Kalman filter based remote elderly health assessment state prediction system

Abstract

The application belongs to the technical field of health care, and particularly relates to a remote old-age health assessment state prediction system based on Kalman optimization trees. The system comprises a data acquisition and synchronization unit, a global health prediction factor generation unit and a state prediction unit. The data acquisition and synchronization unit is used for uniformly setting Kalman optimization tree root node identifiers for all health data acquisition nodes at a local end. The global health prediction factor generation unit is used for one-time distribution of health data sequences sent by each health data acquisition node according to a Kalman optimization tree topology structure, so as to obtain a global health prediction factor sequence. The state prediction unit is used for generating an old-age health assessment prediction result based on the global health prediction factor sequence. The application has the advantages of high time sequence consistency and high risk identification accuracy.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of health care, and particularly relates to a remote old-age health assessment state prediction system based on Kalman optimization trees. BACKGROUND

[0002] Under the background of the current aging society, remote health monitoring and state assessment have become an important part of the old-age medical service system. Especially in the scenes of chronic disease management, daily vital sign tracking and sudden health event warning, how to efficiently and accurately identify potential health risks from multi-source physiological data is becoming the core research direction of medical information processing and intelligent wearable technology. Existing remote health monitoring systems mostly rely on wearable devices to collect the basic vital signs of the elderly, such as heart rate, blood pressure, blood oxygen, body temperature, etc., and upload them to the background server or cloud platform for centralized analysis through the network. Although such systems have a high popularity and real-time performance in data collection, they still have significant deficiencies in data fusion modeling, time sequence consistency management, multi-node coordinated analysis and high-risk prediction, which limit their application accuracy and response speed in the health warning of the elderly.

[0003] From the technical architecture, most of the traditional systems adopt a flat collection model, that is, each terminal node independently samples and uploads the data in timestamp package to the cloud for unified modeling. For example, common time series modeling methods such as LSTM (Long Short-Term Memory Network), GRU (Gated Recurrent Unit) neural network model, or linear regression, support vector machine shallow machine learning model are widely used in server-side health trend prediction tasks. However, these models rely on large-scale labeled data sets for training, and the generalization ability is sensitive to the differences between individual users, and their black box characteristics make it difficult to provide explainable causal chains in the medical field. In addition, the flat structure means that all terminal devices are logically equivalent, lacking hierarchical aggregation capability, and difficult to handle the problems of asynchrony, channel delay and network jitter between multiple sensors in a distributed environment, resulting in the final prediction model having deviations in time sequence consistency and structural stability. SUMMARY

[0004] The main purpose of the present application is to provide a remote elderly health assessment state prediction system based on Kalman optimization tree, which realizes the synchronous acquisition, time sequence consistent processing and multi-dimensional fusion analysis of multi-node health data by constructing a Kalman optimization tree with hierarchical topology; the system introduces high-order Hankel tensor reconstruction, quaternion rotation alignment and double-layer difference processing, effectively enhances the sensitivity to local dynamic changes, and combines recursive non-transparent transpose traversal and multi-scale chain extraction mechanism to realize accurate identification of high-risk nodes and hierarchical evaluation of health status, has beneficial effects such as high time sequence consistency and high risk identification accuracy, and is suitable for remote medical treatment and elderly health management scenes.

[0005] To solve the above technical problems, the present application provides a remote elderly health assessment state prediction system based on Kalman optimization tree, which comprises: a data acquisition and synchronization unit, a global health prediction factor generation unit and a state prediction unit; the data acquisition and synchronization unit is used for uniformly setting the Kalman optimization tree root node identifier for all health data acquisition nodes at the local end, and establishing the corresponding synchronization time stamp buffer inside all health data acquisition nodes to ensure the time sequence consistency of the acquired health data sequence; the global health prediction factor generation unit is used for distributing the health data sequence sent by each health data acquisition node according to the Kalman optimization tree topology structure, mapping the health data sequence in the same time period to the corresponding Kalman optimization tree leaf node; at the same time, multi-dimensional health vector difference fusion processing is performed on each Kalman optimization tree intermediate node to obtain the global health prediction factor sequence; the state prediction unit is used for triggering a round of recursive non-transparent transpose traversal at the Kalman optimization tree root node based on the global health prediction factor sequence, outputting a high-risk node set, and generating an elderly health assessment prediction result according to the position of the number of nodes in the high-risk node set in the preset health judgment multi-threshold interval.

[0006] Further, the data acquisition and synchronization unit takes the clock source of the Kalman optimization tree root node as the reference clock, sends the time synchronization mark signal to all health data acquisition nodes through periodic broadcast or multicast mode, and the time synchronization mark signal carries the reference clock; after each health data acquisition node receives the reference clock, the reference clock is extracted, and the local clock in the synchronization time stamp buffer is calibrated based on the reference clock, so that the local clock inside all health data acquisition nodes is consistent with the reference clock; the time stamp recorded in the calibrated synchronization time stamp buffer is taken as the unified time sequence basis.

[0007] Further, the process of generating the global health prediction factor sequence by the global health prediction factor generating unit includes: in the same sampling period, each intermediate node of the Kalman optimization tree sequentially reads health data sequences of all direct child nodes thereof, and reconstructs a high-order Hankel tensor based on a fixed-length sliding window to capture local time correlation explicitly; the high-order Hankel tensor is rotated along the order of the tensor by a quaternion operator to complete alignment of the local state tensor in a latent manifold coordinate system; a double-layer difference processing is performed on the rotated local state tensor in the latent manifold coordinate system: first, a first-order difference vector between spatial dimensions is calculated, and then fractional-order difference is performed on the difference vector sequence according to time dimensions to obtain a double-layer difference vector set; a Euclidean norm of the double-layer difference vector set is calculated, and a difference intensity ordering queue is generated in a norm increasing order, and the ordering result is taken as a multi-dimensional health state estimation vector of the current intermediate node; according to the topology of the Kalman optimization tree, the multi-dimensional health state estimation vector of the current node is transmitted to the upper-level intermediate node or the root node; at the root node of the Kalman optimization tree, the multi-dimensional health state estimation vectors from all sub-trees are time-series spliced and mean filtered, and finally a global health prediction factor sequence covering the current sampling period is output.

[0008] Further, the global health prediction factor generating unit reconstructs a high-order Hankel tensor based on the same period data by a fixed-length sliding window through the following process: the start time and the end time of the current sampling period and the length of the sliding window are set; for each direct child node, a health data sequence arranged in time order is obtained in the sampling period; starting from the start time of the sampling period, a continuous sub-sequence of equal length is obtained by sliding with a step of one sampling point, so that the length of each sub-sequence is equal to the preset sliding window length; the sampling values in the same sub-sequence are sequentially filled into the Hankel matrix according to the sampling order, so that the row index of the Hankel matrix represents the sampling offset and the column index represents the window number; the Hankel matrices corresponding to all direct child nodes are stacked according to the sub-node number dimension to construct a three-order Hankel tensor containing the sub-node dimension, the row offset dimension and the column offset dimension, thereby explicitly capturing the local time correlation.

[0009] Furthermore, the global health prediction factor generation unit performs a compound rotation on the high-order Hankel tensor along the order through the quaternion operator through the following process: performing high-order singular value decomposition on the third-order Hankel tensor along the sub-node dimension, row offset dimension and column offset dimension respectively to extract the corresponding principal component matrix; mapping each principal component matrix to the quaternion space to construct a quaternion set representing the rotation axis and rotation angle information; obtaining the global alignment quaternion by solving the Lie group mean under the maximum variance constraint for the quaternion set; multiplying the global alignment quaternion in the order of sub-node dimension, row offset dimension and column offset dimension in sequence to generate a compound rotation operator, and performing left multiplication and right multiplication transformations on the third-order Hankel tensor respectively to complete the alignment of the local state tensor in the potential manifold coordinate system.

[0010] Furthermore, the health data sequence includes: multiple consecutive health data entries indexed by a unified timestamp recorded in a synchronous time stamp buffer; each health data entry includes in sequence: a data acquisition node identifier, used to uniquely identify the corresponding health data acquisition node; a timing offset corresponding to the unified timestamp, used to characterize the specific sampling position of the health data entry within the sampling period; a multi-dimensional health measurement vector, including, in a preset order: heart rate sampling value, systolic blood pressure sampling value, diastolic blood pressure sampling value, blood oxygen saturation sampling value, respiratory rate sampling value, body temperature sampling value, three-axis motion acceleration value, and three-axis posture angle value.

