CN-121980150-A - Track tensor completion and anomaly repair method based on singular value weighted truncation

CN121980150ACN 121980150 ACN121980150 ACN 121980150ACN-121980150-A

Abstract

The invention discloses a track tensor completion and anomaly repair method based on singular value weighted truncation, and relates to the technical field of flight path data processing. The invention fully utilizes ADS-B track data which is easy to acquire, and excavates the internal rule through intelligent learning capability, simultaneously, aiming at the complex problem of the mutual coupling of the deficiency and the abnormality in the track data, a robust tensor model integrating a self-adaptive weight mechanism, singular value truncation and sparse abnormality constraint is innovatively constructed, the cooperative precise processing of deficiency completion and abnormality repair is realized, and furthermore, an optimization solving strategy based on an alternate direction multiplier method is provided, and the low-rank track tensor, the sparse abnormality tensor and auxiliary variables are subjected to efficient block iterative optimization through an augmented Lagrange method, so that the complete track is accurately recovered in a complex data environment.

Inventors

DU JINGHAN
LI HONGWEI
ZHANG WEINING
LIN YI

Assignees

中国民用航空飞行学院

Dates

Publication Date: 20260505
Application Date: 20260407

Claims (8)

1. A track tensor completion and anomaly repair method based on singular value weighted truncation is characterized by comprising the following steps: collecting flight path data, performing low-rank analysis through an SVD (singular value decomposition) method, and generating a low-rank decomposition result and a track tensor representation; Decomposing track tensor representation, setting auxiliary variables, and constructing a low-rank regularization term by combining an adaptive weight mechanism and a singular value cut-off mechanism; Generating a complement abnormal robust model based on the auxiliary variable, the sparse abnormal constraint term and the low-rank regular term; And carrying out iterative optimization on the complement abnormal robust model by using an alternate direction multiplier method to generate a track tensor optimization result.
2. The method for track tensor completion and anomaly repair based on singular value weighted truncation of claim 1, wherein the constructing a low rank regularization term comprises: decomposing the track tensor representation to generate a low-rank track tensor and a sparse abnormal tensor; Generating auxiliary variables based on the low-rank track tensor and the sparse abnormal tensor by combining the first auxiliary constraint and the second auxiliary constraint; and constructing a low-rank regularization term based on the self-adaptive weight mechanism and the singular value truncation mechanism.
3. The method for track tensor completion and anomaly repair based on singular value weighted truncation of claim 2, wherein the formula corresponding to the low-rank regularization term is: ; Wherein, the Representing along the first Low rank track tensor The obtained first step of expansion The number of matrices to be used in the system, Which represents the adjustment parameters of the device, The rank of the track matrix representation is represented, Represents a singular value cut-off threshold value, Representing a low-rank regularization term, Representing the sum function, Represent the first The number of singular values is chosen to be, Representing the position number of a single track.
4. The method for track tensor completion and anomaly repair based on singular value weighted truncation of claim 1, wherein the generating the complete anomaly robust model comprises: setting an adaptive threshold and according to the formula: ; constructing a sparse anomaly constraint term, wherein, The quantile parameter is represented by a binary number, A sparsity anomaly constraint term is represented, The absolute value is represented by a value of, Representing the value of the adaptive threshold value, Representing the sum function, Represent the first The number of sparse anomaly tensors, Represent the first Individual sparse anomaly tensors At the position of Element values at; and generating a complement abnormal robust model based on the auxiliary variable, the sparse abnormal constraint term and the low-rank regular term.
5. The method for track tensor completion and anomaly repair based on singular value weighted truncation of claim 1, wherein the generating the track tensor optimization result comprises: based on the first auxiliary constraint, the complement abnormal robust model is processed through an augmentation Lagrangian method, and an objective function is generated; Decomposing the objective function to generate a first iteration problem, a second iteration problem, a third iteration problem and a fourth iteration problem; initializing a low-rank track tensor, a sparse anomaly tensor, an auxiliary variable and a Lagrangian multiplier; And carrying out iterative solution on the first iteration problem, the second iteration problem, the third iteration problem and the fourth iteration problem by using an alternate direction multiplier method to generate a track tensor optimization result.
6. The method for track tensor completion and anomaly repair based on singular value weighted truncation of claim 5, wherein the iterative solution to the first, second, third and fourth iteration problems by the alternating direction multiplier method comprises: normalizing the aircraft position point information in the low-rank track tensor and the sparse abnormal tensor, generating corresponding normalized position data, and updating the normalized position data to the low-rank track tensor and the sparse abnormal tensor; updating low-rank track tensors under different modes of the current iteration based on the first iteration problem; Updating the auxiliary variable of the current iteration based on the second iteration problem and each updated low-rank track tensor; updating the sparse abnormal tensor under different modes of the current iteration based on the third iteration problem and the updated auxiliary variable; Updating Lagrangian multipliers in different modes of the current iteration based on a fourth iteration problem and each updated sparse anomaly tensor; and carrying out inverse normalization on each normalized position data based on each updated low-rank track tensor, each updated auxiliary variable, each updated sparse abnormal tensor and each updated Lagrangian multiplier, and judging whether iteration conditions are met or not to generate a track tensor optimization result.
7. The method for track tensor completion and anomaly repair based on singular value weighted truncation of claim 6, wherein the updating the low rank track tensor corresponding formulas under different modes of the current iteration is as follows: ; Wherein, the Representing an updated low-rank track tensor, 、 Respectively represent update matrices A left singular vector matrix and a right singular vector matrix of (c), Represents the set of optimal singular values, Represents the transposed matrix of the image, The tensor folding operator is represented as such, Representing a diagonal matrix.
8. The method for track tensor completion and anomaly repair based on singular value weighted truncation of claim 6, wherein the updating the auxiliary variable of the current iteration corresponds to the formula: ; Wherein, the Representing the auxiliary variable after the update, Representing the sum function, Represent the first A penalty factor in the individual modes of operation, Represent the first The corresponding first iteration The lagrangian multiplier for each modality, Representing an updated low-rank track tensor, Represent the first Sparse anomaly tensors corresponding to the multiple iterations.

