Cross-terminal device educational resource intelligent adaptation method and system

Abstract

The invention discloses a cross-terminal device educational resource intelligent adaptation method and system, and relates to the technical field of educational resource adaptation, and the method comprises the following steps: embedding spread spectrum phase watermark information in a teaching event frame, taking the watermark information as a global time anchor, and carrying out the global time anchor; the method comprises the following steps: extracting a watermark from a locally received teaching event frame by each terminal device and recording a local receiving moment of the watermark so as to generate an initial event time sequence containing global relevance; and based on the initial event time sequence, calculating the time difference of arrival of each terminal device relative to the global time anchor, and generating a continuous time difference density curve. According to the method, the global time anchor and the deviation estimation base are constructed to realize consistent modeling and accurate synchronization of a multi-terminal teaching time sequence, and terminal time drift is corrected in real time through residual field inversion, phase heuristic and dynamic anchor point insertion, so that the stability of collaborative teaching, the interaction accuracy and the continuity of user experience are effectively improved.

Description

Technical Field

[0001] This invention relates to the field of educational resource adaptation technology, specifically to a method and system for intelligent adaptation of educational resources across terminal devices. Background Technology

[0002] Intelligent adaptation of educational resources across different terminal devices refers to the process of automatically identifying, optimizing the format of, and adjusting the interaction methods of educational resource content across different types of terminal devices (such as computers, tablets, mobile phones, interactive whiteboards, smart TVs, etc.). This process not only automatically adapts teaching content such as text, images, audio, video, and interactive animations based on the device's hardware characteristics (screen size, resolution, computing power, input method) and operating system environment, but also dynamically adjusts the presentation and interaction logic of resources based on user roles (teachers, students), learning scenarios (classroom teaching, online self-study, examinations and assessments), and network conditions. This ensures a smooth, clear, and fully functional learning experience across different terminals. For example, video courses can be automatically compressed and have their subtitles optimized on mobile devices, while touch annotation and multi-user synchronous interaction are enabled on interactive whiteboards, thus achieving consistent and intelligent use of educational resources across multiple terminal environments.

[0003] The existing technology has the following shortcomings: In existing multi-terminal real-time collaborative teaching scenarios, network jitter exhibits non-uniform and unpredictable dynamic changes in its temporal distribution. The clock compensation mechanism employed by adaptation algorithms can only partially correct short-cycle deviations during long-term operation, failing to effectively suppress the continuous accumulation of minute time errors. As the course duration increases, the latency drift effect gradually amplifies, ultimately leading to significant misalignments in the execution sequence of key teaching elements such as page switching, video playback, and question delivery across different terminals. This causes a severe deviation between the presentation order of teaching content and the triggering logic of teacher-student interaction, resulting in problems such as loss of classroom rhythm, ineffective interactive commands, and disruptions in the learning process, directly impacting the integrity and effectiveness of real-time collaborative teaching.

[0004] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for intelligent adaptation of educational resources across terminal devices, so as to solve the problems in the background art mentioned above.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for intelligent adaptation of educational resources across terminal devices, comprising the following steps: Spread spectrum phase watermark information is embedded in the teaching event frame. The watermark information serves as a global time anchor. Each terminal device extracts the watermark from the teaching event frame it receives locally and records its local reception time to generate an initial event time series containing global correlation. Based on the initial event time series, the arrival time difference of each terminal device relative to the global time anchor is calculated, a continuous time difference density curve is generated, and the feature fingerprint of short-period drift is extracted from the time difference density curve to construct a deviation estimation basis that reflects the terminal time deviation characteristics. Based on the bias estimation basis, the arrival time difference between adjacent global time anchors is subjected to restricted recursive filtering to generate continuous temporal bias trajectories of each terminal device relative to global time, and these bias trajectories are used as the input basis for subsequent temporal registration. In the process of aligning the time series of events on the teacher's end, a two-way residual field is constructed based on the time deviation trajectory. The relative phase error of each terminal device is inverted through the residual field, and the phase error obtained by inversion is integrated to generate the time error growth curve of the corresponding terminal. The time error growth curve is fed back to the global time anchor scheduler. The scheduler performs micro-phase stretching tests on the target terminal based on the time error growth trend, and evaluates the cumulative time error of each terminal based on the residual decrease during the test process. When the accumulated time error exceeds the preset threshold, phase anchor points that do not change the teaching logic are dynamically inserted into the time series of key teaching events. These anchor points include, but are not limited to, buffered screens, silent transition frames, or weak interactive detection commands. The local timing is then dynamically corrected based on the phase offset between the anchor points, thereby eliminating timing deviations caused by delay drift between terminals.

[0007] Preferably, the steps of embedding spread spectrum phase watermark information in the teaching event frame and generating an initial event time series containing global correlations include: The absolute timestamp generated by the high-precision time source is obtained, and the timestamp is spread spectrum modulation and phase encoding is performed to generate a spread spectrum phase watermark signal. The spread spectrum modulation uses a pseudo-random code sequence to XOR spread the timestamp bit stream, and the phase encoding modulates the phase offset based on the spread chip value. The spread spectrum phase watermark signal is embedded into the teaching event frame. When the teaching event frame is a video frame, the watermark is embedded in the mid-to-high frequency phase position after using discrete cosine transform or discrete wavelet transform. When it is a static courseware image, the phase component is embedded after using discrete Fourier transform. When it is an audio clip, the high frequency phase information is embedded after using short-time Fourier transform. The teaching event frame with embedded watermark is sent to the terminal device. After receiving the frame, the terminal device performs frequency domain or time-frequency domain transformation in the same way as the embedding method, extracts and demodulates the spread spectrum watermark signal, obtains the absolute timestamp, and records the local reception time of the terminal. The extracted absolute timestamps are paired and organized with the corresponding local receiving times to construct an initial event time series arranged in chronological order.

[0008] Preferably, during the process of extracting the spread spectrum phase watermark signal by the terminal device, the starting position of the watermark is located by performing correlation operation with a preset pseudo-random code sequence, and the demodulated spread spectrum chip stream is subjected to an inverse XOR operation to recover the absolute timestamp.

[0009] Preferably, the step of calculating the time difference of arrival of each terminal device relative to the global time anchor and constructing the bias estimation basis includes: The initial event time series of each terminal device is obtained, the global absolute time in the time series is paired with the local receiving time, and the time series is cleaned to remove duplicate frames, incomplete records and outlier time intervals, so as to obtain the arrival time difference of each record. The arrival time difference sequence is statistically analyzed in chronological order. A fixed time window is set, and the sample density within each time difference interval is calculated to generate a continuous time difference density curve. Perform fast Fourier transform and time-domain analysis on the time difference density curve to extract drift period, fluctuation amplitude, rate of change and phase stability index, and generate short-period drift feature set; Short-period drift features within multiple time windows are concatenated into a drift feature fingerprint, and normalization and similarity analysis are performed in conjunction with device identification and network characteristics to eliminate abnormal fluctuations. Statistical feature vectors are generated based on drift feature fingerprints, and stored in groups according to time order and device identifiers to construct a deviation estimation basis that reflects the terminal time deviation characteristics.