[0011] Furthermore, the state prediction unit, based on the global health prediction factor sequence, triggers a round of recursive non-transparent transposition traversal at the root node of the Kalman optimization tree, and the process includes: selecting the root node of the Kalman optimization tree to the nearest three-layer node as the initial activation domain, and marking all nodes in the domain as a candidate node set; implementing a multi-scale fractal unlinking scan in the candidate node set, peeling off redundant branches of similarity layer by layer in descending order of node confidence labels, retaining the representative chain with maximum time continuity, and obtaining a retained chain; for each node in the retained chain, alternately performing forward recursive and reverse recursive mixed searches until the search depth reaches the set level; in the reverse recursive mixed search process, triggering an abnormal state check for each state transition, and mapping nodes whose trigger times exceed the threshold as high-risk nodes.

[0012] Furthermore, the specific process of obtaining the retention chain includes: setting the fractal analysis scale set , where each scale The corresponding time span window length is Sampling period; for scale , segment the candidate node set continuously according to the node timestamp to obtain the initial chain set , where each initial chain Indicates the window length a sequence of successively reachable nodes; for each initial chain computing a chain belief vector, the chain belief vector being formed by concatenating the node belief labels in the chain in time order; performing cosine similarity computation between the chain belief vector and other chain belief vectors in the same scale to generate a chain similarity matrix; in the chain similarity matrix, if the similarity value of a chain pair is greater than a pre-set redundancy threshold, marking it as a similarity redundancy branch; traversing the initial chain set in order of chain average belief from high to low , and in the traversal process, stripping other chains that form a similarity redundancy branch with the current chain, and only retaining the chain with the highest average belief, to obtain a chain set after redundancy stripping ; for each chain in the chain set , statistics its time continuity length; under the same scale , retaining the chain with the longest time continuity length as the representative chain of the scale ; repeating the above process until all scales are processed, forming a representative chain set ; in the representative chain set , re-computing the time continuity length for each representative chain, and selecting the chain with the longest time continuity length as the retained chain; wherein, is an integer index; is the number of scale sets of fractal analysis scales.

[0013] Further, the specific process of alternately performing forward recursion and backward recursion mixed search for each node of the retained chain includes: initializing a search depth counter for each starting node in the retained chain, and pre-setting a maximum search level and an abnormal state triggering threshold performing a forward recursion step at the current node: retrieving the direct successor node set of the node in the time stamp increasing direction, traversing the successor nodes in the order of decreasing node belief label, and setting the first successor node satisfying the belief label greater than or equal to the global average belief label as the next recursion node; updating the search depth counter, if the current search depth has not reached , performing a backward recursion step: retrieving the direct predecessor node set of the current node in the time stamp decreasing direction, traversing the predecessor nodes in the order of decreasing node belief label, and setting the first predecessor node satisfying the belief label greater than or equal to the global average belief label as the next recursion node; after each forward or backward recursion state transition is completed, triggering an abnormal state check: calculating the Euclidean distance between the new and old node state vectors, if the distance is greater than a pre-set abnormal threshold, the abnormal count of the current node is incremented by one; maintaining an abnormal count register for each node in the retained chain, which is used to record the cumulative number of abnormal state triggers; until the search depth counter reaches or no reachable node meeting the confidence label condition; when the search process terminates, compare the anomaly count of each node with , if the anomaly count is greater than , map the node as a high-risk node, then map the node as a high-risk node, put all high-risk nodes into a set to obtain a high-risk node set.

[0014] The Kalman optimization tree-based remote elderly health assessment state prediction system of the present application has the following beneficial effects: the system constructs a Kalman optimization tree with a topological hierarchical structure, supports multi-level filtering and fusion of health data aggregated from edge nodes upwards in structure, avoids the problems of data isolation and mismatched analysis results in traditional flat structures. Secondly, the system sets a reference clock at the root node, and realizes the consistency of time stamps of all collection nodes through a synchronous time tag buffer, solving the problem of timing drift caused by multi-source asynchronous collection, significantly improving the comparability of cross-node data and the stability of analysis. In addition, the present application introduces high-order tensor reconstruction and multi-dimensional rotation alignment operation in the data processing path, enhances the expression ability of local dynamics under the premise of maintaining the integrity of the original data structure, and can effectively capture the potential nonlinear change trend in the health state. At the same time, the double-layer differential processing strategy further improves the sensitivity of abnormal state in combination with multi-order feature enhancement of spatial dimension and time dimension, especially in early chronic disease mutation identification. Through recursive non-transparent transposition traversal and multi-scale chain screening mechanism, the system can extract the state path with the most prediction value from complex health dynamics while keeping the computational burden controllable, and accurately mark high-risk nodes, providing clear basis for the evaluation result. Overall, the present application can provide higher precision, stronger robustness and better explainability in remote elderly health assessment in a multi-node, complex topology, real-time response health monitoring environment, meeting the dual needs of reliability and intelligence in community medical care, home-based care and other practical application scenarios. BRIEF DESCRIPTION OF DRAWINGS

[0015] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiment or prior art description. Obviously, the drawings in the following description are only embodiments of the present application, and for those skilled in the art, other drawings can be obtained without creative labor on the basis of the provided drawings.

[0016] Figure 1 The system structure schematic diagram of the Kalman optimization tree-based remote elderly health assessment state prediction system provided by the embodiments of the present application is shown in the figure.

[0017] Figure 2 The high-risk node distribution schematic diagram in the Kalman optimization tree topological structure provided by the embodiments of the present application is shown in the figure.

[0018] Figure 3 A schematic diagram of the trend of the global health predictor sequence provided by the embodiment of the present application in the continuous sampling period;

[0019] Figure 4 A schematic diagram of the relationship between the reserved chain and the search path in the recursive non-transparent transpose traversal provided by the embodiment of the present application. DETAILED DESCRIPTION

[0020] The system of the present application will be further described in detail below in combination with the accompanying drawings and the embodiments of the present application.

[0021] Reference Figure 1 , the remote elderly health assessment state prediction system based on Kalman optimization tree, the system comprises: a data acquisition and synchronization unit, a global health predictor generation unit and a state prediction unit; the data acquisition and synchronization unit is used for uniformly setting Kalman optimization tree root node identification for all health data acquisition nodes of the local end, and establishing a corresponding synchronization time buffer in all health data acquisition nodes, so as to ensure the time sequence consistency of the acquired health data sequence; the global health predictor generation unit is used for distributing the health data sequence sent by each health data acquisition node according to the Kalman optimization tree topology structure, mapping the health data sequence in the same time period to the corresponding Kalman optimization tree leaf node; at the same time, multi-dimensional health vector difference fusion processing is performed on each Kalman optimization tree intermediate node, and the global health predictor sequence is obtained; the state prediction unit is used for triggering a round of recursive non-transparent transpose traversal at the Kalman optimization tree root node based on the global health predictor sequence, outputting a high-risk node set, and generating an elderly health assessment prediction result according to the position of the number of nodes in the high-risk node set in the preset health judgment multi-threshold interval.

[0022] In this architecture, the so-called Kalman optimization tree can be regarded as a spatiotemporal hierarchical model that combines the recursive estimation idea of classical Kalman filter with the multi-branch tree topology. The root node assumes the functions of global state prior and clock reference, the intermediate nodes in each layer assume the functions of local state update and error co-compression, and the leaf nodes directly correspond to the health data collection nodes in the physical world. The core principle of the tree connection mode is to extend the "observation-prediction-correction" Kalman recursive cycle to the networked environment: each node is both a filtering terminal of a subsystem and can upload its filtered estimate as a new observation of the parent node. With this vertical iteration, the system can obtain multi-scale information aggregation capability while maintaining real-time performance; with horizontal parallelism, nodes at the same level can share the computational load and suppress the risk of single-point failure. The root node has a unique clock source, which writes a unified time scale into each synchronized time scale buffer through broadcasting. From the signal processing point of view, it is equivalent to projecting all the discrete time series measured by the sensors onto the same sampling grid, thereby avoiding phase drift caused by subsampling when reconstructing the subsequent sliding window.

[0023] After entering the global health predictor generation unit, each leaf-to-root path of the tree performs a recursive chain of local prior ablation and error propagation. The original vectors uploaded by the leaf nodes often contain physiological data and attitude data of different dimensions, and there are significant differences in sampling accuracy and dynamic range between these data. Direct superposition will amplify the dominance of certain indicators and mask the subtle contributions of other indicators to prognosis analysis. To suppress this imbalance, the intermediate nodes first use Hankel reconstruction in a fixed-length sliding window. Hankel reconstruction is essentially a nested operation that embeds one-dimensional time series into high-order tensors, which can encode temporal dependence into the face structure across the tensor order; applying this operation in the tree means that each node can retain rich local dynamic details in the form of a tensor without storing lengthy original sequences. After the tensor is constructed, the system applies quaternion operators to complete complex rotation in the latent manifold coordinate system. The principle of this step is similar to image registration: by spatially rotating the principal components of each order, the vector fields collected on different child nodes are aligned in the relative coordinates, and the phase difference caused by attitude changes or device calibration errors is corrected simultaneously. This "geometric alignment" precedes statistical fusion, which can significantly improve the resolution of abnormal transitions in subsequent difference operations.

