A coastal search and rescue area estimation method based on time series trajectory regression

Abstract

The present application relates to the technical field of computer simulation, and discloses a kind of offshore search and rescue area estimation method based on time sequence trajectory regression, comprising: obtaining target position with sampling time and determining target prediction time, determining prediction node after last sampling time to target prediction time;Time sequence trajectory regression is carried out in order of sampling time to obtain regression position, and surface flow velocity is combined to obtain flow push position;Generate time zone by time zone, determine the water area range according to the coastline coordinates, intersect the water area range with the time zone by time zone and split into water area segments;From the water area segment where the last sampling time target position is located, the reachable segment is recursively calculated according to the non-empty geometric intersection, the reachable segments are merged, and the closed boundary of the search and rescue area is output.The present application is suitable for computer simulation generation and electronic chart display of offshore search and rescue area.

Description

Technical Field

[0001] This invention relates to the field of computer simulation technology, and more specifically, to a method for estimating nearshore search and rescue areas based on time-series trajectory regression. Background Technology

[0002] In nearshore search and rescue operations, the search area is largely generated based on existing location records of the missing target, marine observation or forecast data, and electronic nautical chart data. Location records provide the target's position and sampling time, marine observation or forecast data provides surface current velocity, and electronic nautical chart data provides shoreline coordinates. The search and rescue command system needs to input this data into a computer simulation processing flow to form a search and rescue area that can be displayed on electronic nautical charts or in a geographic information system.

[0003] In existing computational tasks, a common approach is to first estimate the subsequent trajectory based on the target location and sampling time, then combine this with surface current velocity to obtain candidate locations, and finally perform an overall envelope processing on these candidate locations to form a closed region for subsequent search. This method is convenient for quickly generating regions in open sea scenarios, but in scenarios near coastline bends, peninsulas, islands, reefs, or bay mouths, the overall envelope focuses more on the overall coverage of candidate locations, which can easily weaken the sequential relationship between adjacent time periods and make it difficult to distinguish different water areas separated by land.

[0004] In some operations, after the overall envelope is generated, land areas are removed by combining it with shoreline coordinates to reduce the number of areas that clearly fall into land areas. However, this processing occurs after the overall envelope has been generated, and it cannot recover the generation source of candidate locations in adjacent time periods, nor can it directly determine whether a certain water segment can be continuously reached from water segments in previous time periods. For scenarios with dense changes in nearshore land-sea boundaries, relying solely on the overall envelope and subsequent removal may still result in search and rescue areas that are inconsistent with the actual reachability of the water areas.

[0005] Therefore, in the computer simulation process, there is a need for a search and rescue area estimation method that can simultaneously utilize the target location, sampling time, surface current velocity, and shoreline coordinates. This method would preserve the order of adjacent time periods during the area generation process, divide the water area into segments within each time period, and then recursively infer reachable segments based on the non-empty geometric intersection between water segments in adjacent time periods. This would output a closed boundary of the search and rescue area that can be directly used for electronic nautical chart display. Summary of the Invention

[0006] This invention provides a method for estimating nearshore search and rescue areas based on time-series trajectory regression, which solves the technical problems mentioned in the background art.

[0007] To achieve the above-mentioned objectives, the present invention provides the following technical solution.

[0008] A method for estimating nearshore search and rescue areas based on time-series trajectory regression, executed by a computer, includes:

[0009] Obtain the target location with the sampling time and determine the target prediction time;

[0010] The prediction nodes are determined in chronological order from the last sampling time to the target prediction time, and include the prediction nodes corresponding to the target prediction time.

[0011] Perform temporal trajectory regression on the target location according to the sampling time sequence to obtain the regression position of the predicted node;

[0012] Obtain the surface velocity corresponding to the last sampling time and the prediction node, and obtain the flow push position corresponding to the target position and the regression position of the prediction node at the last sampling time based on the surface velocity.

[0013] Hourly slices are generated, where the hourly slice of the first time period is generated by the target position at the last sampling time, the streaming position corresponding to the target position, the regression position and streaming position of the adjacent prediction node, and the hourly slice of the subsequent time periods is generated by the regression position and streaming position of the two adjacent prediction nodes.

[0014] The water area is determined based on the shoreline coordinates. The intersection of the time-by-time zone and the water area is processed and then split into water area segments according to geometric connectivity.

[0015] Starting from the water segment where the target location is located at the last sampling time, according to the order of the predicted nodes, only the water segments that have a non-empty geometric intersection with the reachable segments of the previous time period are determined as reachable segments of the current time period;

[0016] Merge the reachable segments sequentially up to the last time period ending at the target prediction time, and output the closed boundary of the search and rescue area.

