Radar task scheduling optimization solution method based on efficacy gradient approximation

Abstract

The invention relates to a radar task scheduling optimization solving method based on efficacy gradient approximation, which is based on a Q-RAM method and a current task demand, and comprises the following steps of: firstly, establishing a task model, and then constructing a task scheduling optimization objective function based on a multi-task efficacy by utilizing association mapping of task parameters and an efficacy function; establishing a task scheduling optimization model under the constraint of the total quantity of resources; a task scheduling model optimization solution problem is decomposed into two steps, task selection and optimization of partial task parameters are realized by using an efficacy gradient approximation method, dimension reduction and equivalent transformation are carried out on an efficacy function, optimization of residual task parameters is completed by using the efficacy gradient approximation method, and optimal scheduling of radar tasks is realized. Compared with other task scheduling solving methods, the method has the advantages that the calculation complexity and the solving speed are remarkably reduced, and rapid and efficient radar task scheduling optimization solving is realized.

Description

Technical Field

[0001] The present invention relates to the field of information technology, and in particular to a method for optimizing and solving radar task scheduling based on efficacy gradient approximation. Background Art

[0002] Radar resource management refers to optimizing the allocation of radar resources under the constraints of limited resources, so as to improve the efficiency and performance of the radar. Task scheduling is the core content of radar resource management, including task selection and task parameter optimization. During the detection process, the radar generates a task request list in real time based on mission requirements and detection targets. Task scheduling is to respond to task requests, select whether to execute the tasks in the requests, and optimize the parameters of the tasks to be executed (such as dwell time, execution time, etc.) to give full play to the radar performance as much as possible.

[0003] Most of the current research on task scheduling in radar resource management is based on task priorities, which are fixed reference indicators set by human experience. Even though various research results over the years have made the priority settings fine enough, it is still difficult to fully reflect the cognition of the dynamic target environment. In addition, the traditional radar resource management problem model generally uses the task loss cost as the optimization objective function, focusing on the lost tasks, but does not consider the different efficacies achieved by task execution. The Quality-of-Service based Radar Allocation and Management (Q-RAM) model provides a more accurate and effective method for radar resource management and task scheduling. On the one hand, it starts from the overall efficacy of tasks and takes the efficacy of task execution as the goal, which can more intuitively reflect the task scheduling effect; on the other hand, it integrates the experience-based task priorities into the quality-of-service function related to the environment and target state, which can more objectively reflect the task performance and improve the accuracy of task scheduling.

[0004] Task scheduling and optimization in the Q-RAM model is an NP-hard problem. To achieve task selection and task parameter optimization by solving the Q-RAM problem model, it is necessary to find the global optimal value of the mapping surface from the task parameters corresponding to resources to efficacy in the resource-efficacy (R-U) function of the task as the optimal task parameter selection, and use this to judge the acceptance or rejection of each task. However, due to the discreteness of task selection, the diversity of parameters, and the uncertainty of scheduling time, the R-U function is often not a convex function, and it is difficult to obtain the global optimal solution through convex optimization methods. The current solution methods generally use rule-based or heuristic algorithms to solve. However, the rule-based algorithms cannot flexibly optimize multi-dimensional task parameters, and it is difficult to achieve the optimal scheduling efficiency; the current heuristic algorithms mainly use the Earliest Start Time (EST) algorithm for tasks and its derivative methods. Such methods can obtain an approximate optimal solution of task parameters through iterative search, but they require complex calculations and consume a lot of time, making it difficult to be applied in practice. Summary of the Invention

[0005] To solve the NP-hard problem of optimizing the parameters of the existing radar task scheduling model based on Q-RAM, the present invention provides a method for optimizing the solution of radar task scheduling based on efficacy gradient approximation.

[0006] The specific content of the present invention is as follows: A method for optimizing the solution of radar task scheduling based on efficacy gradient approximation. Based on the Q-RAM method and the current task requirements, first establish a task model, and then use the correlation mapping between task parameters and the efficacy function to construct an optimization objective function for task scheduling based on multi-task efficacy, and establish a task scheduling optimization model under the constraint of the total resource amount; decompose the problem of optimizing the solution of the task scheduling model into two steps. First, use the efficacy gradient approximation method to realize the optimization of task selection and some task parameters. Finally, reduce the dimension of the efficacy function and perform an equivalent transformation, and use the efficacy gradient approximation method to complete the optimization of the remaining task parameters to achieve the optimal scheduling of radar tasks.