[0024] The double-layer differential fusion processing is another core of the unit. First, the first-order difference is calculated in the vector space to filter out the static baseline, and then the fractional-order difference is performed on the time axis to extract high-frequency details. The idea behind this is from the impulse response analysis: the first-order difference highlights the trend inflection point, and the fractional-order difference retains weak non-stationary characteristics, and the combination of the two can capture both slowly changing chronic disease signals and acute emergency signals. After the difference, the norm sorting is used instead of directly using the covariance to avoid the singularity of the high-dimensional covariance matrix under a small sample window. The intensity queue obtained by the norm sorting expresses the health state fluctuation amplitude in a monotonic scale form, which reduces the computational complexity and is easy to incrementally splice with the parent node. The root node converges the differential intensity vectors from each sub-tree, performs time series splicing and mean filtering again, which is equivalent to performing a global Kalman smoothing at the top of the tree to further attenuate the estimation error of the multi-path uplink. Finally, a global health prediction factor sequence spanning the entire sampling period is generated.

[0025] The state prediction unit triggers recursive non-transparent transposition traversal from the root node. The "non-transparent" means that the parent confidence label details are not disclosed to the lower level during traversal to avoid local overfitting diffusion; "transposition" means that the traversal direction switches between time positive order and inverse order to enhance the symmetric search of the neighborhood on both sides of the abnormal point. Before traversal, a multi-scale fractal unzipping scan is constructed. This process divides the candidate node set into multiple initial chains according to different time resolutions, and then removes redundancy using the cosine similarity between chain confidence vectors. The key idea here is to regard the confidence label sequence as a fractal line, and find the longest and most "robust" main chain through scale transformation; compared with the conventional depth-first or breadth-first algorithm, the fractal scan can find the most representative trajectory with optimal time continuity without increasing the complexity. After the reserved chain is determined, the system alternately performs forward and backward recursive search around the trajectory. The alternating strategy can be regarded as running a pair of opposite Markov chains on the time series graph: the forward recursion pulls the trend line extension, and the backward recursion backtracks potential missed detection. The dynamic weight of high and low confidence nodes is gated by the global average confidence label, so the search path can automatically adjust around the most credible interval.

[0026] The recursive search is accompanied by an anomaly state check to realize the high-risk node mapping. The check rule uses the Euclidean distance instead of the Mahalanobis distance, which is based on the fact that the distribution of the state vector of each node in the tree does not necessarily satisfy the Gaussian assumption. Directly measuring the difference between the new and old states with the L2 norm can avoid the error of covariance matrix estimation. The anomaly count register accumulates the number of triggers, which is compared with the threshold value. This is inspired by the bathtub curve in reliability engineering: short-term continuous triggering is considered to be temporary disturbance, and only continuous triggering across the window is considered to be real risk. The high-risk node set is finally mapped to the health judgment multi-threshold interval. The risk level is divided from coarse to fine, and the threshold itself can be adjusted according to the characteristics of the population through offline training. The online link only does fast interval positioning, so as to balance adaptability and real-time performance. The prediction result contains the timestamp and confidence summary of the high-risk node when it is returned to the medical terminal and family terminal, which is convenient for medical staff to make further intervention.

[0027] The whole process shows the essential advantages of Kalman optimization tree in multi-source time series fusion: its tree topology provides distributed collection and synchronization at the physical level, Kalman recursion provides progressive error suppression at the algorithm level, high-order tensor reconstruction and quaternion alignment ensure the homogeneity of multi-dimensional dynamic features at the geometric level, double difference and norm sorting highlight key fluctuations at the signal level, and fractal scanning and recursive search release the structural information hidden in the time series relationship at the graph theory level. It is this cross-layer cooperation that enables the remote elderly health assessment state prediction system to continuously output reliable health risk warnings in a low-power device and limited bandwidth environment, providing fast, accurate, and engineering-oriented digital support for home-based care and community health care.

[0028] After the state prediction unit completes the recursive non-transparent transpose traversal, the high-risk node set has recorded all the nodes whose anomaly count exceeds the threshold in this round of search. Since the hierarchical structure of the Kalman optimization tree has clustered the multi-dimensional health measurement vector by time and semantics, the high-risk node actually represents the distribution range and intensity of abnormal activities in the tree topology. The system holds a set of health judgment multi-threshold intervals at the root node in advance, each interval corresponding to a health assessment level. The threshold interval is not simply equidistant, but is obtained through offline model training combined with historical labeled data, so that the low interval remains sensitive to the number of nodes, and the high interval has discrimination for large-scale risk scenarios. At runtime, the system first calculates the number of nodes in the high-risk node set, and then performs interval positioning with the multi-threshold interval. The positioning process uses the sequential comparison method: starting from the lowest interval and comparing sequentially until the node number falls into a certain interval, the system considers that the current prediction is at the health assessment level corresponding to the interval. The reason for using sequential comparison instead of proportional mapping is to ensure the interpretability of the evaluation scale under high-dimensional heterogeneous data; each threshold interval is explicitly characterized by the upper and lower bounds of the node number, ensuring consistent risk scale for different populations and different sensor layouts.

[0029] After the interval positioning, the system generates an easy-to-understand health assessment prediction result according to the interval and level mapping table. If the number of nodes is in the lowest interval, the prediction result is "stable state", prompting only routine monitoring is needed; if it is in the next lowest interval, the output is "mild fluctuation", suggesting that the user pay attention to life habits; the middle interval corresponds to "moderate warning", triggering remote inquiry of community nursing staff; a higher interval outputs "severe risk", the system immediately links the family and medical emergency channels; the highest interval corresponds to "emergency", the system not only sends real-time alerts, but also packages the timestamp and confidence summary of the abnormal node to the doctor's end, providing positioning information for rapid diagnosis and treatment. The entire mapping process only involves comparing the number of nodes with static thresholds, without high-dimensional matrix operations, so it can be completed in milliseconds on a low-power gateway; at the same time, the multi-threshold design makes the prediction result ladder-like progressive, when the number of nodes fluctuates near the critical value, the system will do a sliding window majority vote on consecutive multiple sampling periods, avoiding frequent jumps in levels caused by short-term jitter, thus balancing real-time and stability. The final health assessment prediction result of the elderly is returned to the medical and family terminals in the form of structured messages, including health assessment level, trigger interval number, high-risk node number, and recommended action suggestions, helping medical staff and family members make intervention decisions accordingly, realizing the closed loop of remote health management of the elderly.

[0030] Further, in the remote health assessment state prediction system based on Kalman optimization tree, the core principle of time unification is to place all distributed health data collection nodes on the same logical time plane, so that subsequent signal processing can be seamlessly aligned along the tree topology. The reference clock inside the root node is chosen because it is at the highest layer of the topology and naturally has a complete perspective of the global state prior; once its timing becomes the only trusted source in the network, the system can treat time as a public resource that can be broadcasted like data. The data collection and synchronization unit takes advantage of this feature to spread time synchronization marker signals to the network edge through periodic broadcast or multicast. The signal actually plays the role of "time courier": when it propagates in the channel, any intermediate hop count, queuing delay, or jitter can cause random drift in the reception time. In order to suppress the impact of drift on calibration accuracy, the time synchronization marker signal carries the instantaneous reading of the reference clock immediately when it leaves the transmission buffer. This carrying method allows the receiving node to obtain a "time sample" at the moment of arrival, and then compare it with the local clock. The synchronization timestamp buffer thus becomes a difference storage area: it does not directly modify the hardware clock, but records the difference as a continuously updated offset, and all subsequent local clock readings are subtracted by the offset before writing to the data packet, which appears to the outside world as if the local clock has been pulled to the reference clock.