[0017] Compared with the prior art, the present invention has the following substantial features and significant progress:

[0018] This invention utilizes the target location, surface current velocity, and shoreline coordinates at sampling times to generate hourly zones in computer simulation processing. After dividing the water area into segments, reachable segments are recursively extrapolated, ensuring that the search and rescue area retains the sampling time sequence, surface current velocity displacement, and real shoreline constraints from the generation stage. Compared to methods that generate the total envelope all at once, the output closed boundary reduces instances of crossing land areas or unconnected waterways, facilitating direct display on electronic charts or geographic information systems, and enabling search and rescue command systems to determine subsequent search areas. Attached Figure Description

[0019] Figure 1 This is a diagram of the near-shore search and rescue area estimation calculation architecture of the present invention;

[0020] Figure 2 This is a flowchart of the near-shore search and rescue area estimation method of the present invention;

[0021] Figure 3 This is a comparative data chart of the present invention. Detailed Implementation

[0022] The following description is provided in conjunction with the accompanying drawings. It should be understood that the following embodiments are for illustrative purposes only and are not intended to limit the invention; those skilled in the art can make equivalent substitutions or combinations for the specific implementations.

[0023] like Figure 1 As shown, this invention relates to a method for estimating nearshore search and rescue areas based on time-series trajectory regression, executed by a computer, and belonging to the computer simulation processing of nearshore search and rescue area generation. This method takes the target location with sampling time, the target prediction time, surface current velocity, and shoreline coordinates as inputs, generates a search and rescue area under the same coordinate reference, and outputs it in the form of a closed boundary. Specifically, Figure 1 The computational architecture shown includes a target location acquisition module 111, a prediction node determination module 112, a time-series trajectory regression module 113, a flow-driven location generation module 114, a time-by-time strip generation module 115, a water area segment generation module 116, a reachable segment recursion module 117, and a search and rescue area output module 118.

[0024] Offshore search and rescue areas are influenced by coastline morphology. Peninsulas, bay mouths, islands, reefs, and coastline bends can separate adjacent locations into different water areas. Traditional methods tend to form a total envelope from candidate locations of multiple predicted nodes at once, resulting in an area that may span land regions and making it difficult to maintain the continuity of water areas between adjacent time periods. This method generates hourly strips according to the time period in which the predicted nodes are formed, and then recursively determines the final search and rescue area through water area segments and reachable segments.

[0025] like Figure 2 As shown, when the computer executes this method, it first obtains the target location and sampling time from the positioning record, and forms a target location sequence according to the sampling time order; then it determines the target prediction time and prediction node, and uses time-series trajectory regression to obtain the regression position of each prediction node; then it obtains the last sampling time and the surface flow velocity corresponding to each prediction node, converts it into spatial displacement and obtains the flow-driven position; then it sequentially generates time-by-time strips, water area segments and reachable segments, and outputs the closed boundary of the search and rescue area after merging the reachable segments.

[0026] like Figure 1 and Figure 2As shown, in step S211, the target location acquisition module 111 acquires the target location with the sampling time. The target location is the spatial location of the target at the sampling time, and the sampling time is the time when the target location is acquired. The computer obtains the one-to-one corresponding target location and sampling time from the positioning record, and arranges the target locations from earliest to latest according to the sampling time to form a target location sequence for time-series trajectory regression.

[0027] The sources of positioning records include search and rescue command systems, electronic chart systems, positioning terminals, or other existing positioning record storage systems. Each positioning record includes at least the target location and the sampling time. The target location is used for spatial geometric calculations, and the sampling time is used to determine the target location sequence, relative time, prediction step size, and prediction node. A one-to-one correspondence is maintained between the target location and the sampling time.

[0028] The target location can be represented as Where i is the sampling index of the target position in the target position sequence. The horizontal axis is... The vertical axis represents the sampling time. The target location sequence is arranged in ascending order of ti. The last sampling time after the sequence is the last sampling time, and the target location at the last sampling time is used as the starting point for determining the reachable segment in the first time period.

[0029] After sorting by sampling time, the computer saves the target location sequence. This sequence not only provides the location data needed for regression but also indicates the chronological order of each target location. This chronological order is used to establish a regression relationship between target locations and sampling times, and to generate prediction nodes in chronological order after the last sampling time.

[0030] The target location sequence can be stored in the computer as a record table or array. Each record includes a sampling number, sampling time, horizontal coordinate, and vertical coordinate. The sampling number only indicates the order, the sampling time retains the actual time, and the horizontal and vertical coordinates use the same unit of length based on the same coordinate system. Through this data organization method, time-series trajectory regression can directly read the horizontal and vertical coordinates and relative time, and the time-by-time strip generation process can also directly obtain the target location at the last sampling time.

[0031] When the target location is derived from latitude and longitude coordinates, the computer first unifies the coordinate references before generating a sequence of target locations. The same coordinate references are also used to obtain the shoreline coordinates and the location of the surface current velocity.