[0007] Furthermore, it includes: S1, Task model construction: Construct a complete task model according to the radar detection mission requirements and functions; S2, Q-RAM task scheduling model construction: According to the input task request list, establish an R-U function associated with task parameters, and combine the R-U function, the total resource constraint, and the global efficacy maximization objective to construct a radar task scheduling model based on Q-RAM; S3, Calculation of the gradient of the task efficacy function: Project the R-U functions of the search tasks and non-search tasks into the dwell time-efficacy space to obtain the dwell time-efficacy function; use the ratio of the dwell time of the search tasks to the pulse repetition interval of the non-search tasks to normalize the gradient units of the two types of task efficacies; based on the normalized gradient units, calculate the gradient values of the efficacies of the search tasks and non-search tasks corresponding to each discrete dwell time. S4, Dwell time optimization based on task gradient approximation: Add the efficacy of the non-search tasks and the gradient of the efficacy of the search tasks, and take the absolute value of the result. Retrieve the discrete point closest to 0 in this gradient sum vector, which is the point where the gradients of the two types of task efficacy functions are most approximated. Use the dwell time value corresponding to this point as the optimal choice for the dwell time of the non-search tasks. S5, Search task selection: Calculate its total required and time resources based on the optimal choice of the dwell time of the non-search tasks. Combine the total time resources of the scheduling tasks to calculate the remaining available time resources for the search tasks. According to the fixed dwell time value of the search tasks, calculate the maximum number of search tasks that can be selected. S6. Optimization and solution of task execution time: Substitute the determined non-search task residence time and task selection into the total task R-U function to obtain the execution time-power function. Use the linear mapping of independent variables to perform equivalent transformation on this execution time-power function, simplify its type based on the characteristics of the new independent variables, and obtain the approximate optimal solution of the new independent variables through convex optimization method after simplification. Then, obtain the corresponding optimal task execution time through linear transformation to complete the solution of the radar task scheduling problem based on Q-RAM.

[0008] Further, in S1, model the task type, azimuth, distance, execution time, pulse repetition interval, residence time, and waveform parameters, and construct the following complete task model: , where, Tp is the task type, Az is the execution azimuth of the task, Pt is the execution pitch of the task, Rg is the scanning distance, dwellT is the task residence time, timeExt ∈ WT, timeExt is the task execution time, and wf is the task waveform; the task scheduling time window WT = [timeEly, timeLast], where timeEly and timeLast are the earliest and latest times when the task can be executed, respectively.

[0009] Further, in S2, the Q-RAM task scheduling model is constructed as follows: , where, U(v) is the total radar power in this time period, which is obtained by summing the powers u list of all tasks T k in the task request list T k , k is the task request serial number k ∈ [1, K]; v = {v1, v2 ……, v N}, representing the entire set of parameters to be optimized in the task request list T list , N is the total number of parameters to be optimized; v k ∈ v represents the parameter to be optimized for task T k , that is, the independent variable in this scheduling model. Let v k = [dwellT k , timeExp k , and the remaining parameters in T k are determined quantities; e k is the environment of the execution azimuth of T k , which affects the value of the power u k , and take e k = 1; r k is the resource requirement of the task, which is determined by the task parameters; q k represents the quality of service corresponding to task T k , which is determined by the task resource requirement rk with the environment e k Joint decision; u k is obtained after normalizing the quality of service, and its value is defined as a real number in the range of [0, 1]; w k is the importance weight of the task, which is an arbitrary positive real number, and its value is determined by the radar detection mission requirements and the task type; u k (q k (r k (v k ), e k )) represents the multi-level mapping function of task parameters to environment-resource-service quality-task efficacy; R represents the total amount of radar resources during this time period.

[0010] Furthermore, in S3, the calculation of the task efficacy function gradient includes: Project the R-U functions of all tasks into the dwell time-efficacy space to construct the following two R-U functions: , where U F and U S are the non-search dwell time-non-search task efficacy and non-search dwell time-search task efficacy functions respectively; in the formula, the quantities of "~" and "∧" respectively represent the corresponding variables or mappings of non-search tasks and search tasks; dwellT F represents the dwell time of non-search tasks, and K F is the total number of non-search task requests; is the resource amount corresponding to the search task dwell time and is a fixed value; Ks(dwellT F ) represents the maximum number of search tasks that the remaining resources can accommodate under the condition of using the non-search task dwell time dwellT F : , where, The symbol represents rounding down; Unify the step size unit of the R-U function gradient, and calculate the ratio g r of the search task dwell time to the non-search task pulse repetition interval, and use g r times the non-search task pulse repetition interval as the unified gradient step size unit. The discrete gradient functions of the two R-U functions are: , where G F and G S are the gradients of the non-search task and search task R-U functions respectively; in the formula, U F ＇ and U S＇ respectively represent the derivatives of the non-search task and the search task R-U function with respect to the dwell time, dwellT F (k) represents the dwell time of the non-search task taking k times the pulse repetition interval of the non-search task. Let the maximum value of k here be k max , usually k max takes about four times of g r . The variable n is a positive integer and n ∈ [1, k max -g r +1]; through the above gradient function, calculate the gradients G max -g r +1 discrete dwell times dwellT F (n) of the non-search task and the search task R-U function F and G S .

[0011] Furthermore, in S4, the dwell time optimization based on task gradient approximation includes: Let G = |G F + G S | represent the absolute value of the sum of the gradient functions: , calculate the gradient vector of G(n) corresponding to k max -g r +1 discrete dwell times dwellT F (n) , and through search, find the dwell time corresponding to the value closest to 0 in FG , which is the optimal dwell time dwellT

[0012] Furthermore, in S5, the search task selection includes: Substitute the optimal dwell time of the non-search task and the total amount of resources into the formula for the maximum number of search tasks K S (dwellT F ) to obtain the optimal number of search tasks K SG as: , Sort all the search tasks in the task request list T list in descending order of the requested execution time, and select the first K SG search tasks to join the task queue to be executed. The search tasks outside K SG are added to the deferral list and will be added to the new task request list when a task request is generated in the next scheduling interval.