[0031] The reason for using a buffer instead of direct correction for the offset is to reduce the risk of oscillation: if the network is jittering, the local clock will not jump frequently immediately, but will slowly converge through the sliding average mechanism in the buffer to obtain a gentle and continuous correction curve. When the sampling task is triggered, the node calls the synchronization timestamp buffer to generate a unified timestamp, which forms a data entry together with a multi-dimensional health measurement vector; after uploading the entry, it is vertically aggregated along the Kalman optimization tree inside the global health prediction factor generation unit. Since the timestamps have been aligned at the leaf layer, all intermediate nodes no longer need additional interpolation or padding, but can directly perform operations such as sliding window reconstruction, quaternion alignment, and double-layer difference. The essential meaning of this is to convert uncertain network latency into controllable local offset, and then use the buffer mechanism to stabilize the injection of offset into the sampling process, achieving timing consistency with 1 calibration and multiple reuse. This makes the entire tree from the bottom sensor to the top prediction based on a shared time reference, thereby ensuring the comparability and reliability of the health assessment results.

[0032] Further, in the Kalman optimization tree-based remote elderly health assessment state prediction system, the core idea of the global health prediction factor generation unit is to transform the time-series health data distributed in each leaf node into a concise factor sequence with the most information about the future state. Each intermediate node in the Kalman optimization tree first reads the health data sequences of all its direct child nodes in the same sampling period, and then uses a fixed-length sliding window to reconstruct the data in the same time period into a high-order Hankel tensor. This reconstruction distributes the one-dimensional time series according to the window number and sampling offset to multiple orders, making the local time correlation explicit in the tensor structure, and at the same time, through the stacking in the child node dimension, the data at different collection positions can be compared in the same geometric framework. Subsequently, the system calls the quaternion operator to perform composite rotation on the tensor along the order, aligning the local state tensor in the latent manifold coordinate system. The quaternion operator here plays the role of rigid transformation in multi-dimensional space, which solves the rotation of each order principal component and combines the rotation axis and rotation angle under the constraint of Lie group average, thereby unifying the phase reference and energy distribution between different child nodes, making the measurement vector with time drift obtain a common reference system, avoiding deviation in subsequent analysis due to direction difference.

[0033] In the Kalman optimization tree-based remote elderly health assessment state prediction system, the core idea of the global health prediction factor generation unit is to transform the time series health data distributed in each leaf node into a concise factor sequence with the most information about the future state layer by layer. Each intermediate node in the Kalman optimization tree first reads the health data sequences of all its direct child nodes in the same sampling period, and then uses a fixed-length sliding window to reconstruct the data in the same time period into a high-order Hankel tensor. This reconstruction distributes one-dimensional time series according to the window number and sampling offset to multiple orders, explicitly displays the local temporal correlation in the tensor structure, and makes the data at different collection positions comparable in the same geometric framework through stacking in the child node dimension. Subsequently, the system calls the quaternion operator to perform complex rotation on the tensor along the order, aligning the local state tensors in the latent manifold coordinate system. The quaternion operator here plays the role of rigid transformation in multi-dimensional space, which solves the rotation of principal components of each order and combines the rotation axis and rotation angle under the constraint of Lie group average, thereby unifying the phase reference and energy distribution between different child nodes, making the measurement vectors drifting over time obtain a common reference system and avoiding deviation in subsequent analysis due to direction difference.

[0034] When the multi-dimensional health state estimation vector reaches the root node of the Kalman optimization tree, the system performs time series splicing and mean filtering on the vectors from all sub-trees. Time series splicing preserves the time order of each uplink path, allowing estimates from different spatial sources to be side by side on the global time axis; mean filtering slides over the spliced results to take the average, smoothing transient noise and preserving the true trend. The sequence output by the root node covers the current sampling period, so it is called the global health prediction factor sequence, and the subsequent state prediction unit only needs to focus on this sequence to complete the recursive analysis of health risk. At this point, the mapping link from the original measurement vector to the global health prediction factor sequence has completed the layer-by-layer conversion of local temporal correlation capture, spatial alignment, double-layer difference enhancement, intensity ordering compression, and cross-sub-tree fusion. The core principle is to make the data exist in the form that best expresses dynamic information and is easy to upload at each level, and to use the natural hierarchical structure of the Kalman optimization tree to gradually aggregate local estimates into globally decidable health prediction factors.

[0035] Further, in the remote elderly health assessment state prediction system based on Kalman optimization tree, the construction of high-order Hankel tensor plays a key role in mapping one-dimensional time series to multi-dimensional geometric space. The core principle is to rearrange the time series information into a planar structure using a sliding window, and then encode the spatial distribution into a voxel tensor by stacking across nodes, so as to explicitly expose the local time correlation in the intrinsic form of data. First, the system determines the starting time and the ending time within each sampling period, and gives a fixed length sliding window, so that the length of the window covers multiple sampling points. For any direct child node, the window slides along the time axis with a step size of 1, and the equal-length subsequence intercepted by the window is like a continuous "time slice" cut out of the original sequence. These time slices are then moved into the Hankel matrix: the row index is used to record the offset of the sampling value inside the subsequence from the first position, and the column index is used to identify the number of the window on the entire timeline. Since the Hankel matrix naturally keeps the diagonal elements with the same time delay, this arrangement allows horizontally adjacent elements to share the same sampling offset, and vertically adjacent elements to share the same window number, thereby fixing the autocorrelation pattern of the local sequence as the stripe texture of the matrix.

[0036] When all direct child nodes complete their sequence conversion to the Hankel matrix, the system stacks the matrix in the "child node number" dimension to form a three-order Hankel tensor containing the child node dimension, the row offset dimension, and the column offset dimension. The three-order structure means that each voxel carries both the time position (determined by the row offset and the column offset) and the spatial source (determined by the child node number), so it is equivalent to generating a regular coordinate grid inside the tensor to capture the coupling of local time correlation and cross-node spatial homomorphism. In other words, adjacent observations on the time axis maintain the distance relationship by being placed in adjacent cells in the tensor patch, and data from adjacent nodes in space maintain the topological relationship by being placed in adjacent sections in the tensor body layer, and the resulting high-order Hankel tensor is like a multi-dimensional data crystal with time texture and space layering. When the subsequent quaternion operator performs complex rotation, the order of the tensor remains unchanged, but its geometric orientation is reshaped, so that the phase reference between different child nodes converges in the same potential manifold coordinate system; when the double-layer difference is expanded in this coordinate system, the local changes in the time dimension and the space dimension are amplified synchronously, without being canceled out by each other due to the misalignment of the original sequence. Therefore, the construction of high-order Hankel tensor is not only a simple dimensionality increase of data shape, but also a coupling of sequence autocorrelation, window translation, and multi-node distribution into a tensor topology that can be directly utilized by subsequent geometric alignment and difference operations.

[0037] Three-order Hankel tensor is represented as:

[0038] ; ;

[0039] ;

[0040] wherein, is a third-order Hankel tensor, the tensor order corresponds to the "child node dimension, row offset dimension, column offset dimension"; is the index of the child node dimension, the subscript range ; is the index of the row offset dimension, corresponding to the sampling offset within the sliding window; is the index of the column offset dimension, corresponding to the window number; is the child node health data sampling value at the uniform timestamp ; is the starting uniform timestamp of the current sampling period; is the number of direct child nodes; is the fixed-length sliding window length; is the total number of sampling points in the current sampling period; is the column offset dimension length, equal to .

[0041] Let be the multi-dimensional health vector obtained by expanding the rotated local state tensor at node , time ; is the first-order difference vector of node at time ; is the fractional order difference order, the value range ; is the fractional order difference truncation length, used for finite sum approximation to realize fractional order operation; is the fractional order difference vector of node at time , belonging to the double-layer difference vector set; is the Euclidean norm of the double-layer difference vector of node at time ; is the Euclidean norm, used to measure the amplitude of the multi-dimensional vector; is the difference intensity sorting queue, arranged from small to large according to value, as the sorting result of the multi-dimensional health state estimation vector; is the local index of the current intermediate node in the Kalman optimization tree; then the following equation group is obtained:

[0042] ;

[0043] ;

[0044] ;

[0045] ;

[0046] where sort is a sorting function that sorts the values in a collection.