[0032] In step S212, the prediction node determination module 112 determines the target prediction time and determines prediction nodes arranged in chronological order from the last sampling time to the target prediction time, including those corresponding to the target prediction time. The target prediction time is the time corresponding to the search and rescue area that needs to be output. Prediction nodes are discrete time nodes between the last sampling time and the target prediction time, and adjacent prediction nodes or the last sampling time and adjacent prediction nodes form a time period.

[0033] The computer first converts the sampling times into a uniform time unit. The difference between adjacent sampling times is the time interval. During the calculation, the time intervals are arranged in ascending order of value; when the number of time intervals is odd, the median is taken as the middle item after sorting; when the number of time intervals is even, the median is taken as the arithmetic mean of the two middle items after sorting.

[0034] The prediction nodes are determined based on the last sampling time, the target prediction time, and the prediction step size. The computer starts calculations from the last sampling time, arranges prediction nodes sequentially according to the prediction step size, and lists the target prediction time as the last prediction node. Each time period records its start and end times and duration. The duration represents the actual time length within the prediction step size that participates in the calculation of the current time period; except for the time period containing the last prediction node, the duration is equal to the prediction step size; the duration of the time period containing the last prediction node is the actual time difference not exceeding the prediction step size.

[0035] The first time period begins with the last sampling time and ends at the first prediction node after the last sampling time. Subsequent time periods are determined by two adjacent prediction nodes. In this way, the target prediction time is always included in the prediction nodes, and when merging reachable segments, processing can continue up to the last time period ending at the target prediction time.

[0036] After the prediction nodes are generated, the computer saves the node sequence number, node time, previous node time, and time period duration for each prediction node. The node sequence number is used to determine the reading order, the node time is used to obtain the surface flow velocity value, and the time period duration is used to convert the surface flow velocity into spatial displacement. The last sampling time is used as a known sampling node and, together with the first prediction node, determines the boundary control position of the first time period.

[0037] The prediction step size is obtained from the median of the time intervals, and the target prediction time is still used as the prediction endpoint. The number of time intervals is determined by the last sampling time, the target prediction time, and the prediction step size. The computer builds subsequent time-series slices in the order of the time intervals, and each time-series slice corresponds to only one specific time interval.

[0038] In step S213, the temporal trajectory regression module 113 performs temporal trajectory regression on the target position according to the sampling time sequence to obtain the regression position of the predicted node. The temporal trajectory regression provides the corresponding regression position on the predicted node based on the relationship between the target position and the sampling time. The regression position provides the positional basis for subsequent generation of streaming positions and time-by-time slices.

[0039] Under the same coordinate system, the computer decomposes the target position into horizontal and vertical coordinates and converts the sampling time into relative time. The relative time τ is the value obtained by converting the time difference according to the selected time unit. When the prediction step size is used as the selected time unit, τ is the dimensionless value obtained by dividing the time difference between the sampling time and the baseline sampling time by the prediction step size. When other fixed time units are used, the horizontal and vertical coefficients are determined accordingly, ensuring that the regression output remains in coordinate units.

[0040] One specific implementation employs quadratic ordinary least squares regression. The computer determines the horizontal and vertical coefficients based on the horizontal and vertical coordinates and relative time in the target location sequence, establishing a regression relationship between the horizontal and vertical coordinates and relative time. The horizontal and vertical coefficients are calculated from the target location sequence, and their values ​​are derived from the target location and sampling time in the location record.

[0041] The horizontal and vertical coefficients can be solved using the existing ordinary least squares algorithm. The computer uses relative time as the independent variable and either the horizontal or vertical coordinate as the dependent variable, fitting the horizontal and vertical coordinate regression outputs respectively. The node time of the predicted node is first converted to relative time and then substituted into the regression relationship. The resulting horizontal and vertical coordinate regression outputs have the same coordinate units as the target location.

[0042] The regressed locations are used to form position points in subsequent geometric calculations. The computer continues to combine surface current velocities to generate current-driven locations, and then recursively calculates the search and rescue area through hourly strips, water area extent, and reachable segments. After this processing, the regression relationship provides a time trend, and the shoreline coordinates and water area extent provide nearshore land-sea constraints.

[0043]

[0044]

[0045] in, This represents the horizontal coordinate regression output corresponding to the relative time τ. This represents the longitudinal coordinate regression output corresponding to the relative time τ; , and The horizontal coefficient, , and This is the vertical coefficient.

[0046] Substituting the relative time corresponding to the predicted node into the above regression relationship yields the horizontal and vertical coordinate regression outputs of the predicted node, which together constitute the regression position of the predicted node. The target position at the last sampling time is used as a known starting point in the calculation of the first time period. The regression position of the predicted node is then used to generate the subsequent streaming positions and hourly strips for the corresponding predicted node.