[0013] Furthermore, in S6, the optimization solution of the task execution time includes: Reduce the total mission R-U function to the mission execution time - efficacy space, substitute the determined non-search mission dwell time and mission selection into the total mission R-U function, and the mission execution time optimization model based on the mission execution time - efficacy function is obtained as follows: , where U E (timeExt) is the mission execution time - efficacy function, that is, the optimization objective of the above mission execution time optimization model, is the set of execution times of all missions.

[0014] Furthermore, if the radar is a fixed array, the mission execution time does not need to be optimized anymore; if the radar is a mechanical rotation plus electronic scanning, the mission execution time needs to be optimized, and the optimization method is as follows: For a certain mission T k with a fixed execution azimuth Az k , but its execution time timeExt k is linearly related to the array normal azimuth AzAn k AzAn k= α + β·timeExt k , where α is a certain fixed angle, β is the fixed array rotation angular velocity, and the deviation angle between the beam direction Az k and the array normal AzAn k is AzDelta k= AZ k -AzAn k , so the execution time timeExt k is also linearly related to the deviation angle AzDelta k , and the efficacy function of mission T k can be expressed as , where represents the mission efficacy when AzDelta k = 0, that is, the maximum mission efficacy; The original mission execution time optimization model is transformed into an optimization model based on the deviation angle - efficacy function: , Classified by search missions and non-search missions, the total efficacy function is expressed as: , , where AzF KN is the execution azimuth of the KNth non-search mission, K N ≤ K F , so the value of AzDelta p has at most K F types; Solve task T through convex optimization method k The corresponding optimal task execution azimuth and the set of deviation angles AzDelta between the array normal G , based on the above approximate optimal AzDelta G , through the linear transformation timeExt G =(Az - AzDelta G - α) / β, obtain the approximate optimal task execution time set timeExt G .

[0015] Based on the analysis of the radar task mechanism, the present invention decomposes the task selection and task parameter optimization problems coupled in the process of solving the scheduling problem into two steps: First, by searching for the position where the gradient of the resource - efficacy function of different types of tasks is closest approximated, an approximate optimal solution for some task parameters and task selection is achieved; then, when some task parameters and task selection are determined, an optimization model for the remaining task parameters to be optimized is constructed, and methods such as model equivalent transformation are used to reduce the model complexity, and the optimal solution of the remaining task parameters to be optimized is obtained through the convex optimization method. Compared with other task scheduling solution methods, this method significantly reduces the computational complexity and solution speed, and realizes the fast and efficient optimization solution of radar task scheduling. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The following further clarifies the specific embodiments of the present invention with reference to the accompanying drawings.

[0017] Figure 1 It is a schematic diagram for searching task parameters and efficacy functions Figure 2 It is a schematic diagram for non - searching task parameters and efficacy functions Figure 3 It is an example diagram of the non - searching task dwell time and the total task efficacy distribution Figure 4 It is an example diagram of the non - searching task dwell time and the total number of searching tasks distribution Figure 5 It is a schematic diagram of the approximation result of the non - searching task dwell time - efficacy function gradient and the searching task efficacy gradient Figure 6 It is a schematic diagram of the execution time - efficacy function of a single non - searching task Figure 7 It is a process diagram of the present invention Figure 8 It is an example diagram of task requests Figure 9 It is an example diagram of the task scheduling result using the method of the present invention DETAILED DESCRIPTION OF THE INVENTION

[0018] Combined with Figures 1 - 9, the present invention proposes an optimization solution method for radar task scheduling based on efficacy gradient approximation. Based on the Q-RAM method and current task requirements, a task model is first established, and then an objective function for task scheduling optimization based on multi-task efficacy is constructed by using the correlation mapping between task parameters and efficacy functions. A task scheduling optimization model is established under the constraint of total resource volume. Then, by analyzing the task scheduling mechanism, the problem of optimizing the solution of the task scheduling model is decomposed into two steps. First, the efficacy gradient approximation method is used to realize the optimization of task selection and some task parameters. Finally, the efficacy function is dimensionally reduced and equivalently transformed, and the remaining task parameters are optimized by using the efficacy gradient approximation method, so as to realize the optimal scheduling of radar tasks. Compared with the traditional heuristic Q-RAM model solution method, it does not require multiple iterations and searches. Instead, the optimization of task scheduling parameters and task selection are decoupled into two separately optimizable processes. First, the optimal task dwell time is calculated by approximating the efficacy gradients of different tasks, and then the task selection is completed. Then, using the optimized dwell time and task selection, the optimization model is dimensionally reduced, and then the dimension of the independent variable of the objective function is simplified through equivalent transformation. The optimal solution is obtained by the convex optimization method and transformed into the corresponding optimal task execution time, realizing the fast and accurate optimization solution of the radar Q-RAM model.