[0047] Further, the third-order Hankel tensor has sub-node dimension, row offset dimension and column offset dimension, each of which can have independent phase and direction offsets due to sensor position difference, time window sliding or window number misplacement. The system first performs high-order singular value decomposition along each of the three dimensions, and the decomposition process concentrates the energy of the tensor in the corresponding dimension into a set of orthogonal principal component matrices, which are essentially orthogonal bases describing the principal direction of local data distribution. When the principal component matrices are mapped to the quaternion space, each column of the orthogonal bases is regarded as a rotation axis in the Euclidean space, and the coherent energy hidden in the principal component matrices is converted into the size of the rotation angle, thereby generating a batch of quaternions representing "how to rotate from the local coordinate system to the principal direction coordinate system". Since the quaternion is isomorphic to the group structure of three-dimensional rotation, it avoids the problem of gimbal lock of Euler angles and maintains numerical stability when continuously interpolating. The system then puts the batch of quaternions into the Lie group averaging framework to solve the globally aligned quaternion under the maximum variance constraint; this averaging operation is equivalent to finding a geometric centroid on the rotation group manifold, so that the tensor is statistically closest to the same reference direction after rotation in each dimension, while ensuring that the total amount of rotation is not excessively compressed to preserve the natural dispersion of the data. After obtaining the globally aligned quaternion, the system sequentially performs multiplication according to the order of the sub-node dimension, row offset dimension and column offset dimension, and regards the multiplication result as a composite rotation operator. The composite rotation operator not only encodes the cumulative effect of independent rotation in each dimension, but also explicitly records the order of the dimensions in its multiplication structure, which enables the subsequent left and right multiplication transformations to act simultaneously on the tensor row and column sides. Left multiplication is equivalent to multiplying the composite rotation matrix before each slice to reshape the column vector direction; right multiplication is equivalent to multiplying the transpose of the composite rotation matrix after each slice to reshape the row vector direction. The bidirectional transformation ensures that the local block of the tensor is completely registered in the latent manifold coordinate system: it not only corrects the spatial deflection introduced by different sampling nodes, but also eliminates the time phase error caused by the moving window at the same time. Finally, the local state tensor and the global reference system are aligned, and the spatial and temporal semantic directions of each voxel in the tensor are re-unified. Compared with direct normalization or simple translation, this quaternion-driven composite rotation can maximize the elimination of direction noise while preserving the original energy distribution, providing a high-fidelity and low-distortion data basis for subsequent double-layer differential processing.

[0048] Further, the uniform timestamp comes from the synchronized time buffer, which is not simply recording the "current time", but freezing the calibrated global clock reading as a discrete grid point, so that all leaf node observations fall on the same time grid; this approach folds all physical clock differences in the distributed sampling environment into the buffer offset, ensuring that the system no longer worries about the timing misalignment when making horizontal comparisons of any healthy data entries. The data collection node identifier that follows the uniform timestamp assumes the topology mapping function: when the sequence propagates upwards, the Kalman optimization tree can locate which leaf-to-root path the entry belongs to in constant time by virtue of this identifier, and accordingly decide which sub-node dimension profile the entry should be stacked into when reconstructing the tensor; this way it directly binds the physical source of the data to the geometry of the tree, avoiding subsequent algorithms from causing mutual information leakage due to node aggregation.

[0049] The timing offset corresponding to the uniform timestamp further refines the relative position within the sampling period. The reason is that the elderly vital signs have the characteristics of coexistence of rhythm drift and short-term abnormalities, and it is often difficult to distinguish a respiratory pause from a normal respiratory gap using absolute time, while the timing offset provides positioning for the micro-rhythm within the current sampling period, so that the sliding window can accurately align the observation values on the same rhythm when reconstructing the Hankel matrix, keeping the local periodic pattern within the diagonal structure. The multi-dimensional health measurement vector packs the heart rate sample value, the systolic pressure sample value, the diastolic pressure sample value, the blood oxygen saturation sample value, the respiratory rate sample value, the body temperature sample value, the three-axis motion acceleration value and the three-axis attitude angle value in a fixed order. The reason for adopting this order is that the cardiovascular indicators to the kinematics indicators roughly present an "inward-outward" layered relationship in the physiological regulation link; arranging them in this order can form a natural hierarchical semantics within the vector, and the subsequent quaternion composite rotation is easier to concentrate similar energy patterns on adjacent bases when doing principal component alignment, reducing energy leakage in the rotation solving process.

[0050] The dimensional difference within the vector is aligned by the system's built-in uniform scale mapping, so that numbers like heart rate and acceleration can be differentiated and normed in the same number field without relying on additional normalization markers; this step is particularly crucial for the double-layer difference, because fractional-order difference is extremely sensitive to high-frequency content, and inconsistent dimensions can misjudge high-frequency noise of acceleration as abnormal pulses when normed. The fixed field order also makes the byte layout of each data entry constant, so that the node's firmware can use low-power DMA to map sensor FIFO content to the buffer directly, without parsing each field, thus reducing the edge node's power consumption. As the sampling event triggers, new entries are appended to the health data sequence, and if packet loss occurs within the same sampling period, the sequence can be occupied by default node identifiers and special offset markers; the root node will perform local interpolation on these placeholders when time-series splicing, ensuring that the tensor rank remains stable without singular decomposition caused by missing values.

[0051] Further, the state prediction unit starts a recursive non-transparent transpose traversal immediately after the root node receives the global health prediction factor sequence. The first step of the traversal is to define the initial activation domain: the root node extends down to all branches of the last three layers of nodes, which are collectively included, and each node in the domain is marked as a candidate node set. The root node is limited to three layers because there is an empirical coupling between the level depth of the Kalman optimization tree and the length of the sampling period, and these three layers usually cover the main dynamics across a sampling period without missing key trends or introducing long-range redundancy. After the candidate node set is determined, the system performs a multi-scale fractal unbinding scan on the set; the core of the scan is to divide the candidate nodes into several fractal scales of different proportions on the time axis, form several continuous initial chains at each scale, and calculate the chain confidence vectors of these chains. The chain confidence vector is a discrete signal formed by concatenating the node confidence labels in the chain in time order, and its length is consistent with the time span covered by the chain. The system uses a cosine similarity matrix to compare chain confidence vectors of the same scale two by two, and marks chain pairs with high similarity as similarity redundant branches. Then, in descending order of node confidence labels, the chain set is scanned, and chains that are redundant with the current scanning chain are stripped one by one until only one chain is left in the entire scale; this chain is considered to be the representative chain with the strongest time continuity and the highest confidence at that scale. Multi-scale processing allows the system to focus on both long-period slow disease trends and short-period acute signals; after all scales have completed the redundancy stripping, the representative chain set may still contain multiple chains with different time continuity lengths, so the system reorders the time continuity lengths of these chains, and finally retains the longest chain that covers the most complete time interval, called the retained chain. The retained chain can be seen as the most representative main track of the health dynamics in this traversal round, which points down to the leaf node and seamlessly connects to the global health prediction factor sequence.

[0052] When entering the recursive search phase, the system initializes a search depth counter for each node in the reservation chain and sets a maximum search level. The search process alternates forward recursion with backward recursion to improve the ability to capture non-stationary fluctuations. Forward recursion retrieves the direct successor node set of the current node in the ascending direction of the timestamp and traverses in descending order of the node confidence label; the first successor node that meets the confidence label greater than or equal to the global average confidence label is selected as the next recursive node, and the search depth counter is incremented by one. When the search depth has not reached the set level, the algorithm immediately switches to backward recursion: retrieve the direct predecessor node set in the descending direction of the timestamp, and select the predecessor node according to the same confidence gating criterion; this alternation makes the search path zigzag along the time axis, which can capture both time-delay feedback and rapid transitions. After each state transition, the system triggers an abnormal state check by calculating the Euclidean distance between the new and old node state vectors. If the distance is greater than the abnormal threshold, the abnormality count register of the current node is incremented by one; the cumulative value of the register tracks the number of high-amplitude deviations exhibited by the node during the recursion process, better simulating the persistence rather than the transience of vital sign abnormalities.

[0053] The recursive search continues until the search depth reaches the maximum search level or there are no more nodes that meet the confidence gating criterion. When the search terminates, the system traverses the abnormality count registers of all nodes in the reservation chain, and maps nodes with trigger counts exceeding the threshold to high-risk nodes to form a high-risk node set. The high-risk node set will be used in the next phase to compare with the health judgment multi-threshold interval to produce the final prediction result of the elderly health assessment. Through this recursive non-transparent traversal, the state prediction unit connects macro trends with micro abnormalities using the hierarchical topology of the Kalman optimization tree, and strips out irrelevant noise and multiple redundancies using fractal unzipping scanning and hybrid recursive search, so that high-risk nodes truly represent potential dangerous areas of the current health status of the elderly, providing a reliable basis for real-time early warning.