[0047] In step S214, the flow propagation position generation module 114 obtains the surface flow velocity corresponding to the last sampling time and the prediction node, and obtains the flow propagation position corresponding to the target position at the last sampling time and the regression position of the prediction node based on the surface flow velocity. The surface flow velocity is the velocity data of the surface water body at the corresponding time and position, including velocity components in the lateral and longitudinal directions.

[0048] Surface velocity data includes data input given at each node and data obtained from an existing regular grid surface velocity field. When using a regular grid surface velocity field, the computer obtains the velocity field corresponding to the last sampling time or prediction node through linear interpolation over time, and then performs bilinear spatial interpolation based on the spatial location of the target or regression position to obtain the surface velocity corresponding to that time and location. For the last sampling time, the value location is the target position at the last sampling time; for prediction nodes, the value location is the regression position of the same prediction node.

[0049] The computer converts surface flow velocity into spatial displacement within a prediction step size according to the duration of the time period. The duration of the time period is the actual time length within the prediction step size that is involved in the calculation of the current time period; except for the time period of the last prediction node, the duration of the time period is equal to the prediction step size; the time period of the last prediction node is the actual time difference to the target prediction time that does not exceed the prediction step size.

[0050] The velocity component of the surface flow velocity is expressed in units of coordinate length per unit of time. After adopting the same time unit for the duration of each time period, the surface flow velocity is multiplied by the duration of the time period to obtain the spatial displacement components in the lateral and longitudinal directions. These spatial displacement components are superimposed on the regression position of the same prediction node to obtain the flow propagation position of that prediction node; for the last sampling time, they are superimposed on the target position at the last sampling time.

[0051] When surface velocity data is saved as node records, the record fields include node number, node time, value location, lateral velocity component, and longitudinal velocity component. The node number maps the surface velocity to the regression location of the same prediction node. After the flow propagation location is generated, the computer saves the pairing relationship between the regression location and the flow propagation location, which is directly used in subsequent hourly slices.

[0052]

[0053]

[0054] in, This represents the surface flow velocity corresponding to the k-th prediction node. This represents the duration of the k-th time period, which is the prediction step size or the actual time difference within the last time period of the target prediction time that does not exceed the prediction step size. This represents the spatial displacement corresponding to the surface flow velocity within the prediction step. This indicates the streaming position corresponding to the k-th prediction node. This represents the regression position of the k-th prediction node. For the last sampling time, the computer uses the target position at the last sampling time as the position affected by spatial displacement to obtain the corresponding flow position.

[0055] In step S215, the time-by-time strip generation module 115 generates time-by-time strips. Each time-by-time strip is a local candidate region corresponding to a time period. Each time-by-time strip is generated separately according to the time period, so that subsequent water segments and reachable segments remain consistent with the order of the predicted nodes.

[0056] The hourly slice of the first time period is generated from the target position at the last sampling time, the corresponding streaming position, the regression position of the adjacent prediction node, and the streaming position. The adjacent prediction node is the first prediction node after the last sampling time. The hourly slice of subsequent time periods is generated from the regression position and streaming position of two adjacent prediction nodes. Each subsequent time period uses the regression position and streaming position of the prediction node at the start and end of the time period.

[0057] The computer identifies the target position, regression position, and streaming position involved in generating the time-series slices within the same time period as boundary control positions, and performs convex hull processing on these boundary control positions to obtain the time-series slices. The boundary control positions for the first time period include the target position at the last sampling time, the corresponding streaming position, the regression position of the first prediction node, and the streaming position of the first prediction node. The boundary control positions for subsequent time periods include the regression positions of two adjacent prediction nodes and the streaming positions of two adjacent prediction nodes.

[0058] The convex hull processing is implemented using existing two-dimensional geometric algorithms. The input is the boundary control positions within the same time period, and the output is a closed polygon covering these boundary control positions. Hourly slices are generated separately for each time period to avoid the mixing of boundary control positions of non-adjacent prediction nodes across time periods.

[0059]

[0060]

[0061] in, This indicates the hourly strip of the first time period. This indicates the target location at the last sampling time. This indicates the stream push position corresponding to the target location. This indicates the regression position of the first predicted node. This indicates the position of the first predicted node in the flow push; This represents the hourly slice of the k-th time period. and This indicates the regression positions of two adjacent prediction nodes. and This indicates the flow propagation position of two adjacent prediction nodes. This indicates convex hull processing.