[0019] The implementation process of the present invention is as Figure 7 shown, and the specific implementation process is divided into 6 stages: task model construction, Q-RAM task scheduling model construction, task efficacy function gradient calculation, dwell time optimization based on task gradient approximation, search task selection, and task execution time optimization solution.

[0020] The specific implementation steps of the present invention are as follows:

[0021] According to the radar detection mission requirements and functions, model the task type, azimuth, distance, execution time, pulse repetition interval, dwell time, waveform parameters, etc., to form a complete task model as follows:

[0022] Among them, Tp is the task type, Az is the execution azimuth of the task, Pt is the execution pitch of the task, Rg is the scanning distance, dwellT is the task dwell time, timeExt is the task execution time, wf is the task waveform (usually a fixed waveform, determined by the task type Tp, so the present invention does not involve the content of waveform optimization); the task scheduling time window WT = [timeEly, timeLast], where timeEly and timeLast are the earliest and latest times when the task can be executed respectively, and timeExt ∈ WT.

[0023] When scheduling radar tasks, the tasks generated by the radar task request module include search, tracking, confirmation, loss-of-track capture, etc. Let the task request list within a certain task scheduling interval be T list ={T1, T2, ……, T k}, where K is the total number of task requests, and the task request list contains K tasks described by the above task model T. Assume that in a certain example scenario, the radar needs to perform resource scheduling and allocation for 2 non-search task requests and several search task requests within 0.5 s. The radar task requests for this scenario are as Figure 8 shown.

[0024] 2. Construction of the Q-RAM Task Scheduling Model Before constructing the task scheduling model, it is necessary to first determine the objects of each task scheduling according to the radar detection mission requirements, which generally include two categories: task selection and task parameters. The priority of non-search tasks is generally higher than that of search tasks. By default, all non-search tasks in the request list will be selected. Since the number of search task requests is generally large, task selection usually needs to be performed; the parameters of the tasks to be scheduled are mainly the dwell time and execution time. Among them, the dwell time of search tasks is generally fixed, and only the execution time needs to be scheduled. Therefore, the objects to be scheduled for search tasks are mainly task selection and the execution time of each task, and the objects to be scheduled for non-search tasks are mainly the dwell time and execution time of each task.

[0025] After clarifying the objects to be scheduled for tasks, the Q-RAM task scheduling model is constructed based on the task model as , , ,

[0026] where U(v) is the total radar efficiency during this time period, which is obtained by summing the efficiencies u list of all tasks T k in the task request list T k , k is the task request sequence number k ∈ [1, K]; v = {v1, v2, ……, v N}, representing the entire set of parameters to be optimized for the task request list T list , N is the total number of parameters to be optimized. Since tasks also need to be selected, the total number of parameters to be optimized N is an uncertain integer; v k ∈ v represents the parameter to be optimized for task T k , that is, the independent variable in this scheduling model. Let v k = [dwellT k , timeExp k , T kThe remaining parameters are determined values; e k is T k The environment of the execution orientation affects the efficacy u k The value of, generally takes a real number in the range of [0,1]. In this scenario, it is assumed to be an ideal environment, and e is taken k = 1; r k is the resource requirement of the task, determined by the task parameters; q k represents the task T k The corresponding quality of service, determined by the task resource requirement r k and the environment e k jointly determined. The definition dimensions of the quality of service for different types of tasks are different. For example, for a search task, the quality of service q k is the false alarm probability p fa = 10 -6 The effective detection distance at; for tasks such as confirmation and tracking, the quality of service q k is the target track accuracy, that is, the estimation accuracy of the azimuth of the tracked target track under the 3dB beam width of the radar; u k is obtained after normalizing the quality of service, used to uniformly analyze the effects of different tasks, and its value is defined as a real number in the range of [0,1]; w k is the importance weight of the task, which is an arbitrary positive real number, and its value is determined by the radar detection mission requirements and the task type. The weight of non-search tasks is generally greater than that of search tasks; u k (q k (r k (v k ), e k )) represents the multi-level mapping function of task parameters and environment-resource-quality of service-task efficacy; R represents the total radar resource in this time period.

[0027] In the above task scheduling model, the U(v) function is the R-U function of all tasks and also the optimization objective function for solving the task scheduling model; the meanings of the 3 constraint formulas are as follows: 1) The sum of the resources of each task shall not exceed the resource total limit; 2) The task execution time must be within the task time window; 3) The task dwell time does not overlap, that is, there are no multiple tasks executed simultaneously.

[0028] 3. Gradient calculation of task efficacy function Since the R-U function of all tasks is a non-convex function and is relatively complex, the global optimal solution cannot be obtained through convex optimization. Through the analysis of the internal relationship between the task R-U function and the parameters, the main reason for the discrete jump of the R-U function is the strong coupling of task selection and dwell time optimization in the solution process, while the coupling between task execution time and the former two is relatively weak. In addition, taking a typical non-search task as an example, the mapping curve of its execution time and its corresponding efficacy is as Figure 6As shown, its curve gradient is much smaller than the gradient that causes jumps in the dwell time (see Figure 3 ). Obviously, the dwell time has a stronger impact on the total task efficacy. Therefore, the optimization solution is carried out in the order of first dwell time and task selection, and then execution time.