[0010] Preferably, when performing frequency domain analysis on the time difference density curve, the main frequency component is extracted by fast Fourier transform, and the phase stability index is calculated based on the phase change trend corresponding to the main frequency and the drift amplitude fluctuation range within the sliding window, so as to improve the discrimination accuracy of the drift feature fingerprint on the terminal time deviation trend.

[0011] Preferably, the step of generating a continuous time-series deviation trajectory includes: In the bias estimation basis, the drift period, drift amplitude and phase stability index of the corresponding terminal device in the current global time anchor interval are selected, and the original arrival time difference sequence in the interval is screened to remove outliers and mark intermittent bursts. A constrained recursive filter parameter set is constructed based on the filtered arrival time difference sequence. The recursive filter is constructed using state transition equations and observation equations. The filter gain is constrained by the phase stability index, and the state update rate is limited by the drift period. The state estimation results within each time anchor interval are spliced ​​together, and the boundary states of adjacent intervals are fused using a weighted smooth transition method. The slope of the deviation curve is dynamically corrected in combination with historical drift trends. The spliced ​​continuous deviation curves are normalized, and a time index and global time anchor number are added. Then, a standardized time deviation trajectory is generated through interpolation and point supplementation, which serves as the input basis for subsequent time registration.

[0012] Preferably, the steps of constructing the two-way residual field and generating the time error growth curve include: Based on the time series of events on the teacher's end, the continuous time series deviation trajectories of each terminal device are aligned to generate an initial residual sequence; The residual sequence is extended forward and backward, and the mean, variance, and slope of the forward residual field and the residual trend of the backward residual field are calculated respectively to construct a two-way residual field. Based on the two-way residual field, the phase error is inverted, and the residual is weighted by the phase stability index in the bias estimation basis to obtain a continuous phase error sequence. Perform discrete integration on the phase error sequence and smooth it to generate the time error growth curve of the terminal device relative to the teacher's device.

[0013] Preferably, the steps of feeding back the time error growth curve to the global time anchor scheduler and performing phase stretching probes include: The time error growth curve of each terminal device is fed back to the global time anchor scheduler, and the error growth slope, fluctuation amplitude and inflection point position are extracted. Based on the trend characteristics of the error growth curve, select the target terminal device and set the magnitude and duration of phase stretching; Perform micro-amplitude phase stretching on the target terminal device to adjust the event triggering timing by compressing or extending the local time series sampling interval; During the trial process, the magnitude of the residual decrease is calculated, and the adjustment effect is judged in combination with the short-period drift characteristics; The cumulative time error of the terminal equipment is assessed based on the rate of decrease in residual error, and compared with the time error growth curve to determine whether it has entered the safe range.

[0014] Preferably, the steps of dynamically inserting phase anchors and correcting local timing in the time series of key teaching events include: When the accumulated time error of a terminal device exceeds a preset threshold, logical analysis is performed on the time series of the current teaching event to identify candidate positions where phase anchors can be inserted. Based on the candidate position and the magnitude of the cumulative error value, select one or more types of buffer screen, silent transition frame or weak interactive detection command as phase anchor point for insertion. After inserting a phase anchor point, record the difference between the occurrence time of the anchor point under the global time reference and the local reception time, and calculate the phase offset curve between consecutive anchor points. Based on the slope of the phase offset curve and the cumulative drift value, the local timing of the terminal device is slightly compressed or extended to achieve dynamic correction of delay drift.

[0015] The intelligent adaptation system for educational resources across terminal devices includes a global time anchor construction module, a time difference density analysis module, a time series deviation filtering module, a residual inversion calculation module, a phase stretching and control module, and a time series dynamic correction module. The global time anchor construction module embeds spread spectrum phase watermark information into the teaching event frame. The watermark information serves as the global time anchor. Each terminal device extracts the watermark from the teaching event frame it receives locally and records its local reception time to generate an initial event time series containing global correlation. The time difference density analysis module calculates the arrival time difference of each terminal device relative to the global time anchor based on the initial event time series, generates a continuous time difference density curve, and extracts the feature fingerprint of short-period drift from the time difference density curve to construct a deviation estimation basis that reflects the terminal time deviation characteristics. The timing deviation filtering module, based on the deviation estimation basis, performs restricted recursive filtering on the arrival time difference between adjacent global time anchors to generate continuous timing deviation trajectories of each terminal device relative to the global time. The residual inversion calculation module constructs a two-way residual field based on the time series deviation trajectory during the alignment of the teacher's event time series. It then inverts the relative phase error of each terminal device through the residual field and performs integral calculation on the inverted phase error to generate the time error growth curve of the corresponding terminal. The phase stretching control module feeds back the time error growth curve to the global time anchor scheduler. The scheduler performs micro-phase stretching trials on the target terminal based on the time error growth trend, and evaluates the cumulative time error of each terminal based on the residual decrease during the trial process. The timing dynamic correction module dynamically inserts phase anchors that do not change the teaching logic into the time series of key teaching events when the accumulated time error exceeds a preset threshold. It also dynamically corrects the local timing based on the phase offset between the anchors, eliminating timing deviations caused by delay drift between terminals.

[0016] The technical effects and advantages provided by the present invention in the above technical solution are as follows: This invention embeds spread spectrum phase watermark information into teaching event frames and establishes a global time anchor, enabling each terminal device to accurately extract synchronization reference points in its independent operating environment and generate an initial event time series with global time consistency. This fundamentally breaks through the error accumulation bottleneck caused by traditional passive clock synchronization protocols. Based on this, combined with continuous time difference density analysis and short-period drift feature fingerprint extraction, a bias estimation basis oriented towards individual terminals is effectively established, achieving highly robust and high-precision time series modeling. This mechanism can significantly improve the time consistency of multiple terminals in teaching activities, especially in scenarios with long course durations or frequent network fluctuations. It can still ensure the synchronous presentation of teaching content on each terminal, maintain the continuity of the classroom rhythm and the accuracy of interactive commands, and enhance the overall stability of the remote collaborative teaching experience.

[0017] This invention achieves real-time dynamic adjustment of the terminal's local timing by constructing a bidirectional residual field, performing phase error inversion and generating time error growth curves, and combining a scheduler-led micro-amplitude phase stretching probing mechanism with a dynamically inserted phase anchor calibration mechanism. Especially when error accumulation exceeds a threshold, inserting buffered images, silent transition frames, or weak interactive probe commands that do not alter the teaching logic not only smooths timing jumps but also effectively alleviates execution misalignment problems caused by drift. This solution can flexibly correct the terminal-side timing without interrupting teaching content or causing abrupt changes in user perception, significantly improving the consistency of teaching event triggering, the controllability of the interaction process, and the logical integrity and user experience continuity of the entire teaching activity during multi-terminal collaboration. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0019] Figure 1 This is a flowchart of the intelligent adaptation method for educational resources across terminal devices according to the present invention. Figure 2 This is a structural diagram of the intelligent adaptation system for educational resources across terminal devices according to the present invention. Detailed Implementation

[0020] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the description of this disclosure will be more complete and fully convey the concept of the exemplary embodiments to those skilled in the art.