[0062] When expanding the time-series slices based on the maximum deviation, the computer first determines the positional difference between the target position at each sampling time and the regression position at the same sampling time as the positional deviation, and then determines the maximum value among the positional deviations as the maximum deviation. The expansion adopts the surface region buffering process in existing planar geometry, using the maximum deviation as the buffer distance, and expands the boundary of the time-series slices obtained by convex hull processing at equal intervals; the buffer connection adopts rounded corner connection, and the arc is discretized by eight line segments in every quarter circle. The closed surface region after the buffer surface region and the original time-series slice are merged is used as the time-series slice for that time period.

[0063]

[0064]

[0065] in, This represents the position deviation at the i-th sampling time. This represents the target position at the i-th sampling time. This represents the regression position at the same sampling time, and r represents the maximum deviation. and The subscript i represents the position under the same coordinate reference.

[0066] Each time-series slice is saved as closed surface region data, and its corresponding time period number is recorded. The time period number is used by the reachable segment recursion module to read the time-series slices according to the prediction node order. The boundary vertex order of the time-series slices is saved in the existing planar polygon data format for subsequent intersection processing.

[0067] In step S216, the water area segment generation module 116 determines the water area range based on the shoreline coordinates and performs intersection processing on the hourly zone slices and the water area range; the intersection result is split into water area segments according to geometric connectivity in step S217. The shoreline coordinates are coordinates describing the geometric position near the coastline, the calculation region is the region where spatial operations of the shoreline coordinates and the hourly zone slices are performed, the land region is the land portion enclosed by the shoreline coordinates within the calculation region, and the water area range is the portion of the calculation region excluding the land region.

[0068] The shoreline coordinates are arranged as a boundary point sequence according to the shoreline direction. Land areas are formed by closing this boundary point sequence with the boundary of the computational region using existing geographic information area construction methods. The shoreline coordinates corresponding to islands and reefs serve as independent closed boundaries to form land areas. Land areas with internal cavities are expressed using existing polygon inner ring methods. When the shoreline coordinates carry a land-side attribute, the computer determines the side of the land area according to this attribute; when the shoreline coordinates do not carry a land-side attribute, the computer determines the land area using the existing polygon convention of representing the outer boundary of the land area with clockwise point order and the inner boundary with counter-clockwise point order.

[0069] The computational domain covers the hourly time-series patches and the shoreline represented by the shoreline coordinates. The computer constructs a land region within the computational domain, and uses the area of ​​the computational domain minus the land region as the water boundary. After the water boundary is determined, each hourly time-series patch is intersected with the water boundary to obtain the intersection results of the hourly time-series patches within the water boundary.

[0070] Before shoreline coordinates are used in area construction, the computer transforms them to the same coordinate datum as the target location. Land areas, water areas, and time-series patches are all calculated as closed areas. Intersection processing uses area intersection operations from existing geographic information systems, outputting area data under the same coordinate datum. This area data is then split into water segments based on geometric connectivity.

[0071] The determination of the water area extent precedes the completion of the reachable segment recursion. After the water area extent is defined, the portions of the time-series slices located in land areas are excluded, and the remaining intersection results only correspond to the portions within the water area extent. At this point, the recursive object is transformed from the candidate space to the water area segments within the actual water area.

[0072]

[0073]

[0074] in, Indicates the calculation area. Indicates land area, Indicates the extent of a water area. This represents the hourly slice of the k-th time period. This represents the intersection result for the k-th time interval, with the intersection symbol indicating the intersection process.

[0075] In step S217, the water segment generation module 116 splits the intersection result into water segments according to geometric connectivity. Geometric connectivity is determined based on the connected components of the closed surface region; one connected component corresponds to one water segment. A water segment is represented as follows: , where k represents the time period number and j represents the water segment number within the same time period.

[0076] When the intersection result is divided into multiple unconnected water surface segments due to land area separation, the computer saves each water surface segment separately. These segments are used as the basis for recursively judging subsequent reachable segments. Each water surface segment corresponds to a continuous water surface area, and the computer checks each segment individually to determine if it has a non-empty geometric intersection with the reachable segments from the previous time period.

[0077] The water segment record includes a time period number, a water segment number, boundary vertices, and the order of the boundary vertices. The water segment number distinguishes different connected components only within the same time period. Using the time period number and the water segment number, the computer can associate each water segment with its source time-sequential slice and read them sequentially by time period during the recursive process.

[0078] In step S218, the reachable segment recursion module 117 starts from the water segment where the target location is located at the last sampling time, and determines only the water segments that have a non-empty geometric intersection with the reachable segments of the previous time period as reachable segments of the current time period, according to the order of prediction nodes. Reachable segments are water segments retained based on non-empty geometric intersection, which is the relationship between two water segments that have a common part in space.

[0079] The reachable segments for the first time period are determined by the water segment containing the target location at the last sampling time. The computer uses the containment relationship of closed regions to determine whether the target location is located within a water segment, and the boundary of the water segment belongs to that water segment. When multiple water segments contain the target location at the last sampling time, all multiple water segments are considered as the reachable segments for the first time period.