[0029] The strong coupling between task selection and dwell time optimization is mainly reflected in that an increase in the dwell time of non-search tasks will preempt the total time resources available for search tasks, resulting in a discrete change in the total number of search tasks. Considering that the priority of non-search tasks is generally higher than that of search tasks, and the discrete granularity of the dwell time is finer, the dwell time of non-search tasks is optimized first.

[0030] The present invention adopts the method of gradient approximation of the efficacy function. First, project the R-U functions of all tasks into the dwell time-efficacy space to construct the following two R-U functions: , , where U F and U S are the non-search dwell time-non-search task efficacy and non-search dwell time-search task efficacy functions respectively. The corresponding function curves are as shown in Figure 5 Figures (a) and (b), where Figure 5 the actual efficacy curve in Figure (b) has jumps due to changes in the number of task selections; in the formula, the quantities with the tilde "~" and hat "∧" superscripts represent the corresponding variables or mappings of non-search tasks and search tasks respectively; dwellT F represents the dwell time of non-search tasks, and K F is the total number of non-search task requests; is the resource amount corresponding to the search task dwell time and is a fixed value; Ks(dwellT F ) represents the maximum number of search tasks that the remaining resources can accommodate under the condition of using the non-search task dwell time dwellT F : ,

[0031] where the symbol represents rounding down.

[0032] The independent variables of the above two R-U functions are both the non-search task dwell time dwellT F . However, due to the discrete jump of v, the step units of the gradients of the two R-U functions are inconsistent. Therefore, they need to be unified. Calculate the ratio g r (rounding down) of the search task dwell time to the non-search task pulse repetition interval, and use g rTaking the pulse repetition interval of the non-search task as the unified gradient step unit, the discrete gradient functions of the two R-U functions are as follows: , , where G F and G S are the gradients of the R-U functions for the non-search task and the search task respectively. The corresponding function curves are shown in Figure 5 Figures (c) and (d); in the formula, U F ＇ and U S ＇ represent the derivatives of the R-U functions for the non-search task and the search task with respect to the dwell time respectively. dwellT F (k) represents the dwell time of the non-search task taking k times the pulse repetition interval of the non-search task. Let the maximum value of k here be k max . Usually, k max takes about four times of g r . The variable n is a positive integer and n ∈ [1, k max -g r +1]; in the formula, through the summation operation of g r discrete derivatives, the calculation of the efficacy gradient with a unified step unit is realized, such as the calculation from the fitted efficacy curve in Figure 5 Figure (b) to the gradient curve with a unified step in Figure (d).

[0033] Through the above gradient functions, the gradients G max -g r +1 discrete dwell times dwellT F (n) of the R-U functions for the non-search task and the search task can be calculated, and the gradients G F and G S .

[0034] 4. Optimization of Dwell Time Based on Task Gradient Approximation Due to the constraint of the total resource amount, there is a negative correlation between the dwell time of the non-search task and the efficacies of the non-search task and the search task. That is, as the value of dwellT F increases, U F and U S increase and decrease respectively, as shown in Figure 5 Figures (a) and (b). The gradients G F and G S are positive and negative values respectively. It can be seen from Figure 5 Figures (c) and (d) that the value of G F gradually decreases to approach zero, while the value of G S remains basically constant. Obviously, as dwellT FAs the value increases, the total task efficiency U = U F +U S will first increase and then decrease overall (in fact, due to the discrete jumps of G S , the task efficiency fluctuates up and down within small intervals as shown in Figure 5 (d) where the original step size is as shown by the gradient curve, but after adopting a unified gradient step size, the gradient curve becomes smooth, so the sum of gradients is a smooth curve). The gradients G F and G S The dwell T F corresponding to the point where the absolute values are closest is the dwell T F corresponding to the global maximum total task efficiency.

[0035] Using the method of adding gradient functions and taking the absolute value, search for the point where the absolute values of gradients G F and G S are closest. Let G = |G F +G S | represent the absolute value of the sum of gradient functions: , The curve of the function G(n) is as shown in Figure 5 (e).

[0036] Calculate the gradient vector of G(n) corresponding to k max -g r +1 discrete dwell times dwell T F (n), and through simple search, find the dwell time corresponding to the value closest to 0 in , such as the abscissa value corresponding to the position marked by the green circle in (e), which is the optimal dwell time dwell T Figure 5 for the non-search task. FG .

[0037] 5. Search task selection Substitute the optimal dwell time of the non-search task and the total amount of resources into the formula for the maximum number of search tasks K S (dwell T F ), and the optimal number of search tasks K SG can be obtained as: , For all search tasks in the task request list T list , sort them in descending order of the requested execution time, and select the first K SG search tasks to add to the task queue to be executed. The search tasks outside K SG are added to the deferral list and will be added to the new task request list when new task requests are generated in the next scheduling interval.

[0038] According to the above method, the optimal search task selection can be achieved.

