A Multi-Sensor Layout Method and Device Based on Gaussian Process

Abstract

The present invention relates to the technical field of sensor layout, and particularly to a multi-sensor layout method and device based on Gaussian process. The method includes: S1. Modeling the monitoring situation of sensors using a univariate sensor spatio-temporal model based on Gaussian process; S2. Transitioning the univariate sensor model to the multi-variable sensor situation to obtain a multi-variable sensor spatio-temporal model; S3. Constructing and simplifying a multi-sensor layout objective function based on the multi-variable sensor spatio-temporal model; S4. Further simplifying the multi-sensor layout objective function using a spatio-temporally separable covariance function; S5. Solving the simplified multi-sensor layout objective function using a greedy algorithm to obtain the optimal sensor layout. The present invention can effectively optimize the multi-sensor layout, has the best prediction effect on unmonitored positions, requires fewer sensors, and significantly reduces the calculation time required to obtain the layout result.

Description

Technical Field

[0001] The present invention relates to the technical field of sensor layout, and particularly to a multi-sensor layout method and device based on Gaussian process. Background Art

[0002] Sensor networks are playing an increasingly important role in environmental monitoring, such as exploring ecosystem changes in the ocean and on land, monitoring air quality and pollution, monitoring forest fires, monitoring the indoor environment, etc. As is well known, the denser the deployment of sensor nodes, the more comprehensively the sensor network can perceive the entire target area. However, when too many sensors are deployed at the monitoring locations, these sensors will generate similar data samples, resulting in a large amount of redundancy in the measured data. During long-term monitoring, the excessive number of sensors and redundant measurements will bring many problems to the sensor network, such as high installation and maintenance costs, high energy consumption, and will greatly increase the complexity of data analysis and the computing cost. Therefore, how to layout a smaller number of sensors at appropriate nodes to efficiently monitor the target area and collect effective information is a major goal in sensor research. Summary of the Invention

[0003] The present invention provides a multi-sensor layout method and device based on Gaussian process. The technical solution is as follows:

[0004] On the one hand, a multi-sensor layout method based on Gaussian process is provided. This method is implemented by an electronic device and includes:

[0005] S1. Based on Gaussian process, use a univariate sensor spatio-temporal model to model the sensor monitoring situation;

[0006] S2. Transition the univariate sensor model to the multivariate sensor situation to obtain a multivariate sensor spatio-temporal model;

[0007] S3. Based on the multivariate sensor spatio-temporal model, construct and simplify the multi-sensor layout objective function;

[0008] S4. Use a spatio-temporally separable covariance function to further simplify the multi-sensor layout objective function;

[0009] S5. Use a greedy algorithm to solve the simplified multi-sensor layout objective function to obtain the optimal sensor layout.

[0010] Optionally, the S1 specifically includes:

[0011] Let g be the number of all candidate positions of sensors in the target area, n be the number of positions of deployed sensors, and N be the number of positions of un-deployed sensors, where g = n + N; assume that there are n sensors of the same type located at positions The time when the sensor makes a measurement is defined as The measurement values collected by the sensor at all times are where represents the measurement values at all positions at time t u and represents the measurement value at time t u and position s p ;

[0012] A univariate sensor spatio-temporal model is used to model the sensor monitoring situation:

[0013] Y t,s = X t,s β + W t,s + ε t,s (1-1)

[0014] In Equation (1-1): Y t,s is the measurement value of the sensor; X t,s is the reference covariate; β is the coefficient of the covariate; W t,s is a latent random variable modeled by a zero-mean Gaussian process; ε t,s is an independent and uniformly distributed noise that follows a normal distribution with zero mean and variance τ 2 .