[0080] Starting from the second time period, the computer reads the water segments of the current time period in the order of prediction nodes and determines whether there is a non-empty geometric intersection between the water segments of the current time period and the reachable segments of the previous time period. A non-empty geometric intersection is defined as a non-empty intersection of closed surface regions; the common parts in point, line, or surface forms all satisfy this condition. If there are multiple water segments reachable from the previous time period, the judgment object is the union of the reachable segments from the previous time period.

[0081] If a water segment in the current time period satisfies a non-empty geometric intersection, the computer determines that water segment as a reachable segment for the current time period. If multiple water segments satisfy the condition in the same current time period, these multiple water segments together constitute a reachable segment for the current time period. The recursive process is executed sequentially by time period until the last time period ending at the target prediction time is reached.

[0082] The reachable fragment record inherits the boundary vertices and their order from the water segment, and increments by the time period number to which the reachable fragment belongs. When processing the current time period, the computer only reads reachable fragments from the previous time period for evaluation, without reading earlier water segments across time periods. This order ensures that the retention relationship of reachable fragments is consistent with the order of predicted nodes.

[0083]

[0084]

[0085] in, This represents the reachable segment of the first time period. This represents the j-th water segment within the first time period. Indicates the target position at the last sampling time; This represents the reachable segment in the k-th time period. Let represent the j-th water segment in the k-th time period, and is not equal to the empty set, which represents the non-empty geometric intersection. This represents the merged region of reachable segments from the previous time period. When the previous time period contains multiple reachable segments, the merged region is first formed by union in the above judgment and then participates in the intersection process.

[0086] The reachable segment recursion maintains the continuity of water areas in adjacent time periods. Water segments obtained by intersecting the time-by-time strip with the water area are included in the current time period's reachable segments only if they share a common portion with a reachable segment from the previous time period. This recursive chain starts from the water segment where the target location was located at the last sampling time and progresses sequentially along the prediction nodes towards the target prediction time.

[0087] In step S219, the search and rescue area output module 118 merges the reachable segments determined sequentially up to the last time period ending at the target prediction time, and outputs the closed boundary of the search and rescue area. The search and rescue area is the near-shore search and rescue area obtained after merging the reachable segments. The closed boundary is the closed polygonal boundary representing the search and rescue area. The boundary vertices are the vertices that constitute the closed boundary.

[0088] The computer performs a union operation on the reachable segments for each time period to obtain the search and rescue area. Reachable segments originate from water area segments, which are derived from the intersection of time-series strips and the water area; therefore, the search and rescue area lies within the water area. Reachable segments are obtained recursively according to the predicted node order, thus preserving the continuity of water areas between adjacent time periods.

[0089]

[0090] in, Indicates the search and rescue area. to This represents the reachable segments determined sequentially from the first time period to the last time period ending at the target prediction time, where m represents the number of time periods formed from the last sampling time to the target prediction time. This indicates merging reachable fragments.

[0091] The computer extracts the closed boundaries of the search and rescue area and outputs them according to the boundary vertices and their order. When the search and rescue area consists of multiple regions, each region outputs its corresponding closed boundary; when the search and rescue area has an inner boundary, the outer and inner boundaries are output according to their respective boundary vertex order. The boundary vertex sequence can reconstruct a closed polygon, enabling electronic chart systems or geographic information systems to read and display the search and rescue area. When outputting closed boundaries, the computer retains the same coordinate reference as the search and rescue area. For areas that need to be displayed in latitude and longitude coordinates, the boundary vertices are converted to latitude and longitude coordinates according to the aforementioned coordinate transformation relationship before being output. The output data includes at least the boundary vertices, the order of the boundary vertices, and the identifier of the search and rescue area to which the closed boundary belongs, enabling subsequent systems to directly draw the search and rescue area.

[0092] Example 1: The following are comparative implementation examples.

[0093] This use case is calculated in the same local plane coordinate system, with the coordinate unit being meters and the sampling time expressed in minutes. The comparative example uses a processing method that forms a total envelope by combining all future regression positions and all future flow positions at once. The embodiment uses the above method to generate hourly strips based on adjacent prediction nodes, limits the hourly strips to the water area to obtain water segment, and recursively extrapolates reachable segments starting from the water segment where the target position is located at the last sampling time.

[0094] The shared input data includes seven target locations and their corresponding sampling times: target location (220, 90) for sampling number 0, sampling time 0 minutes; target location (423, 280) for sampling number 1, sampling time 10 minutes; target location (662, 425) for sampling number 2, sampling time 20 minutes; target location (817, 650) for sampling number 3, sampling time 30 minutes; target location (1023, 840) for sampling number 40 minutes; target location (1145, 1115) for sampling number 50 minutes; and target location (1268, 1360) for sampling time 60 minutes. The seven target locations are arranged in ascending order of sampling time to form a target location sequence.