[0039] 6. Optimization and solution of task execution time When the task selection and the dwell time of non-search tasks are determined, the task scheduling problem only remains to optimize and solve the task execution time. First, reduce the total task R-U function to the task execution time - efficacy space: substitute the determined dwell time of non-search tasks and task selection into the total task R-U function, and the task execution time optimization model based on the task execution time - efficacy function is obtained as: , ,

[0040] where, U E (timeExt) is the task execution time - efficacy function, and it is also the optimization objective of the above task execution time optimization model. is the set of execution times of all tasks.

[0041] This optimization problem needs to be considered in two cases. The first case is that the radar has a fixed array surface, and the azimuth of the task beam is controlled by electronic scanning. In this case, the task execution time does not affect the angle between the task beam and the normal of the array surface, the task beam width is determined, and the task efficacy is also fixed. Therefore, the task execution time does not need to be optimized anymore, and it can be arranged in the order of execution time in the task request list. The second case is that the radar is mechanically rotated plus electronically scanned. The task execution time is linearly related to the azimuth of the array surface normal, and the angle between the azimuth of the task beam and the azimuth of the array surface normal determines the task beam width. The larger the angle, the wider the beam broadening, and the lower the task efficacy. In this case, the task execution time needs to be optimized.

[0042] For the above second case, the execution time - efficacy function curve of a single task is as Figure 6 shown. Obviously, this function is a convex function. Using the convex optimization method, the optimal task execution time corresponding to the maximum task efficacy can be directly found. For the multi-task case, the execution time - efficacy function U E (timeExt) is a convex function in the multi-dimensional space. Similarly, it can be solved by the convex optimization method, but the convex optimization process is more complicated due to more independent variables. Here, a simple method to obtain an approximate optimal solution is given.

[0043] For a task T k with a fixed execution azimuth Az k , but its execution time timeExt k is linearly related to the azimuth of the array surface normal AzAn k AzAn k=α + β·timeExt k where α is a certain fixed angle, β is the fixed angular velocity of the array surface rotation, and the beam direction Az k and the deviation angle between the array surface normal AzAn k is AzDelta k= AZ k - AzAn k Therefore, the execution time timeExt k is also linearly related to the deviation angle AzDelta k , and the efficacy function of task T k can be expressed as where represents the task efficacy when AzDelta k = 0, that is, the maximum task efficacy. Thus, the original task execution time optimization model can be transformed into an optimization model based on the deviation angle - efficacy function: , , , This is the equivalent transformation of the original model with AzDelta k as the independent variable, and the task execution time optimization problem becomes finding the deviation angles corresponding to the maximum total efficacy above.

[0044] Considering the radar task request generation mechanism, there is a request list for non - search tasks and search tasks respectively. The initial requested task execution time is arranged in order according to the task execution azimuth AZ k sequence and the dwell time, starting from the scheduling start time. For search tasks, the deviation angle AzDelta k0 corresponding to the timeExt k corresponding to its original task request time = 0. That is to say, if there are no non - search tasks, the original search task request is already the optimal solution for task scheduling. For non - search tasks, their original task request times are also arranged in order from the scheduling start time, but their execution azimuths are consistent with the target azimuths. Therefore, the original task request execution time does not meet the requirement of maximum efficacy. And according to Figure 6 the execution time with the maximum efficacy in it, it will occupy part of the search task execution time and delay it, resulting in a decrease in the overall task efficacy. Classified by search tasks and non - search tasks, the total efficacy function is expressed as: , ,

[0045] where AzF KN is the execution azimuth of the KN - th non - search task, K N ≤KF , so AzDelta p can have at most K F values.

[0046] Based on the above transformation, the number of independent variables AzDelta is reduced from K F + K SG to 2K F , greatly reducing the complexity. The optimal task execution azimuth and the set of deviation angles AzDelta F corresponding to task T can be solved by a simple convex optimization method. G . Note that the obtained AzDelta G at this time is an approximate optimal solution of the original deviation angle - efficacy function. This is because during the simplification process of the independent variable AzDelta, there may be a situation where the overall search task deviation angle is slightly larger due to angle discretization. However, through experiments, it is found that the probability of this situation is small (less than 5%), and the efficacy gap between the sub - optimal solution and the optimal solution is extremely small (less than 0.3). It can be considered to meet the requirements of optimization solution. Based on the above approximate optimal AzDelta G , through the linear transformation timeExt G =(Az - AzDelta G - α) / β, the approximate optimal set of task execution times timeExt G can be obtained. To visually display the effect of the present invention, an example of the optimal solution of the task execution time obtained by using the method of the present invention in the corresponding scenario is given, as shown in Figure 8 Figure 9 .

[0047] Integrating the above steps, the optimal solution of the radar task scheduling problem based on Q - RAM is realized, and the task selection and task parameter optimization of the task scheduling problem are completed.