[0015] Optionally, the S2 specifically includes:

[0016] Suppose there are k different types of sensors monitoring k different variables, and there are n sensors of each type. All types of sensors are embedded on the same board, and different types of sensors are located at the same position s. The collected measurement values are expressed as:

[0017] Y t,s = X t,s β + W t,s + ε t,s (1-2)

[0018] In Equation (1-2): represents the measurement values of k types of sensors at time t and position s, where is the measurement value of the i-th type of sensor, and Y t,s follows a multivariate Gaussian distribution MGD, Y t,s ~ MGD(μ, Σ), μ = E(Y t,s ) is the mean, and Σ is the multivariate covariance matrix, expressed as:

[0019]

[0020]

[0021]

[0022] The covariance matrix represents the correlation of the observed values in time and space; where represents the coefficient corresponding to the i-th covariate; the covariate matrix X t,s is expressed as:

[0023]

[0024] where: represents the covariate value corresponding to the i-th variable;

[0025] W t,s is a process vector, modeled by a multi-variate Gaussian process MVGP, W t,s ~MVGP(0, Ψ), with a mean of 0, and the covariance matrix Ψ is expressed as:

[0026]

[0027] In Equation (1-7): I is the identity matrix; represents the variance of the i-th variable; ε t,s ~N(0, τ 2 ) is the measurement error defined by Gaussian white noise.

[0028] Optionally, the S3 specifically includes:

[0029] Let respectively represent the positions and times in space and time that are not monitored and need to be predicted using the monitoring data of existing sensors. Generally, the number of positions to be predicted is much larger than the number of observed positions, N >> n. Let represent the latent random process of the required prediction time and position, which has a joint distribution with the observed value Y t,s Since Y t,s follows a multi-variate Gaussian distribution, from the multi-variate Gaussian marginal distribution, we get:

[0030]

[0031] In Equation (1-8): μ and Σ are respectively the mean and covariance matrix of Y t,s ; μ Z and are respectively the mean vector and covariance matrix of ; is the cross-covariance matrix representing the correlation between Y t,s and . According to Equation (1-8), given the observed value Y t,s , it is deduced that The conditional distribution is shown in Equation (1-9):

[0032]

[0033] Wherein:

[0034]

[0035]

[0036] The key to sensor layout optimization lies in being able to minimize the prediction error at unmonitored positions. It can be deduced from Equation (1-9) that, given the observed value Y t,s under the condition, the prediction uncertainty at the unobserved position time (t M , s N ) is related to the covariance matrix . Equation (1-11) shows that the diagonal elements of the covariance matrix represent the prediction variance values. Therefore, the sensor layout optimization problem is transformed into the problem of minimizing the diagonal element values of the covariance matrix ;

[0037] Let G be a set containing all possible placement positions of the sensors. The cardinality of G is g, and C is a subset of G . The cardinality of C is n. The goal of sensor layout optimization is to find a subset C in G such that when the sensors are located at the positions in C, the prediction error at unobserved positions can be reduced the most. Therefore, the objective function of sensor layout optimization is expressed as:

[0038]

[0039] Where: C opt is the set of the best layout positions of the sensors. In Equation (1-11), since is the covariance matrix at the unobserved spatio-temporal position (t M , s N ), it does not depend on C. At the same time, since there is a negative sign before , Equation (1-12) is simplified to: Since tr(AB) = tr(BA), Equation (1-13) is simplified to:

[0040]

[0041]

[0042]

[0043] Optionally, the S4 specifically includes:

[0044] ​If the correlation between data is separable in space and time, its covariance matrix Σ is expressed as:

[0045]

[0046] Where: Σ (s) is a pure spatial covariance matrix containing only spatial covariance values; Σ (t) is a pure temporal covariance matrix containing only temporal covariance values;

[0047] Because the spatio-temporal covariance function is separable, the cross-covariance matrix Σ YZ is rewritten as:

[0048]

[0049] Where: and represent the pure spatial and pure temporal cross-covariance matrices between Y t,s and respectively. According to the Kronecker product, the expression of the trace in Equation (1-14) is rewritten as:

[0050]

[0051] Therefore, we get:

[0052]