[0021] This invention provides, for example Figure 1 The method for intelligent adaptation of educational resources across terminal devices, as shown, includes the following steps: Spread spectrum phase watermark information is embedded in the teaching event frame. The watermark information serves as a global time anchor. Each terminal device extracts the watermark from the teaching event frame it receives locally and records its local reception time to generate an initial event time series containing global correlation. The intelligent adaptation method for educational resources across terminal devices embeds spread spectrum phase watermark information into teaching event frames when establishing a global time anchor. This allows each terminal device to accurately extract the watermark information and record the corresponding reception time locally when it receives a teaching event frame, thereby generating an initial event time series containing global correlations and forming a unified time benchmark. This process includes the following steps: When generating teaching event frames for transmission, an absolute timestamp generated by a high-precision time source (such as an atomic clock or BeiDou time service) is obtained and subjected to spread spectrum modulation and phase coding. During spread spectrum modulation, the absolute timestamp is first converted into a binary bit stream. Then, a pseudo-random code sequence (PN sequence) is selected as the spreading code. The timestamp bit stream is XORed with the PN sequence to expand the chip, increasing the signal bandwidth to hundreds of times the original bit rate. This disperses signal energy and improves its survivability under network transmission compression, resampling, and interference environments. During phase coding, a sine or cosine carrier is used as the phase modulation carrier. The phase offset (e.g., 0° or 180°, or four-phase modulation such as 0°, 90°, 180°, 270°) is selected based on the spread chip value. The phase of the coded signal is changed according to a predetermined rule, generating a spread spectrum phase watermark signal that can be directly embedded into the teaching event frame. The amplitude, phase variation range, and spreading code length of the signal can all be precisely set during the generation stage according to the type and bandwidth conditions of the teaching event frame, so as to ensure that the watermark signal is both highly robust and imperceptible at the perception level.

[0022] The generated spread-spectrum phase watermark signal is embedded into the teaching event frame to be sent. If the teaching event frame is a video frame, the video frame is first subjected to Discrete Cosine Transform (DCT) or Discrete Wavelet Transform (DWT) to obtain frequency domain coefficients. Coefficients in the mid-to-high frequency range with low visual sensitivity to the human eye are selected, and the spread-spectrum phase watermark signal is embedded into the phase portion of these coefficients according to phase modulation rules. If the teaching event frame is a static courseware image, the amplitude and phase information are obtained through Discrete Fourier Transform (DFT), and the watermark is embedded into the phase component, while controlling the embedding strength to not exceed 2% of the original phase offset to avoid a decrease in image sharpness. If the teaching event frame is an audio segment, short-time Fourier Transform (STFT) is used for framing, and the watermark is embedded into the high-frequency phase characteristics, making it imperceptible to the human ear but accurately extractable by the algorithm. After embedding, the frame data containing the watermark is inversely transformed to restore a playable format, ensuring that the embedding process does not damage the usability and quality of the teaching content. During this process, the embedding position and power of the watermark signal need to be dynamically adjusted according to the complexity of the teaching content and the frame size in order to maximize the watermark extraction success rate while maintaining the clarity of the content.

[0023] After receiving a teaching event frame with an embedded spread spectrum phase watermark, the terminal device performs a watermark extraction process. During extraction, the received event frame is first transformed in the same frequency domain or time-frequency domain as the embedding process to extract the phase data at the corresponding position. Then, using a known pseudo-random code sequence and phase modulation rules, the location of the spread spectrum signal is detected through correlation operations, and the original spread spectrum chip stream is recovered through demodulation. Next, the spread spectrum chip stream and the PN sequence are inversely XORed to obtain the embedded absolute timestamp information. Finally, this absolute timestamp is simultaneously saved along with the terminal's local high-precision reception time (recorded by a local clock or high-precision time synchronization hardware). At this point, the terminal device obtains two precise and corresponding time data: one is the absolute time identified by the global time anchor, and the other is the reception time of the frame arriving at the terminal's local time, which provides the necessary condition for subsequent global and local time alignment.

[0024] Finally, the global absolute time recorded by the terminal device is paired and organized with the local reception time, and then sorted according to the order of occurrence of teaching events to construct an initial event time series containing multiple time pairing records. To ensure the reliability of this time series, consistency checks are performed on all records. For example, abnormal records with abnormally large changes in reception delay exceeding a set threshold are removed, duplicate frame records caused by network retransmissions are removed, and interpolation methods are used to fill time gaps caused by packet loss. The organized initial event time series not only accurately reflects the occurrence time of each teaching event on the global timeline, but also retains the actual arrival time differences of the event locally, forming a time data foundation with high global correlation and traceability. This time series can be directly used for subsequent time difference density calculation, drift feature extraction, and cross-terminal time series correction, thereby ensuring that different terminals maintain strict consistency in their understanding and presentation order of teaching events under complex conditions such as network jitter, latency variations, and differences in device performance.

[0025] Through the above steps, not only was it possible to stably embed spread spectrum phase watermark information into teaching event frames, but it also ensured high-fidelity extraction of watermark information in various transmission and playback environments. Furthermore, a global time anchor shared across terminals was constructed through dual time recording, providing a technical foundation for high-precision synchronous adaptation of educational resources across terminals.

[0026] Based on the initial event time series, the arrival time difference of each terminal device relative to the global time anchor is calculated, a continuous time difference density curve is generated, and the feature fingerprint of short-period drift is extracted from the time difference density curve to construct a deviation estimation basis that reflects the terminal time deviation characteristics. To accurately grasp the time difference characteristics between each terminal device and the global time anchor during the intelligent adaptation of cross-terminal educational resources, and to provide high-precision reference data for subsequent drift prediction and timing correction, this embodiment introduces a method for constructing a deviation estimation basis based on initial event time series. This method starts with the initial event time series generated by each terminal device through the extraction of spread spectrum phase watermark information. Through continuous calculation of arrival time difference, density analysis, and short-period drift feature extraction, a deviation estimation basis that reflects the terminal time deviation characteristics is ultimately formed. The method includes the following steps: The initial event time series of each terminal device is acquired and synchronized, and each record in the time series is matched one-to-one with the absolute time of the corresponding global time anchor. Each record contains two time elements: the global absolute time (obtained by decoding the spread spectrum phase watermark) and the local reception time of the frame at the terminal. To ensure the accuracy of the matching, the time series needs to be preprocessed, including removing duplicate frame records, removing incomplete records caused by network packet loss, and detecting and marking outliers in time intervals. After data cleaning, the difference between the local reception time and the global absolute time is calculated for each record. This difference is the single-point arrival time difference of the terminal device relative to the global time anchor. Through this process, a complete arrival time difference sequence can be obtained, providing the raw data foundation for subsequent analysis.