[0054] Further, the fractal analysis scale set divides time into a series of windows that expand by a factor of two, the basic purpose of which is to simulate the self-similar characteristics of health status at different time granularities. The system first cuts a set of initial chains of continuous accessibility along the node timestamps with each window length as the sliding scale within the candidate node set; each initial chain obtained in this way is a sequence of nodes without time gaps in the corresponding scale, which is equivalent to extracting a self-consistent local trajectory on the health dynamic curve. Then the system splices the confidence labels for each initial chain in node order to obtain a chain confidence vector. The chain confidence vector not only inherits the reliability of individual nodes, but also maps the beat of dynamic evolution into a vector shape; the smoother the vector, the smaller the confidence fluctuations within the chain, and the more consistent the trend. In order to eliminate homogeneous information, the system pairs all chain confidence vectors in the same scale by cosine similarity; if the similarity of two chains exceeds the set redundancy threshold, it means that they can almost replace each other in shape, so they are marked as similarity redundancy branches. Then the system traverses the initial chain set from high to low according to the average confidence of the chain; when a chain is traversed, if it has a redundancy relationship with the retained chain, the one with lower confidence is discarded, and only the one with the highest average confidence is retained. This process compresses all repeated and less reliable paths in the same time scale. After compression, the chain set is obtained after redundancy stripping; the system then counts the actual length of time covered by each chain to measure the time continuity. In the same scale, the chain with the longest time continuity and that has passed the confidence gate is considered as the representative chain of the scale. In this way, the system has a set of representative chains across time granularities. Since the lengths of representative chains at different scales are not the same, the time continuity length is also compared within the set to select the longest one as the retained chain. The retained chain can represent the main trajectory of health dynamics because it has undergone three constraints of multi-scale selection, confidence sorting, and similarity redundancy stripping, which not only preserves the self-similar structure across scales, but also ensures the reliability of each node on the chain in the sense of observation, and maximizes the overall integrity of the trajectory with the principle of time continuity. It is this combination of fractal scaling and recursive stripping that enables the system to quickly lock the most representative and reliable continuous path in multiple time windows even when faced with a large number of candidate nodes with significant confidence label differences.

[0055] Further, the reserved chain bears the pivotal function of transitioning the global health predictor sequence to deep risk localization. The system initiates one recursive trajectory for each node on the reserved chain, and configures the trajectory with a search depth counter, a maximum search level Dmax, and an abnormal state triggering threshold Terr to ensure the search has sufficient depth and terminates within a controllable time. The recursive trajectory first performs forward recursion: the algorithm retrieves the direct successor node set of the current node in the timestamp increasing direction, and traverses in the order of decreasing node confidence label; when the first successor node with a confidence label not lower than the global average confidence label is encountered, it is immediately locked as the next recursive node. The principle of this is to let the trajectory always preferentially occupy the path with high confidence and large amount of information, and try to avoid falling into the low-trust noise area. The recursion depth is incremented by one with each node jump, and as long as Dmax has not been touched, the algorithm switches to the timestamp decreasing direction on the same trajectory to perform reverse recursion search. In the reverse phase, the system retrieves the direct predecessor node set, and selects the first eligible predecessor node as the next recursive node with the same confidence gating strategy. The alternation of forward and reverse makes the search trajectory zigzag forward on the time axis, and can capture both lagging feedback and advanced anomalies - which is particularly important for the common heart rate fluctuations or sudden blood pressure spikes in the elderly population.

[0056] After each forward or reverse state transition is completed, the system immediately triggers an abnormal state check: calculate the Euclidean distance between the new and old node state vectors, and if the distance exceeds the preset abnormal threshold, increment the abnormal count register of the current node by one. The Euclidean metric is independent of the covariance structure between nodes, and remains robust under non-Gaussian distribution; and accumulating anomalies in the form of counting rather than immediate decision-making takes advantage of the fact that health events often need to be observed for a long time to be diagnosed. The abnormal count register is maintained independently for each node, avoiding dilution of abnormal information between different recursive trajectories. When the recursion depth counter reaches Dmax, or there are no reachable nodes that meet the confidence gating conditions, the trajectory naturally converges at that node. After the search terminates, the system compares the abnormal count of each node on the reserved chain with Terr, and any node with a count greater than the threshold is mapped as a high-risk node. All high-risk nodes are collected into the same high-risk node set, providing direct input for subsequent multi-threshold interval mapping.

[0057] A minimal executable embodiment is given below, for the sake of brevity, only two health data collection nodes (HR1 and HR2) are demonstrated, and the heart rate signal of each node in one sampling period is shown. The other dimensions (systolic pressure, diastolic pressure, blood oxygen saturation, respiratory rate, body temperature, three-axis motion acceleration value, three-axis attitude angle value) can be processed in parallel according to the same process.

[0058] Uniform timestamp at the start of the sampling period Total number of sampling points , which lasts for 6 seconds. Sliding window length , so the column offset length .node Heart rate sampling sequence ;node Heart rate sampling sequence .

[0059] According to the formula ;

[0060] available .

[0061] Put two Hankel matrices are stacked in the subnode dimension to obtain a third-order tensor .

[0062] right Flatten along the child node dimension (mode-1) Matrix, singular value decomposition obtained . It is the principal component matrix extracted after performing high-order singular value decomposition (HOSVD) on the matrix obtained by expanding the tensor along the sub-node dimension (that is, the dimension corresponding to the health data acquisition node) when processing a high-order Hankel tensor. More specifically: the three dimensions of the third-order Hankel tensor are: sub-node dimension (representing different acquisition nodes, such as multiple sensors or devices); row offset dimension (representing the sampling offset within the sliding window); column offset dimension (representing the time position of the sliding window). In order to analyze the main change direction of the tensor in different directions, the system will unfold the tensor in these three dimensions respectively to obtain three matrices. Perform singular value decomposition on the matrix obtained after flattening the tensor in the sub-node dimension direction to obtain: ;in: (If there is subnodes); each column represents the principal component in the subnode dimension direction; the first column usually represents the most important direction of change in that dimension, which is used for subsequent quaternion construction and tensor rotation. The principal component matrix extracted along the sub-node dimension is an orthogonal basis representing the main change structure of health data between different acquisition nodes. It is used to construct the rotation alignment quaternion and complete the direction unification of the tensor in the potential manifold.

[0063] The row offset dimension (mode-2) is flattened to Matrix, singular value decomposition principal component first column The column offset dimension (mode-3) is flattened to Matrix, singular value decomposition principal component first column .

[0064] Each column of principal component vectors is regarded as a rotation axis and the rotation angle is denoted as ; is a unit rotation vector. For the first column is normalized to get the axis . The quaternion is obtained. For the first column is normalized to get the axis . For the first column is normalized to get the axis . .

[0065] Lie group average takes the geometric center under the "maximum variance constraint" ; numericalization gets ; ⊗ represents quaternion multiplication; ||⋅|| is the norm operator of quaternion.

[0066] The composite rotation operator is constructed in order to rotate the three-order Hankel tensor in multi-dimensional space, so as to complete the alignment of the local state tensor in the latent manifold coordinate system: ; convert into a rotation matrix . Multiply on the left and right of the matrix form of the tensor after the row mode-2 and column mode-3 offset, which is equivalent to rotating to the latent manifold coordinate system. In specific operation, the three-order Hankel tensor is unfolded into a matrix in the mode-2 (row offset dimension) and mode-3 (column offset dimension) directions, that is, the original tensor is "flattened" into a two-dimensional matrix along different dimensions, so that matrix multiplication can be applied. The left multiplication operation is to act on the row vectors of the row offset dimension unfolding matrix with the rotation matrix , which is equivalent to rotating and aligning the local time structure within each window; the right multiplication operation is to act on the column vectors of the column offset dimension unfolding matrix with the rotation matrix , which is equivalent to adjusting the overall direction between the time window sequences. Through the cooperation of left and right multiplication, the tensor completes the transformation from the original observation coordinate system to the latent manifold coordinate system in the spatial structure, so that the state tensors between different acquisition nodes and different time windows have comparability in the same geometric reference system.

[0067] Take the node as an example of the local state vector at the center of the first window after rotation: .

[0068] First-order difference Fractional order Truncation length Second-order difference

[0069] .

[0070] Let the previous two points be ;

[0071] .

[0072] Then .

[0073] Euclidean norm:

[0074] Repeat to A sequence of is obtained; after merging with the of node , an ascending order is arranged to obtain the difference intensity sorting queue . Larger indicates significant fluctuations.

[0075] The values of the two nodes at each timestamp are spliced into . Then use the moving average filter with length ; get the smoothed global health prediction factor sequence. Assume that the smoothed value at is . Initial activation domain: the root node down to three layers, a total of nodes. Multi-scale fractal unzipping scanning in scale set . After running, the remaining chain contains nodes. Perform alternating recursion on the remaining chain, set . In the second step of forward recursion, the state jump norm of node is . The abnormal count is incremented; the node accumulates abnormalities in the whole process , so it is mapped to a high-risk node. The final high-risk node set size is , falling into the second bin of the health judgment multi-threshold interval, and the system outputs "mild fluctuation" and generates the corresponding prompt.

