087] Step (5): Real-time target trajectory prediction.

[0088] The optimized network is applied to real-time target trajectory prediction. The prediction method is as follows: obtain the sensor data collected by the optoelectronic system at the current moment as the network input, and calculate the prediction results through equations (1) and (2).

[0089] What has been described above is a specific embodiment of the present invention. Any feature disclosed in this specification, unless otherwise stated in the claims, may be replaced by other equivalent or alternative features having similar purposes.

Claims

1. A trajectory prediction method based on a deleted and merged deep echo state network, characterized by: The implementation steps are as follows: Step (1): Initialize and construct a deep echo state network with redundant node numbers. The judgment index for node redundancy is: the number of network layers is greater than 1, and the number of nodes in each layer is greater than or equal to 10; Step (2): Iteratively use the node deletion-merging optimization method based on similarity evaluation to perform degenerate optimization on each reserve pool node, reduce the network size, and keep the prediction error within a reasonable range until the expected goal is achieved; The implementation steps of the node deletion-merging optimization method based on similarity evaluation are as follows: Step (21): Evaluate the similarity of the two nodes by a node similarity evaluation method to find the two most similar nodes; the node similarity evaluation method adopts the reciprocal of the Euclidean distance, or the Pearson correlation coefficient, or the Spearman correlation coefficient, or the Kendall correlation coefficient to evaluate the similarity of the two nodes; Step (22): Determine whether the two nodes selected in step (21) are in the same reserve pool. If so, go to step (31); otherwise, go to step (32). Step (31): Merge the two nodes selected in step (21) as parent nodes into a new child node, select a merging coefficient β, and adjust the input weight coefficient of the original parent node according to Perform weighted summation and weight the output weight coefficients of the original parent node at a ratio of 1:1; the merging coefficient β should be between 0 and 1; Step (32): discard the node at the higher level of the two nodes selected in step (21); Step (3): Use the optimized deep echo state network to perform real-time target trajectory prediction.

2. The trajectory prediction method based on the deleted and merged deep echo state network according to claim 1 is characterized in that: Step (2) anticipates the optimization goal, and its termination condition is determined by reaching the upper limit of the tolerable generalization error. The tolerable generalization error can be, but is not limited to, the normalized root mean square error.

3. The trajectory prediction method based on the deleted and merged deep echo state network according to claim 1 is characterized in that: The application field is optoelectronic systems, specifically defined as optical systems controlled by electrical signals. Its application scenario is target trajectory prediction of optoelectronic tracking systems.

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