[0027] Arrival time difference sequences are arranged chronologically, and sliding statistics are performed within a fixed time window to generate a continuous time difference density curve. Specifically, an appropriate time window length (e.g., 5 seconds or 10 seconds) is first selected, and the number of samples falling into each time difference interval is counted within this window. The statistical results are then normalized into density values, representing the probability distribution of different delay values ​​occurring within that time period. Then, the time window is slid forward sequentially, and the above statistical process is repeated, ultimately yielding a set of continuous density distribution curves. This curve not only reflects the dynamic changes in delay distribution over time but also reveals the impact trends of factors such as network jitter and equipment processing performance fluctuations on timing synchronization.

[0028] A joint frequency and time domain analysis was performed on the generated continuous time difference density curves to extract the characteristic fingerprints of short-period drift. Short-period drift refers to the periodic fluctuations of delay values ​​over a short time scale, which are often caused by network scheduling strategies, buffering mechanisms, or small clock drifts. In the extraction process, a Fast Fourier Transform (FFT) was first used to convert the time series of the density curves into a spectral representation to locate the main energy peak frequencies and determine the dominant frequency components of the drift period. Subsequently, the phase changes of the corresponding frequency components were analyzed in the time domain to extract the amplitude, rate of change, and stability indicators of the drift. These frequency and phase features together constitute the preliminary feature set of short-period drift.

[0029] Based on the aforementioned feature set, a drift feature fingerprint with temporal continuity and device specificity is constructed. Specifically, short-period drift features of the same terminal device within multiple consecutive time windows are sequentially concatenated, and unique device identification information and network environment characteristics (such as bandwidth and packet loss rate) are appended as fingerprint metadata. Simultaneously, the fingerprint data is normalized to ensure comparability under different sampling frequencies and data sizes. By introducing a sliding correlation analysis method, the similarity between fingerprints at different time periods is calculated, eliminating interference from occasional fluctuations, so that the final drift feature fingerprint can stably reflect the inherent temporal drift characteristics and network transmission conditions of the terminal device.

[0030] Finally, a bias estimation basis is constructed using the aforementioned drift feature fingerprints. This basis is a reference dataset containing multidimensional information, recording the average time difference of arrival, short-cycle drift period, drift amplitude, and phase stability index of each terminal device over different time periods. During construction, the drift feature fingerprints are stored in chronological order and grouped by device, and a statistical feature vector is generated for each group to describe the overall bias characteristics of that group of data under a global time anchor reference. The bias estimation basis will serve as input in subsequent steps to guide recursive filtering and temporal registration operations, thereby enabling the prediction of future time bias trends based on historical drift features, achieving early intervention and dynamic correction of drift accumulation.

[0031] Through the specific steps described above, this method can not only accurately quantify the time difference of arrival between each terminal device and the global time anchor, but also extract unique and traceable short-period drift features, and construct a robust bias estimation basis accordingly. This method can effectively address the non-uniform dynamic changes in network latency in cross-terminal real-time collaborative teaching scenarios.

[0032] Based on the bias estimation basis, the arrival time difference between adjacent global time anchors is subjected to restricted recursive filtering to generate continuous temporal bias trajectories of each terminal device relative to global time, and these bias trajectories are used as the input basis for subsequent temporal registration. To transform the delay characteristic data in the deviation estimation basis into a high-precision dynamic trajectory suitable for time-series registration, this embodiment employs a continuous time-series deviation trajectory generation method based on restricted recursive filtering. This method dynamically filters the arrival time difference between each terminal device and the global time anchor within the time range of adjacent global time anchors. It also combines short-period drift characteristics and stability indices stored in the deviation estimation basis to selectively suppress sudden noise interference and unstable drift components, thereby generating a continuous time-series deviation trajectory that accurately reflects the true time drift trend of the terminal devices. Specifically, it includes the following steps: In the bias estimation basis, short-period drift period, drift amplitude, and phase stability indices for the corresponding terminal device within the current global time anchor interval are selected and correlated with the original time difference of arrival (TDOA) sequence within that interval. To ensure the reliability of the input data, the original TDOA sequence undergoes preliminary constraint screening to remove outliers that significantly exceed the upper limit of the drift amplitude in the bias estimation basis. Intermittent delay spikes caused by network jitter are also marked to prevent outliers from biasing the subsequent recursive filtering calculations. After data screening, the data for each adjacent global time anchor interval is segmented and organized to ensure that each segment contains a sufficient number of sample points to support filtering calculations while avoiding crossing different time anchor intervals to prevent the introduction of additional time drift differences.

[0033] Based on the filtered arrival time difference sequence, an initial parameter set for a constrained recursive filter is constructed. The recursive filter employs a variant Kalman filter structure, where the state transition equation describes the natural variation trend of the time deviation between adjacent sampling points, and the observation equation maps the actually observed arrival time difference to the state estimate. The constraints are manifested in two aspects: first, the filter's gain adjustment range is constrained by the phase stability index in the deviation estimation basis. When phase stability is low, the filter's confidence in new observations decreases to avoid drift noise entering the state estimate; second, the state update rate is limited by the short-period drift period. When the frequency of observation changes is close to the drift period, the filter will appropriately delay the state update to avoid misjudging normal drift as abnormal changes. This constrained recursive mechanism ensures that the filter's output curve retains the true drift trend while suppressing transient jitter and random noise to the greatest extent.

[0034] During the filtering calculation, the state estimation results between adjacent global time anchors are continuously spliced ​​together to form a continuous time-series deviation curve. To avoid abrupt changes at the splicing points, a smooth transition segment is introduced at the boundary between two time anchor intervals. A weighted average is used to fuse the final state of the previous interval with the initial state of the next interval, ensuring the time-series deviation curve maintains visual and mathematical continuity. Furthermore, by incorporating historical drift trend data from the deviation estimation base, the local slope of the curve is dynamically corrected to ensure that the curve reflects the gradual characteristics of deviation changes rather than sudden jumps, even as network conditions change. Through this method, the final time-series deviation curve not only possesses high accuracy and continuity but also reflects the cumulative drift pattern of terminal devices during long-term operation.

[0035] The generated continuous temporal deviation curves are standardized into temporal deviation trajectories, which serve as the input basis for subsequent temporal registration steps. During standardization, the curves are first normalized to map deviation values ​​from different terminal devices to a unified numerical range, facilitating cross-device comparisons during registration. Secondly, a time index and corresponding global time anchor number are appended to the trajectory to ensure that each deviation value in the trajectory precisely corresponds to a specific global time point. Finally, interpolation is performed on the trajectory to fill gaps caused by missing individual sample points, ensuring consistent sampling intervals along the time axis. The standardized continuous temporal deviation trajectory provides a complete and high-confidence temporal deviation input for subsequent two-way residual field construction, enabling temporal registration to more accurately invert the relative phase of each terminal device and predict future temporal error trends.