[0076] In order to accurately map the discrete quantity "high-risk node set size" into an operational health assessment level, the system pre-stores a set of multi-threshold intervals ​;in The upper and lower boundaries of the interval are calibrated offline based on historical retrospective data, so that the sample size of cases falling into each level is approximately balanced. When the system is running, it first calculates the size of the high-risk node set. ; Then call the mapping function .in

[0077] , , , , , .because , we can conclude The system then generates a structured prompt message, the logical content of which includes: Current assessment level Triggering basis: High-risk node set size , located in the interval Node location: Topological index path of high-risk nodes, e.g. , and its timestamp Status summary: The node's cumulative abnormal count , the most recent abnormal Euclidean distance Recommended action: Continue routine monitoring, remind people to drink water and rest, and if the same abnormality occurs again within 12 hours, it will automatically be upgraded to . Messages are serialized into the following key-value format when transmitted over the network:

[0078] { "level": "Mild Fluctuation", "evidence": { "risk_node_count":1, "threshold_interval": "(0,2]"}, "nodes": [ { "path": [0,3,7], "timestamp": 4, "exceptions": 3, "last_distance": 3.21} ], "recommendation": "Maintain monitoring, pay attention to rest and hydration; if the same exception is triggered again within 12 hours, it will automatically be upgraded to a moderate warning."}

[0079] After receiving the JSON, the medical terminal decodes it into human-computer interface elements: the evaluation level is displayed as a yellow circle with a pop-up text "mild fluctuation", the abnormal node path is highlighted in the Kalman optimization tree visualization panel, and the heart rate curve segment corresponding to the timestamp is colored. The system also records the timestamp of this output. If the cumulative abnormal count of the same node exceeds the threshold again within the next twelve hours, it will jump directly to the interval And trigger "moderate warning"; otherwise, automatically clear the abnormal count register in the next natural day to avoid false alarm spread.

[0080] Figure 2 The tree topology in the Kalman optimization tree-based remote elderly health assessment state prediction system and its high-risk node identification results are demonstrated. The figure adopts a hierarchical tree structure, which is divided into four levels from top to bottom: root node layer, two layers of intermediate node layer, and leaf node layer. The root node is located at the top of the tree structure, serving as the control center of the entire Kalman optimization tree, responsible for setting the root node identifier of all health data acquisition nodes uniformly, and coordinating the global time synchronization mechanism. The second layer contains three intermediate nodes, corresponding to different health data acquisition areas or functional modules. These intermediate nodes undertake the key task of multi-dimensional health vector difference fusion processing, performing one-time allocation and mapping processing of health data sequences from lower-level nodes. The third layer also contains six intermediate nodes, further refining the granularity of data processing, ensuring that health data sequences within the same time period can be accurately mapped to the corresponding Kalman optimization tree leaf nodes.

[0081] The leaf node layer contains nine data acquisition terminals, directly responsible for collecting various physiological parameters of the elderly, including heart rate sample values, systolic pressure sample values, diastolic pressure sample values, blood oxygen saturation sample values, respiratory rate sample values, body temperature sample values, three-axis motion acceleration values, and three-axis attitude angle values. The distribution of high-risk nodes and normal-risk nodes is clearly identified in the figure through black and white contrast. The black-filled nodes represent high-risk nodes identified through recursive non-transparent transpose traversal, and the white-filled nodes represent normal-risk nodes. From the distribution results, it can be observed that high-risk nodes are mainly concentrated in the intermediate nodes of the second layer and specific positions in the third layer and leaf node layer. This distribution pattern reflects the potential health risk areas identified by the system during the execution of multi-scale fractal unzipping scanning and abnormal state checking processes.

[0082] Figure 3The time series variation of the global health predictor sequence generated by the global health predictor generation unit in consecutive sampling periods is presented. The horizontal axis represents the consecutive sampling periods from T1 to T8, and the vertical axis represents the numerical range of the predictor intensity from 0.0 to 1.0. The figure demonstrates the significant difference between the predictor sequence under normal and abnormal health conditions through comparative analysis. The data curve of the normal health condition presents a relatively stable fluctuation pattern, and the predictor intensity value mainly maintains at a low level of about 0.2, with a small change amplitude between each sampling period. This stability reflects the normal fluctuation range of physiological indicators in the daily life of healthy elderly people. After processing by the high-order Hankel tensor reconstructed by the fixed-length sliding window, the Euclidean norm of the double-layer difference vector set remains below the safety threshold. In contrast, the data curve of the abnormal health condition shows a clear upward trend, gradually rising from the initial 0.2 to a high-risk level close to 1.0. This increasing pattern indicates that the system successfully captures the deterioration process of the elderly's health condition. After the T3 sampling period, the abnormal state curve breaks through the abnormal detection threshold line of 0.4 and continues to rise, eventually reaching a dangerous level at T8. The abnormal detection threshold line in the figure is set at 0.4, serving as an important discriminant standard to distinguish between normal and abnormal health conditions. When the global health predictor sequence exceeds this threshold, the system will trigger further health risk assessment procedures. The alignment of the local state tensor in the latent manifold coordinate system completed by the quaternion operator performing complex rotation on the tensor along the order ensures the accuracy and reliability of the predictor sequence.

[0083] Figure 4The complex relationship between the preserved chain and various search paths in the execution of the recursive non-transparent transposition traversal process by the state prediction unit is elaborated in detail. The graph takes the time series as the horizontal coordinate axis and the search depth as the vertical coordinate axis, and constructs a two-dimensional analysis space to show the execution process and results of the traversal algorithm. The preserved chain path is represented by a thick solid line, which shows the representative chain with the maximum time continuity after multi-scale fractal unzipping scanning. This preserved chain starts from search depth 0 at time t0, and gradually increases the search depth while advancing forward along the time axis, and finally reaches search depth 7 at time t7. The selection of this path is based on the chain confidence vector calculation and similarity redundancy branch stripping processing at each scale in the fractal analysis scale set. The forward recursive path is represented by a short dashed line, which shows the search process of retrieving the direct successor node set in the increasing direction of the timestamp. This path traverses the successor nodes in descending order of node confidence labels, and selects the first successor node that satisfies the confidence label greater than or equal to the global average confidence label as the next recursive node. The reverse recursive path is represented by a long dashed line, which shows the reverse search mechanism of retrieving the direct predecessor node set in the decreasing direction of the timestamp. The key nodes in the graph are marked by a circle and the corresponding confidence label values are labeled. The normal risk nodes are represented by white filling, and the high risk nodes are represented by black filling. From the distribution of the confidence labels, it can be observed that the confidence label values corresponding to the high risk nodes are obviously lower, such as 0.45, 0.38 and 0.32, while the confidence label values of the normal risk nodes are relatively higher, such as 0.95, 0.88 and 0.85. Abnormal state transitions are specially marked by square boxes, which appear at nodes with low confidence labels, indicating abnormal situations detected by the system when performing forward or reverse recursive state transitions. When the Euclidean distance between the new and old node state vectors is greater than the preset abnormal threshold, the abnormal count of the corresponding node will increase, and finally when the abnormal count exceeds the abnormal state triggering threshold, the node is mapped to a high risk node and included in the high risk node set.

[0084] Although the specific embodiments of the present application are described above, those skilled in the art should understand that these specific embodiments are only illustrative, and those skilled in the art can make various omissions, substitutions and changes to the details of the above system without departing from the principles and essence of the present application. For example, the above method steps are combined, and substantially the same functions are performed in substantially the same way to achieve substantially the same results, which is within the scope of the present application. Therefore, the scope of the present application is only limited by the appended claims.