[0048] ​The present invention solves the problem that it is difficult to define the objective function of the Q-RAM task scheduling model: Based on the Q-RAM radar task scheduling method, by examining the internal relationship between task parameters and efficacy, the task parameters, task model, and optimization objective in the Q-RAM radar task scheduling problem are clarified, and the mapping relationship between task parameters and resources is analyzed, thereby providing a basis for the construction of the R-U function and global optimization solution of the Q-RAM radar task scheduling. Solve the problem of difficult optimization selection of multiple tasks and multiple parameters with limited resources: Based on the task selection mechanism, the problem of difficult solution caused by the entanglement of the optimization of task parameters and task selection is decoupled into two steps. By applying the gradient approximation method of the efficacy function of different task types, the optimal solution of the task residence time is obtained, and then the task selection is supported. Based on the optimized residence time and task selection, the relatively complex task execution time optimization problem is simplified, and the approximate optimal solution of the radar task scheduling model is realized. Solve the problem of large computational complexity of the heuristic method for solving the Q-RAM model: Through the step-by-step and decoupling method of scheduling objects, the originally complex optimization solution process of the Q-RAM task scheduling model is simplified, greatly saving the computational complexity and time requirements of the task scheduling optimization solution, making the Q-RAM task scheduling model have practical application value.

[0049] Many specific details are set forth in the above description in order to provide a thorough understanding of the present invention. However, the above description is only a preferred embodiment of the present invention, and the present invention can be implemented in many other ways different from those described herein. Therefore, the present invention is not limited by the specific embodiments disclosed above. At the same time, any person skilled in the art can make many possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the scope of the technical solution of the present invention, or modify it into an equivalent embodiment with equivalent changes. All simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still fall within the scope of the protection of the technical solution of the present invention.

Claims

1. A radar task scheduling optimization solution method based on power gradient approximation, characterized by: Based on the Q-RAM method and current task requirements, the task model is first established. Then, the association mapping between task parameters and efficacy functions is used to construct the task scheduling optimization objective function based on multi-task efficacy, and a task scheduling optimization model is established under the constraint of total resource volume. The task scheduling model optimization problem is decomposed into two steps. First, the efficacy gradient approximation method is used to realize task selection and optimization of some task parameters. Finally, the efficacy function is reduced in dimension and transformed equivalently. The efficacy gradient approximation method is used to optimize the remaining task parameters and achieve the optimal scheduling of radar tasks.

2. The radar task scheduling optimization solution method based on power gradient approximation according to claim 1 is characterized by: include: S1, mission model construction: Build a complete mission model based on the radar detection mission requirements and functions; S2, Q-RAM task scheduling model construction: According to the input task request list, the RU function associated with the task parameters is established, and the radar task scheduling model based on Q-RAM is constructed by combining the RU function, total resource constraints, and the global efficiency maximization goal; S3, task efficacy function gradient calculation: project the RU functions of the search task and the non-search task into the residence time-efficacy space to obtain the residence time-efficacy function; The gradient units of the two types of task efficacy are normalized by using the ratio of the dwell time of the search task to the pulse repetition interval of the non-search task; based on the normalized gradient units, the gradient values ​​of the search task and non-search task efficacy corresponding to each discrete dwell time are calculated; S4, dwell time optimization based on task gradient approximation: add the non-search task efficacy and search task efficacy gradient, take the absolute value of the result, retrieve the discrete point closest to 0 in this gradient sum vector, which is the point where the gradient of the two types of task efficacy functions is closest, and use the dwell time value corresponding to this point as the optimal choice of the dwell time for the non-search task; S5, search task selection: calculate the total required and time resources based on the optimal choice of the residence time of the non-search task, calculate the remaining time resources available for the search task in combination with the total time resources of the scheduled task, and calculate the maximum number of search task selections based on the fixed value of the residence time of the search task; S6, task execution time optimization solution: Substitute the determined non-search task residence time and task selection into the total task RU function to obtain the execution time-efficiency function, and use the linear mapping of the independent variable to perform an equivalent transformation on this execution time-efficiency function. Based on the characteristics of the new independent variable, its type is simplified. After simplification, the approximate optimal solution of the new independent variable is obtained through the convex optimization method, and then the corresponding optimal task execution time is obtained through linear transformation to complete the solution of the radar task scheduling problem based on Q-RAM.

3. The radar task scheduling optimization solution method based on power gradient approximation according to claim 2 is characterized in that: In S1, the type, orientation, distance, execution time, pulse repetition interval, dwell time and waveform parameters of the task are modeled, and the complete task model is constructed as follows: ， Among them, Tp is the task type, Az is the task execution azimuth, Pt is the task execution pitch, Rg is the scanning distance, dwellT is the task residence time, timeExt∈WT, timeExt is the task execution time, wf is the task waveform; the task scheduling time window WT=[timeEly,timeLast], where timeEly and timeLast are the earliest time and latest time when the task can be executed respectively.

4. The radar task scheduling optimization solution method based on power gradient approximation according to claim 3 is characterized in that: In S2, the Q-RAM task scheduling model is constructed as follows: ， Among them, U(v) is the total radar efficiency in this time period, which is determined by the task request list T list All tasks in T k The efficacy of k The sum is obtained, k is the task request number k∈[1,K]; v={v1,v2……,v N }, indicating the task request list T list The total set of parameters to be optimized, N is the total number of parameters to be optimized; v k ∈v represents task T k The parameter to be optimized is the independent variable in this scheduling model. Let v k =[dwellT k ,timeExp k ], T k The remaining parameters in are determined quantities; k T k The environment of the execution location affects the performance k The value of e k =1; r k is the resource requirement of the task, which is determined by the task parameters; k Represents task T k The corresponding service quality is determined by the task resource requirement r k and the environment k Joint decision; k is obtained by normalizing the service quality, and its value is defined as a real number in the range of [0,1]; w k is the importance weight of the task, which is an arbitrary positive real number, and its value is determined by the radar detection mission requirements and task type; u k (q k (r k (v k ), e k )) represents the multi-level mapping function of mission parameters and environment-resources-service quality-mission effectiveness; R represents the total amount of radar resources in this time period.