[0036] This step involves first filtering and organizing the arrival time difference sequences within adjacent global time anchor intervals; second, constructing a restricted recursive filter with a bias estimation basis as a constraint; third, generating a highly continuous time-series bias curve through splicing and smoothing; and finally, standardizing it into a bias trajectory that can be used for time-series registration. This achieves accurate modeling and dynamic tracking of terminal time drift under dynamically changing network latency conditions. This method can effectively reduce synchronization errors caused by instantaneous jitter, short-term network fluctuations, and differences in device processing, providing temporal data support for the intelligent adaptation of cross-terminal educational resources.

[0037] In the process of aligning the time series of events on the teacher's end, a two-way residual field is constructed based on the time deviation trajectory. The relative phase error of each terminal device is inverted through the residual field, and the phase error obtained by inversion is integrated to generate the time error growth curve of the corresponding terminal. To more accurately estimate the time drift development trend of each terminal device during the intelligent adaptation of cross-terminal educational resources, this embodiment relies on the continuous time-series deviation trajectory obtained in the previous step, uses the teacher's event time series as a reference, establishes a two-way residual field, inverts the relative phase error of each terminal device relative to the teacher, and further integrates the inverted phase error to form a time error growth curve that can describe the accumulation trend of delay drift. The method includes the following steps: Using the time series of events on the teacher's end as a benchmark, the continuous temporal deviation trajectories of each terminal device are aligned one by one with the global reference event on the teacher's end. During the alignment process, for each teacher's end event node, the corresponding time point in the terminal deviation trajectory is found, and the difference between the observed deviation value at that time point and the teacher's end reference value is calculated. Through this process, an initial residual sequence describing the difference between the terminal deviation trajectory and the teacher's end reference event can be obtained. However, one-way residuals can only reflect the difference at a certain moment and cannot reveal the combined impact of future and historical factors on this difference. Therefore, this residual sequence needs to be used as basic data to provide input for the subsequent construction of a two-way residual field.

[0038] A two-way residual field is constructed based on the initial residual sequence. Specifically, the residual sequence is extended forward and backward simultaneously, forming residual distributions in two directions: one to describe the impact of historical observations on the current bias, and the other to describe the potential constraints of future observations on the current bias. The forward residual field reflects the stability and drift trend of the terminal equipment over a previous period by calculating the residual mean, variance, and slope characteristics over several past time windows; the backward residual field predicts the residual trend over several future time windows, inferring the possible direction of the current bias evolution. Through this two-way modeling approach, the bias at each time point is determined not only by the current observation value but also by constraints from both historical and future factors. The construction of the two-way residual field effectively avoids the lag and one-sidedness of unidirectional estimation, making residual analysis more comprehensive and forward-looking.

[0039] Based on the two-way residual field, the relative phase error of each terminal device is inverted. The specific inversion process is as follows: First, combining the statistical characteristics of the forward residual field, the baseline value of the phase error at the current time point is estimated; then, combining the predicted trend of the backward residual field, the baseline value is corrected to obtain a phase error estimate that better conforms to the global evolution law. To ensure that the inversion result is not disturbed by instantaneous abnormal residuals, a weighted operation needs to be performed on the residual field, where the weights are provided by the phase stability index in the bias estimation basis. When the phase stability is high, more weight is allocated to the current observed residual; when the phase stability is low, more weight is allocated to the trend characteristics of historical and future residuals. Through this process, a phase error sequence that changes continuously over time can be obtained, which can truly reflect the relative phase difference between the terminal device and the teacher's end.

[0040] The phase error sequence obtained from the inversion is integrated to generate a time error growth curve. The purpose of integration is to accumulate local phase differences, thereby revealing the long-term development trend of delay drift throughout the teaching process. In practice, the phase error sequence is first discretely integrated, that is, the phase errors of adjacent sampling points are accumulated and combined with the time index to form the integral value. Then, the integral curve is smoothed to eliminate the interference of local high-frequency jitter, making the curve more consistent with the physical process of the gradual accumulation of delay drift. The final generated time error growth curve can intuitively show how the time difference between the terminal device and the teacher's end gradually widens during long-term operation. Its growth rate and curve shape provide a direct basis for subsequent time scheduling and error correction. Through this curve, the degree of timing misalignment that may occur at a future point in time can be predicted in advance, thus providing an important reference for the dynamic adjustment of the global time anchor scheduler.

[0041] This embodiment first aligns the timing deviation trajectory with the teacher's reference sequence to obtain the initial residual. Then, it constructs a bidirectional residual field combining forward and backward directions. Next, it inverts the phase error through weighted calculations of the residual field. Finally, it integrates the phase error to generate a time error growth curve, thus achieving dynamic modeling and long-term trend prediction of terminal device time drift. This method not only improves the accuracy and stability of error estimation but also allows for early intervention and correction before delay drift causes severe timing misalignment.

[0042] The time error growth curve is fed back to the global time anchor scheduler. The scheduler performs micro-phase stretching tests on the target terminal based on the time error growth trend, and evaluates the cumulative time error of each terminal based on the residual decrease during the test process. To effectively curb the continuous accumulation of time drift during the intelligent adaptation of cross-terminal educational resources, this embodiment feeds back the time error growth curve generated in the previous stage to the global time anchor scheduler. The scheduler then performs a micro-phase stretching operation on the target terminal device. Combined with the decrease in residuals after the trial, the cumulative time error value of each terminal is quantitatively evaluated. This method includes the following steps: The time error growth curves generated for each terminal device are fed back to the global time anchor scheduler. These curves, obtained from the previous stage through bidirectional residual field inversion and integration, comprehensively record the error accumulation trend of each terminal device over a period of time. Upon receiving these curves, the scheduler analyzes them to extract key features, such as the slope of error growth, fluctuation amplitude, and inflection point. By analyzing these features, the scheduler can determine whether the error growth of a particular terminal device is within a normal range or has entered a dangerous zone of rapid accumulation. This step ensures that subsequent phase probing operations have sufficient quantitative basis, rather than being blindly adjusted, thus avoiding unnecessary interference with the teaching process.

[0043] Based on the trend characteristics of the time error growth curve, target terminal devices requiring phase adjustment are selected, and initial trial parameters for micro-amplitude phase stretching are calculated. During this process, the scheduler uses the slope of the error growth curve to determine the necessity of stretching. When the slope consistently exceeds a set threshold, it indicates rapid error accumulation, necessitating stretching intervention. Simultaneously, the scheduler also considers the curve's fluctuation characteristics. If the error growth trend exhibits regular oscillations, it indicates short-cycle drift, requiring control of the stretching amplitude to avoid overcompensation. The initial trial parameters primarily include the magnitude and duration of phase stretching. The magnitude is typically within the millisecond range to minimize the impact on the terminal's time series; the duration is determined based on the length of the integral interval of the error curve, ensuring the adjustment effect covers the entire drift cycle without premature rebound.