[0095] A quadratic ordinary least squares regression was performed with ten minutes as the relative time unit, where τ is a dimensionless value in ten minutes. The regression relationships of the horizontal and vertical axes relative to the relative time are as follows.

[0096]

[0097]

[0098] The regression positions corresponding to the seven sampling times are approximately (211.190, 99.286), (440.500, 258.929), (648.786, 438.929), (836.048, 639.286), (1002.286, 860.000), (1147.500, 1101.071), and (1271.690, 1362.500), respectively. The corresponding position deviations are approximately 12.800 meters, 27.391 meters, 19.200 meters, 21.854 meters, 28.794 meters, 14.151 meters, and 4.458 meters, respectively, with a maximum deviation of 28.793777672495107 meters. For the main text display, 28.794 meters is used. The time interval between historical sampling moments is 600 seconds, so the prediction step size is 600 seconds; the prediction duration is 3600 seconds, corresponding to six prediction steps.

[0099] The regression positions of the six prediction nodes are (1374.857, 1644.286), (1457.000, 1946.429), (1518.119, 2268.929), (1558.214, 2611.786), (1577.286, 2975.000), and (1575.333, 3358.571), respectively. The surface flow velocities at the last sampling time and the six prediction nodes are (0.20, 0.10) m / s, (0.18, 0.12) m / s, (0.16, 0.14) m / s, (0.14, 0.15) m / s, (0.12, 0.14) m / s, (0.10, 0.12) m / s, and (0.08, 0.10) m / s, respectively. The seven flow propagation positions obtained from the surface flow velocity and prediction step size are (1388.000, 1420.000), (1482.857, 1716.286), (1553.000, 2030.429), (1602.119, 2358.929), (1630.214, 2695.786), (1637.286, 3047.000), and (1623.333, 3418.571).

[0100] The demonstration geometry is represented using a computational region: the computational region extends horizontally from -500 meters to 4000 meters and vertically from -500 meters to 4500 meters; the main landmass extends horizontally from 2800 meters to 4000 meters and vertically covers the entire computational region; the rectangular peninsula extends horizontally from 1400 meters to 2800 meters and vertically from 1200 meters to 1800 meters. The water area is the remaining portion of the computational region after deducting the main landmass and the rectangular peninsula.

[0101] In the comparative example, the computer obtains the regression positions of six predicted nodes based on the same target location sequence and the same regression relationship, and obtains the flow propagation positions of the six predicted nodes based on the surface flow velocities corresponding to the six predicted nodes. The comparative example uses all future regression positions and all future flow propagation positions as candidate positions to form a total envelope, and uses this total envelope as the search and rescue area for the existing scheme. The search and rescue area for the existing scheme is approximately 304,881.842 square meters. Overlaying this output with the demonstration land shows an overlap area of ​​approximately 16,029.084 square meters.

[0102] The implementation uses the same target location sequence, the same prediction step size, the same prediction duration, the same regression relationship, the same surface flow velocity, and the same water area. The hourly strip for the first time period is generated from the target location (1268, 1360) at the last sampling time, the corresponding current propagation location (1388.000, 1420.000), the regression location (1374.857, 1644.286) of the first prediction node, and the current propagation location (1482.857, 1716.286) of the first prediction node. The subsequent five time periods are generated from the regression location and current propagation location of two adjacent prediction nodes, respectively.

[0103] After intersecting the hourly segments with the water area for each time period, the water area retained in time period 0 is approximately 33373.512 square meters; the water area retained in time period 1 is approximately 37757.050 square meters, overlapping with the previous time period by approximately 3040.487 square meters; the overlap between time period 2 and the previous time period is approximately 9946.491 square meters; the overlap between time period 3 and the previous time period is approximately 9690.224 square meters; the overlap between time period 4 and the previous time period is approximately 8971.668 square meters; and the overlap between time period 5 and the previous time period is approximately 7997.756 square meters. The water segment in time period 0 contains the target location at the last sampling time and is determined as the reachable segment in time period 1; the water segments in time periods 1 to 5 all have non-empty geometric intersections with the reachable segments of the previous time period and are thus determined as reachable segments in sequence.

[0104] The embodiment merges the reachable segments from six time periods to obtain the search and rescue area of ​​this scheme, which is approximately 239,168.171 square meters. Since each hourly segment is confined to a water area before entering the reachable segment recursion, the overlap area between the search and rescue area of ​​this scheme and the demonstration land is 0 square meters. This area comparison shows that when generating the search and rescue area recursively based on hourly segments, water segments, and reachable segments, the output closed boundary can reduce the occurrence of crossing land areas or non-connected water areas.