Claims

1. A remote geriatric health assessment state prediction system based on Kalman optimization tree, characterized in that, The system comprises a data acquisition and synchronization unit, a global health prediction factor generation unit and a state prediction unit; the data acquisition and synchronization unit is configured to uniformly set Kalman optimization tree root node identification for all health data acquisition nodes at a local end, and establish a corresponding synchronization time stamp buffer inside all health data acquisition nodes to ensure time sequence consistency of acquired health data sequences; the global health prediction factor generation unit is configured to perform one-time distribution on health data sequences sent by each health data acquisition node according to a Kalman optimization tree topology structure, and map health data sequences in the same time period to corresponding Kalman optimization tree leaf nodes; meanwhile, multi-dimensional health vector difference fusion processing is performed on each Kalman optimization tree intermediate node to obtain a global health prediction factor sequence; the state prediction unit is configured to trigger a round of recursive non-transparent transpose traversal at a Kalman optimization tree root node based on the global health prediction factor sequence, output a high-risk node set, and generate an old person health evaluation prediction result according to the position of the number of nodes in the high-risk node set in a preset health judgment multi-threshold interval. The process of generating the global health prediction factor sequence by the global health prediction factor generation unit comprises: each Kalman optimization tree intermediate node reads health data sequences of all direct child nodes of the intermediate node in the same sampling period in turn, and reconstructs high-order Hankel tensors based on a fixed-length sliding window to capture local time sequence correlation; the high-order Hankel tensors are rotated along orders by a quaternion operator to complete alignment of local state tensors in a latent manifold coordinate system; double-layer difference processing is performed on the rotated local state tensors in the latent manifold coordinate system: first, a first-order difference vector between spatial dimensions is calculated, and then fractional-order difference is performed on the difference vector sequence according to time dimensions to obtain a double-layer difference vector set; the Euclidean norm of the double-layer difference vector set is calculated, and a difference intensity sorting queue is generated in the order of increasing norm, and the sorting result is taken as a multi-dimensional health state estimation vector of the current intermediate node; according to the Kalman optimization tree topology structure, the multi-dimensional health state estimation vector of the current intermediate node is transmitted to a higher-level intermediate node or a root node; at the Kalman optimization tree root node, the multi-dimensional health state estimation vectors from all sub-trees are time-series spliced and mean filtered, and finally a global health prediction factor sequence covering the current sampling period is output.

2. The Kalman optimization tree based remote geriatric health assessment state prediction system as claimed in claim 1, wherein, The data acquisition and synchronization unit takes the clock source of the Kalman optimization tree root node as a reference clock, and sends a time synchronization marker signal to all health data acquisition nodes by periodic broadcasting or multicasting, wherein the time synchronization marker signal carries the reference clock; After each health data acquisition node receives the reference clock, the reference clock is extracted, and the local clock in the synchronization time stamp buffer is calibrated based on the reference clock to ensure that the local clock inside all health data acquisition nodes is consistent with the reference clock; The time stamp recorded in the calibrated synchronization time stamp buffer is taken as a unified time sequence basis.

3. The Kalman optimization tree based remote geriatric health assessment state prediction system as claimed in claim 1, wherein, The global health predictor generation unit reconstructs the high-order Hankel tensor based on the fixed-length sliding window on the same period data through the following process: setting the starting time and ending time of the current sampling period and the length of the sliding window; for each direct child node, obtaining the health data sequence arranged in time sequence in the sampling period; starting from the starting time of the sampling period, slidingly intercepting continuous subsequences of equal length with a step of one sampling point, so that the length of each subsequence is equal to the preset sliding window length; the sampling values in the same subsequence are sequentially filled into the Hankel matrix according to the sampling order, so that the row index of the Hankel matrix represents the sampling offset, and the column index represents the window number; stack the Hankel matrices corresponding to all direct child nodes according to the subnode number dimension to construct a three-order Hankel tensor containing the subnode dimension, the row offset dimension and the column offset dimension, thereby explicitly capturing the local time correlation.

4. The Kalman optimization tree based remote geriatric health assessment state prediction system as claimed in claim 3, wherein, The global health predictor generation unit performs a complex rotation on the tensor along the order through a quaternion operator on the high-order Hankel tensor through the following process: performing high-order singular value decomposition on the three-order Hankel tensor along the subnode dimension, the row offset dimension and the column offset dimension respectively, and extracting the corresponding principal component matrix; mapping each principal component matrix to the quaternion space to construct a set of quaternions representing the rotation axis and rotation angle information; obtaining the global alignment quaternion by solving the Lie group average value under the maximum variance constraint on the quaternion set; The global alignment quaternion is sequentially multiplied according to the order of the subnode dimension, the row offset dimension and the column offset dimension to generate a complex rotation operator, and the left multiplication and right multiplication transformation are performed on the three-order Hankel tensor to complete the alignment of the local state tensor in the latent manifold coordinate system.

5. The Kalman filter tree based remote geriatric health assessment state prediction system as claimed in claim 4, wherein, The health data sequence includes: a plurality of health data entries recorded in a synchronous time buffer and indexed by a uniform timestamp; each health data entry sequentially includes: a data acquisition node identifier for uniquely identifying the corresponding health data acquisition node; a time sequence offset corresponding to the uniform timestamp, used to represent the specific sampling position of the health data entry in the sampling period; a multi-dimensional health measurement vector including, in a predetermined order: a heart rate sampling value, a systolic pressure sampling value, a diastolic pressure sampling value, a blood oxygen saturation sampling value, a respiratory rate sampling value, a body temperature sampling value, a three-axis motion acceleration value, and a three-axis attitude angle value.

6. The Kalman optimization tree based remote geriatric health assessment state prediction system, as recited in claim 5, wherein, The state prediction unit comprises the following steps: based on the global health prediction factor sequence, a process of triggering a round of recursive non-transparent transpose traversal of the Kalman optimization tree root node comprises: selecting the Kalman optimization tree root node to the nearest three layers of nodes as an initial activation domain, and marking all nodes in the domain as a candidate node set; performing multi-scale fractal unzipping scanning in the candidate node set, and sequentially peeling off similar degree redundant branches in a decreasing order of node confidence labels, retaining a representative chain with maximum time continuity to obtain a retained chain; alternately performing forward recursion and backward recursion mixed search for each node of the retained chain until the search depth reaches a set level; in the process of backward recursion mixed search, triggering an abnormal state check for each state transition, and mapping nodes with a number of triggering times exceeding a threshold to high-risk nodes.

7. The Kalman optimization tree based remote geriatric health assessment state prediction system, as recited in claim 6, wherein, The specific process of obtaining the reserved chain includes: setting a set of fractal analysis scales wherein each scale corresponds to a time span window length of sampling periods; for scale , the candidate node set is continuously segmented according to node timestamps to obtain an initial chain set wherein each initial chain represents a sequence of nodes that are continuously reachable within a window length of ; a chain confidence vector is calculated for each initial chain , which is formed by concatenating the node confidence labels in the chain in chronological order; the chain confidence vector is subjected to cosine similarity calculation with other chain confidence vectors in the same scale to generate a chain similarity matrix; in the chain similarity matrix, if the similarity value of a chain pair is greater than a preset redundancy threshold, it is marked as a similarity redundancy branch; the initial chain set is traversed in descending order of chain average confidence , and other chains that form a similarity redundancy branch with the current chain are stripped off in the traversal process, and only the chain with the highest average confidence is retained, to obtain a chain set after redundancy stripping ; the time continuity length of each chain in the chain set is counted; under the same scale , the chain with the longest time continuity length is retained as the representative chain of the scale ; the above process is repeated until all scales are processed, to form a representative chain set ; in the representative chain set R, the time continuity length of each representative chain is recalculated, and the chain with the longest time continuity length is selected as the reserved chain; wherein is an integer index; is the number of scales in the set of fractal analysis scales.

8. The Kalman optimization tree based remote geriatric health assessment state prediction system, as recited in claim 7, wherein, The specific process of alternately performing forward recursion and backward recursion hybrid search for each node of the reserved chain comprises: initializing a search depth counter for each starting node in the reserved chain, and presetting a maximum search level and an abnormal state triggering threshold Performing a forward recursion step at the current node: retrieving a set of direct successor nodes of the node in the time stamp increasing direction, traversing the successor nodes in the order of decreasing node confidence label, and setting the first successor node satisfying the confidence label being greater than or equal to the global average confidence label as the next recursion node; updating the search depth counter, and if the current search depth has not reached , then performing a backward recursion step: retrieving a set of direct predecessor nodes of the current node in the time stamp decreasing direction, traversing the predecessor nodes in the order of decreasing node confidence label, and setting the first predecessor node satisfying the confidence label being greater than or equal to the global average confidence label as the next recursion node; after each forward or backward recursion state transition is completed, triggering an abnormal state check: calculating the Euclidean distance of the new and old node state vectors, and if the distance is greater than a preset abnormal threshold, then adding one to the abnormal count of the current node; maintaining an abnormal count register for each node in the reserved chain, for recording the cumulative number of abnormal state triggers; until the search depth counter reaches or there is no reachable node satisfying the confidence label condition; when the search process terminates, comparing the abnormal count of each node with , if the abnormal count is greater than , then mapping the node as a high-risk node, putting all high-risk nodes into a set, and obtaining a high-risk node set.

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