[0044] A micro-phase stretching probe is implemented on the target terminal device. Phase stretching involves subtle adjustments to the terminal's local time series, specifically by compressing or extending the sampling interval on the timeline to better align the execution sequence of local events with the global time anchor. For example, if the terminal's time error growth curve indicates that its operating speed is relatively slower than the global time, the scheduler will slightly compress its local timeline for a short period, causing subsequent events to trigger slightly earlier; conversely, if the terminal exhibits relative acceleration, events will be delayed through slight extension. During the stretching operation, the scheduler continuously monitors the event triggering time of the target terminal and compares it with the global time anchor to ensure that the probing adjustments do not exceed a pre-set safety range, thereby avoiding abrupt changes in user perception.

[0045] While implementing phase stretching probes, the residual decrease rate during the probe process is calculated in real time. The residual refers to the difference between the actual event trigger time of the target terminal after phase adjustment and the corresponding time of the global time anchor. By continuously calculating the changes in the residual, the effectiveness of the probe operation can be observed. If the residual decreases significantly in a short period, it indicates that the adjustment direction is correct and the magnitude is reasonable; if the residual does not change significantly or even increases in the opposite direction, it indicates that the adjustment strategy needs to be corrected. When calculating the residual decrease rate, it is also necessary to combine the short-period drift characteristics in the bias estimation basis to distinguish between the real improvement brought about by the probe effect and the illusory fluctuations caused by short-period fluctuations. In this way, the actual effectiveness of the phase stretching probe can be evaluated more objectively.

[0046] Finally, based on the statistical results of the residual decrease during the trial, the cumulative time error of each terminal device is evaluated and quantified. Specifically, after the phase trial ends, the scheduler integrates the residual curve to obtain the overall error change of the terminal during the adjustment process, and compares this change with the time error growth curve. In this way, it can be determined whether the trial stretching significantly slows down the rate of error accumulation. If the evaluation results show that the cumulative error value has decreased to within a safe range, it indicates that the time drift of the terminal has been effectively controlled; if the cumulative error value is still too high, it indicates that it is necessary to further increase the stretching amplitude or extend the duration, or combine it with other correction strategies such as dynamically inserting phase anchors. Ultimately, through this quantitative evaluation, the scheduler can establish a real-time updated error accumulation file for each terminal device, which serves as an important reference for subsequent global time scheduling and synchronization optimization.

[0047] This embodiment not only allows for early intervention before errors become severely deteriorated, but also enables continuous correction of strategies through trial adjustments, thereby ensuring the temporal consistency and interactive stability of cross-terminal educational resources in long-term collaborative teaching.

[0048] When the accumulated time error exceeds the preset threshold, phase anchors that do not change the teaching logic are dynamically inserted into the time series of key teaching events. These anchors include, but are not limited to, buffered screens, silent transition frames, or weak interactive detection commands. The local timing is then dynamically corrected based on the phase offset between the anchors, thereby eliminating timing deviations caused by delay drift between terminals. To effectively control the accumulation of time errors and avoid timing misalignment between terminals caused by latency drift during the intelligent adaptation of cross-terminal educational resources, this embodiment, when the evaluated accumulated time error value exceeds a preset threshold, further inserts phase anchor points that do not change the teaching logic into the time series of key teaching events, and uses the phase offset between these anchor points to dynamically correct the local timing of the terminal, thereby achieving real-time suppression of time drift. The method includes the following steps: When the cumulative time error of a terminal device exceeds a preset threshold, a logical analysis is performed on the time series of the current teaching event to identify candidate locations for inserting phase anchors. The preset threshold is typically determined by the requirements of the teaching scenario; for example, the error should not exceed tens of milliseconds in a synchronous classroom and should not exceed hundreds of milliseconds in interactive assessments. The purpose of the logical analysis is to ensure that inserting anchors does not disrupt the integrity and coherence of the teaching content. Therefore, it is necessary to consider the type of teaching event and its contextual relationships. For example, transitions before and after switching courseware pages, camera transitions in video playback, and gaps in teacher-student interaction are all suitable candidate locations because inserting anchors at these points will not change the teaching logic and will not be directly perceived by the user. The identified candidate locations will serve as a reference basis for anchor insertion, providing specific implementation scenarios for subsequent dynamic interventions.

[0049] Based on the characteristics of the candidate positions and the magnitude of the current accumulated error, an appropriate type of phase anchor point is selected for insertion. Phase anchor points can take the form of buffered images, silent transition frames, or weak interactive detection commands. Buffered images are suitable for video or dynamic demonstration content, quickly filling latency differences; silent transition frames are suitable for audio-visual mixed scenarios, adjusting local time without affecting perceptual continuity; weak interactive detection commands are suitable for teaching segments requiring teacher and student participation, such as embedding lightweight detection tasks before question delivery or answer feedback to force each terminal to realign without affecting the teaching process. The selection principle is: when the accumulated error value is small and close to the lower threshold, buffered images with higher perceptuality are preferred; when the accumulated error value is large, weak interactive detection commands are used to achieve stronger alignment constraints. Once an anchor point is selected, it will be inserted into the identified candidate positions, carrying identification information for subsequent phase offset calculation.

[0050] After inserting a phase anchor point, the difference between the anchor point's occurrence time under the global time anchor reference and the local reception time is detected in real time, and this difference is recorded as the phase offset. Since each phase anchor point carries a global time identifier during generation, the terminal can directly extract this identifier and compare it with the local time to obtain the accurate phase offset. Subsequently, the phase offsets between two consecutive anchor points are compared and calculated to obtain the cumulative drift rate of the local time axis relative to the global time. For example, if the interval between two anchor points is 5 seconds, and the offset increases from 20 milliseconds to 50 milliseconds, it means that the terminal has generated an additional 30 milliseconds of drift within those 5 seconds, equivalent to an increase of 6 milliseconds of delay per second. In this way, a phase offset curve based on the anchor points can be formed, which can accurately reflect the drift dynamics of the local timing under intervention conditions.

[0051] Finally, based on the phase offset curve, the local timing of the terminal device is dynamically corrected to eliminate deviations caused by latency drift. During the correction process, the scheduler determines whether to perform minor compression or extension operations on the terminal's local timeline based on the slope and cumulative value of the offset curve. For example, when the offset curve shows that the terminal is gradually lagging behind the global time, the inter-frame interval is shortened to advance event triggering and catch up with the global time; when the offset curve shows that the terminal is gradually ahead, the inter-frame interval is extended to delay event triggering and re-align with the global time. The magnitude of the correction is dynamically calculated by the phase offset, ensuring that the deviation is gradually eliminated without causing abrupt changes to the user experience. Through multiple anchor point insertions and dynamic corrections, the terminal's local timing can maintain consistency with the global time during long-term operation, fundamentally solving the problem of uncontrolled teaching rhythm caused by the continuous accumulation of latency drift.