5. The radar task scheduling optimization solution method based on power gradient approximation according to claim 4 is characterized in that: In S3, the task efficacy function gradient calculation includes: Project the RU functions of all tasks into the residence time-efficiency space and construct the following two RU functions: ， Among them, U F and U S are the non-search dwell time-non-search task efficacy and the non-search dwell time-search task efficacy functions, respectively; where the quantities "~" and "∧" represent the corresponding variables or mappings of the non-search task and the search task, respectively; dwellT F represents the residence time of non-search tasks, K F Total number of requests for non-search tasks; Ks(dwellT F ) indicates that the non-search task residence time dwellT F The maximum number of search tasks that the remaining resources can accommodate is: ， in, The symbol indicates rounding down; The step size unit of the RU function gradient is unified, and the ratio of the search task residence time to the non-search task pulse repetition interval g is calculated. r , in g r The non-search task pulse repetition interval is used as the unified gradient step unit, and the discrete gradient functions of the two RU functions are: ， Among them, G F and G S are the gradients of the RU functions of the non-search task and the search task respectively; where U F ＇ and U S ＇ They represent the derivatives of the RU function of the non-search task and the search task with respect to the dwell time, dwellT F (k) represents the non-search task dwell time which is k times the non-search task pulse repetition interval. Let the maximum value of k here be k max , usually k max Take g r is about four times of, the variable n is a positive integer and n∈[1,k max -g r +1]; through the above gradient function, calculate the RU function corresponding to the non-search task and the search task k max -g r +1 discrete dwell time dwellT F The gradient G of (n) F and G S .

6. The radar task scheduling optimization solution method based on power gradient approximation according to claim 5 is characterized by: In S4, the dwell time optimization based on task gradient approximation includes: Let G = |G F +G S | represents the absolute value of the sum of the gradient functions: , calculate G(n) corresponding to k max -g r +1 discrete dwell time dwellT F The gradient vector of (n) , by searching, find The dwell time corresponding to the value closest to 0 in is the optimal dwell time dwellT for non-search tasks. FG .

7. The radar task scheduling optimization solution method based on power gradient approximation according to claim 6 is characterized by: In S5, the search task selection includes: Substitute the optimal residence time and total resources of non-search tasks into the maximum number of search tasks K that can be accommodated by the remaining resources S (dwellT F ) formula, we get the optimal number of search tasks K SG for: ， Task request list T list All search tasks in the query are sorted from recent to long according to the execution time of the request, and the top K tasks are selected. SG Search tasks are added to the task queue to be executed and ranked in K SG The search tasks other than the ones in the previous one are added to the deferred list, and when the task request is generated in the next scheduling interval, they are added to the new task request list.

8. The radar task scheduling optimization solution method based on power gradient approximation according to claim 7 is characterized in that: In S6, the task execution time optimization solution includes: The total task RU function is reduced to the task execution time-efficacy space, and the determined non-search task residence time and task selection are substituted into the total task RU function. The task execution time optimization model based on the task execution time-efficacy function is obtained as follows: ， Among them, U E (timeExt) is the task execution time-efficiency function, that is, the optimization goal of the above task execution time optimization model. It is the execution time collection of all tasks.

9. The radar task scheduling optimization solution method based on power gradient approximation according to claim 8 is characterized in that: If the radar is a fixed array, the task execution time does not need to be optimized; if the radar is a mechanical rotating electric sweep, the task execution time needs to be optimized. The optimization method is: A task T k Execution direction Az k Fixed, but its execution time is timeExt k and the normal direction of the array AzAn k Linear correlation AzAn k= α+β·timeExt k , where α is a fixed angle, β is a fixed angular velocity of the array, and the beam direction Az k and the array normal AzAn k The deviation angle is AzDelta k= AZ k -AzAn k , so the execution time is timeExt k and deviation angle AzDelta k Also linearly related, task T k The power function can be expressed as ,in Represents AzDelta k =0 task efficiency, that is, the maximum task efficiency; The original task execution time optimization model is transformed into an optimization model based on the deviation angle-efficiency function: ， According to the distinction between search tasks and non-search tasks, the total efficacy function is expressed as: ， Among them, AzF KN is the execution position of the KNth non-search task, K N ≤K F , so AzDelta p The maximum value of F kind; Solve the task T by convex optimization method k The corresponding optimal mission execution azimuth and array normal deviation angle set AzDelta G , based on the above approximate optimal AzDelta G , through the linear transformation timeExt G =(Az-AzDelta G -α) / β, and obtain the approximately optimal task execution time set timeExt G .

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