[0105] Table 1: Comparison Data Table

[0106] Existing solutions 304,881.842 square meters 16029.084 square meters All future regression positions and all future flow positions are combined into a total envelope at once. This plan 239,168.171 square meters 0 square meters Hourly strips are generated based on adjacent prediction nodes, and reachable segments are recursively extrapolated after being limited to a water area.

[0107] like Figure 3 As shown in Table 1, under the same target location, sampling time, target prediction time, prediction step size, surface flow velocity, and demonstration geometry, the search and rescue area of ​​the existing scheme is approximately 304,881.842 square meters, while the search and rescue area of ​​this scheme is approximately 239,168.171 square meters. The difference in area is approximately 65,713.671 square meters, representing a net reduction of approximately 21.554% in search and rescue area compared to the existing scheme.

[0108] Although embodiments of this application have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of this application, and all such modifications and variations fall within the scope defined by the appended claims.

Claims

1. A method for estimating nearshore search and rescue areas based on time-series trajectory regression, executed by a computer, characterized in that, include: Obtain the target location with the sampling time and determine the target prediction time; The prediction nodes are determined in chronological order from the last sampling time to the target prediction time, and include the prediction nodes corresponding to the target prediction time. Perform temporal trajectory regression on the target location according to the sampling time sequence to obtain the regression position of the predicted node; Obtain the surface velocity corresponding to the last sampling time and the prediction node, and obtain the flow push position corresponding to the target position and the regression position of the prediction node at the last sampling time based on the surface velocity. Hourly slices are generated, where the hourly slice of the first time period is generated by the target position at the last sampling time, the streaming position corresponding to the target position, the regression position and streaming position of the adjacent prediction node, and the hourly slice of the subsequent time periods is generated by the regression position and streaming position of the two adjacent prediction nodes. The water area is determined based on the shoreline coordinates. The intersection of the time-by-time zone and the water area is processed and then split into water area segments according to geometric connectivity. Starting from the water segment where the target location is located at the last sampling time, according to the order of the predicted nodes, only the water segments that have a non-empty geometric intersection with the reachable segments of the previous time period are determined as reachable segments of the current time period; Merge the reachable segments sequentially up to the last time period ending at the target prediction time, and output the closed boundary of the search and rescue area.

2. The method for estimating nearshore search and rescue areas based on time-series trajectory regression according to claim 1, characterized in that, The process of obtaining the target location with the sampling time includes obtaining the one-to-one corresponding target location and sampling time from the positioning record, and arranging the target locations from early to late according to the sampling time to form a target location sequence for time-series trajectory regression.

3. The method for estimating nearshore search and rescue areas based on time-series trajectory regression according to claim 1, characterized in that, The time-series trajectory regression includes decomposing the target position into horizontal and vertical coordinates under the same coordinate reference, converting the sampling time into relative time, and establishing regression relationships between the horizontal and vertical coordinates and relative time based on the change of the target position with the sampling time, so as to obtain the regression position at the prediction node.

4. The method for estimating nearshore search and rescue areas based on time-series trajectory regression according to claim 1, characterized in that, The prediction node is determined based on the last sampling time, the target prediction time, and the prediction step size, which is determined based on the median of the time interval between adjacent sampling times.

5. The method for estimating nearshore search and rescue areas based on time-series trajectory regression according to claim 1, characterized in that, The flow propagation position is obtained by converting the surface flow velocity into spatial displacement within the prediction step and applying the spatial displacement to the regression position of the same prediction node.

6. The method for estimating nearshore search and rescue areas based on time-series trajectory regression according to claim 1, characterized in that, The time-by-time strip is obtained by performing convex hull processing on the boundary control positions of the same time period. The boundary control positions are composed of the target position, regression position, and flow push position that participate in the generation of the time-by-time strip in the same time period.

7. The method for estimating nearshore search and rescue areas based on time-series trajectory regression according to claim 6, characterized in that, The time-by-time strip is expanded outward based on the maximum deviation. The positional difference between the target position at each sampling time and the regression position at the same sampling time is determined as the positional deviation, and the maximum value among the positional deviations is determined as the maximum deviation.

8. The method for estimating nearshore search and rescue areas based on time-series trajectory regression according to claim 1, characterized in that, The water area is defined by delineating the land area by shoreline coordinates within a calculation area that covers the hourly strip and the shoreline represented by the shoreline coordinates, and the part of the calculation area other than the land area is defined as the water area. The water area segment is obtained by splitting the intersection results of the time-sequential strip and the water area according to geometric connectivity.

9. The method for estimating nearshore search and rescue areas based on time-series trajectory regression according to claim 1, characterized in that, The closed boundary is output in the order of boundary vertices.

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