[0052] This embodiment not only ensures the logical integrity and coherence of teaching events, but also achieves high-precision cross-terminal time synchronization through implicit or weak interaction means without increasing the user burden, thereby providing timing assurance for real-time collaboration in smart education scenarios.

[0053] This invention embeds spread spectrum phase watermark information into teaching event frames and establishes a global time anchor, enabling each terminal device to accurately extract synchronization reference points in its independent operating environment and generate an initial event time series with global time consistency. This fundamentally breaks through the error accumulation bottleneck caused by traditional passive clock synchronization protocols (such as NTP). Based on this, combined with continuous time difference density analysis and short-period drift feature fingerprint extraction, a bias estimation basis oriented towards individual terminals is effectively established, achieving highly robust and high-precision time series modeling. This mechanism can significantly improve the time consistency of multiple terminals in teaching activities, especially in scenarios with long course durations or frequent network fluctuations. It can still ensure the synchronous presentation of teaching content on each terminal, maintain the continuity of the classroom rhythm and the accuracy of interactive commands, and enhance the overall stability of the remote collaborative teaching experience.

[0054] This invention achieves real-time dynamic adjustment of the terminal's local timing by constructing a bidirectional residual field, performing phase error inversion and generating time error growth curves, and combining a scheduler-led micro-amplitude phase stretching probing mechanism with a dynamically inserted phase anchor calibration mechanism. Especially when error accumulation exceeds a threshold, inserting buffered images, silent transition frames, or weak interactive probe commands that do not alter the teaching logic not only smooths timing jumps but also effectively alleviates execution misalignment problems caused by drift. This solution can flexibly correct the terminal-side timing without interrupting teaching content or causing abrupt changes in user perception, significantly improving the consistency of teaching event triggering, the controllability of the interaction process, and the logical integrity and user experience continuity of the entire teaching activity during multi-terminal collaboration.

[0055] This invention provides, for example Figure 2 The intelligent adaptation system for educational resources across terminal devices shown includes a global time anchor construction module, a time difference density analysis module, a time series deviation filtering module, a residual inversion calculation module, a phase stretching and control module, and a time series dynamic correction module. The global time anchor construction module embeds spread spectrum phase watermark information into the teaching event frame. The watermark information serves as the global time anchor. Each terminal device extracts the watermark from the teaching event frame it receives locally and records its local reception time to generate an initial event time series containing global correlation. The time difference density analysis module calculates the arrival time difference of each terminal device relative to the global time anchor based on the initial event time series, generates a continuous time difference density curve, and extracts the feature fingerprint of short-period drift from the time difference density curve to construct a deviation estimation basis that reflects the terminal time deviation characteristics. The timing deviation filtering module, based on the deviation estimation basis, performs restricted recursive filtering on the arrival time difference between adjacent global time anchors to generate continuous timing deviation trajectories of each terminal device relative to the global time. The residual inversion calculation module constructs a two-way residual field based on the time series deviation trajectory during the alignment of the teacher's event time series. It then inverts the relative phase error of each terminal device through the residual field and performs integral calculation on the inverted phase error to generate the time error growth curve of the corresponding terminal. The phase stretching control module feeds back the time error growth curve to the global time anchor scheduler. The scheduler performs micro-phase stretching trials on the target terminal based on the time error growth trend, and evaluates the cumulative time error of each terminal based on the residual decrease during the trial process. The timing dynamic correction module dynamically inserts phase anchors that do not change the teaching logic into the time series of key teaching events when the accumulated time error exceeds a preset threshold. It also dynamically corrects the local timing based on the phase offset between the anchors, eliminating timing deviations caused by delay drift between terminals.

[0056] The intelligent adaptation method for educational resources across terminal devices provided in this embodiment of the invention is implemented through the aforementioned intelligent adaptation system for educational resources across terminal devices. For details of the specific methods and processes of the intelligent adaptation system for educational resources across terminal devices, please refer to the embodiments of the intelligent adaptation method for educational resources across terminal devices, which will not be repeated here.

[0057] The foregoing has only described certain exemplary embodiments of the present invention by way of illustration. Undoubtedly, those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the foregoing drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

Claims

1. A method for intelligent adaptation of educational resources across terminal devices, characterized in that, Includes the following steps: Spread spectrum phase watermark information is embedded in the teaching event frame. The watermark information serves as a global time anchor. Each terminal device extracts the watermark from the teaching event frame it receives locally and records its local reception time to generate an initial event time series containing global correlation. Based on the initial event time series, the arrival time difference of each terminal device relative to the global time anchor is calculated, a continuous time difference density curve is generated, and the feature fingerprint of short-period drift is extracted from the time difference density curve to construct a deviation estimation basis that reflects the terminal time deviation characteristics. Based on the bias estimation basis, the arrival time difference between adjacent global time anchors is subjected to restricted recursive filtering to generate continuous time-series bias trajectories of each terminal device relative to global time. In the process of aligning the time series of events on the teacher's end, a two-way residual field is constructed based on the time deviation trajectory. The relative phase error of each terminal device is inverted through the residual field, and the phase error obtained by inversion is integrated to generate the time error growth curve of the corresponding terminal. The time error growth curve is fed back to the global time anchor scheduler. The scheduler performs micro-phase stretching tests on the target terminal based on the time error growth trend, and evaluates the cumulative time error of each terminal based on the residual decrease during the test process. When the accumulated time error exceeds the preset threshold, phase anchors that do not change the teaching logic are dynamically inserted into the time series of key teaching events, and the local timing is dynamically corrected according to the phase offset between anchors to eliminate timing deviations caused by delay drift between terminals.

2. The method for intelligent adaptation of educational resources across terminal devices according to claim 1, characterized in that, The steps of embedding spread spectrum phase watermark information into teaching event frames and generating an initial event time series containing global correlations include: The absolute timestamp generated by the high-precision time source is obtained, and the timestamp is spread spectrum modulation and phase encoding is performed to generate a spread spectrum phase watermark signal. The spread spectrum modulation uses a pseudo-random code sequence to XOR spread the timestamp bit stream, and the phase encoding modulates the phase offset based on the spread chip value. The spread spectrum phase watermark signal is embedded into the teaching event frame. When the teaching event frame is a video frame, the watermark is embedded in the mid-to-high frequency phase position after using discrete cosine transform or discrete wavelet transform. When it is a static courseware image, the phase component is embedded after using discrete Fourier transform. When it is an audio clip, the high frequency phase information is embedded after using short-time Fourier transform. The teaching event frame with embedded watermark is sent to the terminal device. After receiving the frame, the terminal device performs frequency domain or time-frequency domain transformation in the same way as the embedding method, extracts and demodulates the spread spectrum watermark signal, obtains the absolute timestamp, and records the local reception time of the terminal. The extracted absolute timestamps are paired and organized with the corresponding local receiving times to construct an initial event time series arranged in chronological order.