Description

Track tensor completion and anomaly repair method based on singular value weighted truncation Technical Field The invention relates to the technical field of flight path data processing, in particular to a flight path tensor completion and anomaly repair method based on singular value weighted truncation. Background In the concept of the next generation air transport system, broadcast automatic correlation monitoring (Automatic Dependent Surveillance-Broadcast, ADS-B) is considered the primary voyage monitoring technology. The aircraft carrying the ADS-B transmitting equipment acquires the real-time position of the flight through the global satellite navigation system, and periodically broadcasts the information to the ground receiving station and other aircraft carrying the ADS-B receiving equipment, so that the perception capability of pilots and air traffic controllers on the situation of an air domain is improved, the coordination of air-ground and air-air is enhanced, and the air traffic running efficiency is improved. Compared with the traditional radar monitoring technology, the ADS-B has the advantages of high positioning precision, quick data updating, low maintenance cost and the like. With the continued development and maturation of ADS-B technology, track data can be readily obtained through public channels (e.g., FLIGHT AWARE and FLIGHT RADAR). As a comprehensive record and objective description of the flight process of the aircraft, the flight path data can support research of various downstream applications such as flight path prediction, air traffic flow prediction, flight conflict monitoring and the like. In particular, with the advent of artificial intelligence and data mining technologies in the field of civil aviation, track data for training intelligent models has become particularly important. However, due to limitations of on-board devices and systems internal factors and various external factors, such as signal strength, communication links, weather conditions, etc., track data inevitably has jump points, leakage points, etc. These problems seriously affect the reliability of the trajectory data and have been the main obstacle for its application. It is therefore desirable to combine the track completion model with the anomaly repair model to improve the integrity and reliability of the track data. In fact, the problem of missing track data and the problem of abnormality are tightly coupled and mutually influenced, the completion accuracy of missing position points is easy to be interfered by abnormal tracks, and the accurate restoration of the abnormal tracks needs to rely on complete track data as a reference standard. However, existing studies mostly separate these two tasks. As a representative track pretreatment method based on a neural network and newton interpolation, one of few technical means capable of simultaneously processing anomaly repair and deletion complement is adopted. However, the method adopts a serial processing strategy of firstly repairing the abnormality and then repairing the deficiency, the interpolation precision of the deficiency position is easily affected by inaccurate identification of the abnormal point of the preamble, and the robustness is limited when the problem of coupling between the deficiency and the abnormality is faced. Furthermore, the problem is further exacerbated by the fact that the track data is not evenly distributed during different phases of flight (e.g., take-off and landing, cruising). When processing large-scale, high-frequency broadcast-type auto-correlation monitoring data, the feasibility and expandability of the algorithm are also affected by excessive time cost. Disclosure of Invention The invention aims to provide a track tensor completion and anomaly repair method based on singular value weighted truncation, which aims to solve the technical problems that the completion precision and repair robustness are limited due to the adoption of a serial separation strategy when the existing track pretreatment method is used for treating data loss and anomaly interference tightly coupled in ADS-B data, and the low-rank structural characteristics and deep relevant information of the track data in multidimensional space-time are difficult to fully mine. In order to achieve the above object, the embodiment of the present invention provides the following technical solutions: A track tensor completion and anomaly repair method based on singular value weighted truncation comprises the following steps: collecting flight path data, performing low-rank analysis through an SVD (singular value decomposition) method, and generating a low-rank decomposition result and a track tensor representation; Decomposing track tensor representation, setting auxiliary variables, and constructing a low-rank regularization term by combining an adaptive weight mechanism and a singular value cut-off mechanism; Generating a complement abnormal robust model based