3. The method for intelligent adaptation of educational resources across terminal devices according to claim 2, characterized in that, During the process of extracting the spread spectrum phase watermark signal in the terminal device, the starting position of the watermark is located by performing correlation operations with the preset pseudo-random code sequence, and the demodulated spread spectrum chip stream is subjected to an inverse XOR operation to recover the absolute timestamp.

4. The method for intelligent adaptation of educational resources across terminal devices according to claim 2, characterized in that, The steps for calculating the time difference of arrival of each terminal device relative to the global time anchor and constructing the bias estimation basis include: The initial event time series of each terminal device is obtained, the global absolute time in the time series is paired with the local receiving time, and the time series is cleaned to obtain the arrival time difference of each record. The arrival time difference sequence is statistically analyzed in chronological order. A fixed time window is set, and the sample density within each time difference interval is calculated to generate a continuous time difference density curve. Perform fast Fourier transform and time-domain analysis on the time difference density curve to extract drift period, fluctuation amplitude, rate of change and phase stability index, and generate short-period drift feature set; Short-period drift features within multiple time windows are concatenated into a drift feature fingerprint, and normalization and similarity analysis are performed in conjunction with device identification and network characteristics to eliminate abnormal fluctuations. Statistical feature vectors are generated based on drift feature fingerprints, and stored in groups according to time order and device identifiers to construct a deviation estimation basis that reflects the terminal time deviation characteristics.

5. The method for intelligent adaptation of educational resources across terminal devices according to claim 4, characterized in that, When performing frequency domain analysis on the time difference density curve, the main frequency component is extracted by fast Fourier transform, and the phase stability index is calculated based on the phase change trend corresponding to the main frequency and the drift amplitude fluctuation range within the sliding window.

6. The method for intelligent adaptation of educational resources across terminal devices according to claim 1, characterized in that, The steps for generating a continuous time-series deviation trajectory include: In the bias estimation basis, the drift period, drift amplitude and phase stability index of the corresponding terminal device in the current global time anchor interval are selected, and the original arrival time difference sequence in the interval is screened to remove outliers and mark intermittent bursts. A constrained recursive filter parameter set is constructed based on the filtered arrival time difference sequence. The recursive filter is constructed using state transition equations and observation equations. The filter gain is constrained by the phase stability index, and the state update rate is limited by the drift period. The state estimation results within each time anchor interval are spliced ​​together, and the boundary states of adjacent intervals are fused using a weighted smooth transition method. The slope of the deviation curve is dynamically corrected in combination with historical drift trends. The spliced ​​continuous deviation curves are normalized, and a time index and global time anchor number are added. Then, a standardized time deviation trajectory is generated by interpolation and point supplementation.

7. The method for intelligent adaptation of educational resources across terminal devices according to claim 6, characterized in that, The steps for constructing a two-way residual field and generating a time error growth curve include: Based on the time series of events on the teacher's end, the continuous time series deviation trajectories of each terminal device are aligned to generate an initial residual sequence; The residual sequence is extended forward and backward, and the mean, variance, and slope of the forward residual field and the residual trend of the backward residual field are calculated respectively to construct a two-way residual field. Based on the two-way residual field, the phase error is inverted, and the residual is weighted by the phase stability index in the bias estimation basis to obtain a continuous phase error sequence. Perform discrete integration on the phase error sequence and smooth it to generate the time error growth curve of the terminal device relative to the teacher's device.

8. The method for intelligent adaptation of educational resources across terminal devices according to claim 7, characterized in that, The steps for feeding back the time error growth curve to the global time anchor scheduler and performing phase stretching probes include: The time error growth curve of each terminal device is fed back to the global time anchor scheduler, and the error growth slope, fluctuation amplitude and inflection point position are extracted. Based on the trend characteristics of the error growth curve, select the target terminal device and set the magnitude and duration of phase stretching; Perform micro-amplitude phase stretching on the target terminal device to adjust the event triggering timing by compressing or extending the local time series sampling interval; During the trial process, the magnitude of the residual decrease is calculated, and the adjustment effect is judged in combination with the short-period drift characteristics; The cumulative time error of the terminal equipment is assessed based on the rate of decrease in residual error, and compared with the time error growth curve to determine whether it has entered a safe range.

9. The method for intelligent adaptation of educational resources across terminal devices according to claim 1, characterized in that, The steps for dynamically inserting phase anchors and correcting local time series in the time series of key teaching events include: When the accumulated time error of a terminal device exceeds a preset threshold, logical analysis is performed on the time series of the current teaching event to identify candidate positions where phase anchors can be inserted. Based on the candidate position and the magnitude of the cumulative error value, select one or more types of buffer screen, silent transition frame or weak interactive detection command as phase anchor point for insertion. After inserting a phase anchor point, record the difference between the occurrence time of the anchor point under the global time reference and the local reception time, and calculate the phase offset curve between consecutive anchor points. Based on the slope of the phase offset curve and the cumulative drift value, the local timing of the terminal device is slightly compressed or extended to dynamically correct the delay drift.

10. A cross-terminal device intelligent adaptation system for educational resources, used to implement the cross-terminal device intelligent adaptation method for educational resources as described in any one of claims 1-9, characterized in that, It includes a global time anchor construction module, a time difference density analysis module, a time series deviation filtering module, a residual inversion calculation module, a phase stretching and control module, and a time series dynamic correction module; The global time anchor construction module embeds spread spectrum phase watermark information into the teaching event frame. The watermark information serves as the global time anchor. Each terminal device extracts the watermark from the teaching event frame it receives locally and records its local reception time to generate an initial event time series containing global correlation. The time difference density analysis module calculates the arrival time difference of each terminal device relative to the global time anchor based on the initial event time series, generates a continuous time difference density curve, and extracts the feature fingerprint of short-period drift from the time difference density curve to construct a deviation estimation basis that reflects the terminal time deviation characteristics. The timing deviation filtering module, based on the deviation estimation basis, performs restricted recursive filtering on the arrival time difference between adjacent global time anchors to generate continuous timing deviation trajectories of each terminal device relative to the global time. The residual inversion calculation module constructs a two-way residual field based on the time series deviation trajectory during the alignment of the teacher's event time series. It then inverts the relative phase error of each terminal device through the residual field and performs integral calculation on the inverted phase error to generate the time error growth curve of the corresponding terminal. The phase stretching control module feeds back the time error growth curve to the global time anchor scheduler. The scheduler performs micro-phase stretching trials on the target terminal based on the time error growth trend, and evaluates the cumulative time error of each terminal based on the residual decrease during the trial process. The timing dynamic correction module dynamically inserts phase anchors that do not change the teaching logic into the time series of key teaching events when the accumulated time error exceeds a preset threshold. It also dynamically corrects the local timing based on the phase offset between the anchors, eliminating timing deviations caused by delay drift between terminals.

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