[0053] Because is a pure temporal covariance matrix, when the positions of the sensors change spatially, will not change. Therefore, the sensor layout optimization problem only depends on spatial changes and has nothing to do with temporal changes. Thus, the objective function of the sensor layout optimization problem is further rewritten as:

[0054]

[0055] Optionally, the S5 specifically includes:

[0056] Define the approximately optimal subset of the sensor layout optimization problem as Assume that the optimal subset is an empty set under the initial conditions,

[0057] Randomly select a position s i , i = 1,..., g from the set G of candidate sensor positions, and substitute each position s i , i = 1,..., g into in Equation (1-19), and a return value can be obtained for each substitution. The position s iis the first candidate for the best sensor location, denoted as s1, and at this time the optimal subset

[0058] Remove the selected location s1 from G, and re-select a location s from the latest set G i , i = 1, ..., g - 1, and temporarily add it to the optimal subset At this time Substitute each location s i , i = 1, ..., g - 1 into the formula in (1-19) , and a return value can be obtained. The location s corresponding to the maximum value among all the return values i is the second candidate for the best sensor location, denoted as s2, and at this time the optimal subset

[0059] The algorithm runs iteratively. In each iteration, the newly obtained candidate for the best sensor location is added to until the cardinality of is n, and the set of the best sensor locations is obtained

[0060] On the other hand, a multi-sensor layout device based on Gaussian process is provided. The device includes:

[0061] The first modeling module is used to model the sensor monitoring situation based on the Gaussian process using the univariate sensor spatio-temporal model;

[0062] The second modeling module is used to transition the univariate sensor model to the multivariate sensor situation to obtain the multivariate sensor spatio-temporal model;

[0063] The construction module is used to construct and simplify the multi-sensor layout objective function based on the multivariate sensor spatio-temporal model;

[0064] The simplification module is used to further simplify the multi-sensor layout objective function using the spatio-temporally separable covariance function;

[0065] The solution module is used to solve the simplified multi-sensor layout objective function using the greedy algorithm to obtain the best sensor layout.

[0066] On the other hand, an electronic device is provided. The electronic device includes a processor and a memory. At least one instruction is stored in the memory, and the at least one instruction is loaded and executed by the processor to implement the above-mentioned multi-sensor layout method based on Gaussian process.

[0067] On the other hand, a computer-readable storage medium is provided, in which at least one instruction is stored, and the at least one instruction is loaded and executed by a processor to implement the above-mentioned multi-sensor layout method based on Gaussian process.

[0068] The beneficial effects brought by the technical solution provided by the present invention at least include:

[0069] The present invention can effectively optimize the multi-sensor layout, has the best prediction effect on the unmonitored positions, requires fewer sensors, and significantly reduces the calculation time required to obtain the layout result. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0071] Figure 1 is a flowchart of a multi-sensor layout method based on Gaussian process provided by an embodiment of the present invention;

[0072] Figure 2 is a block diagram of a multi-sensor layout device based on Gaussian process provided by an embodiment of the present invention;

[0073] Figure 3 is a schematic structural diagram of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0074] To make the technical problems, technical solutions, and advantages to be solved by the present invention clearer, the following will be described in detail with reference to the drawings and specific embodiments.

[0075] An embodiment of the present invention provides a multi-sensor layout method based on Gaussian process. This method can be implemented by an electronic device, which can be a terminal or a server. As Figure 1 shown in a flowchart of a multi-sensor layout method based on Gaussian process, the processing flow of this method can include the following steps:

[0076] S1. Based on Gaussian process, use a univariate sensor spatio-temporal model to model the sensor monitoring situation;

[0077] S2. Transition the univariate sensor model to the multivariate sensor situation to obtain a multivariate sensor spatio-temporal model;

[0078] S3. Based on the multivariate sensor spatio-temporal model, construct and simplify the multi-sensor layout objective function;

[0079] S4. Use a spatio-temporally separable covariance function to further simplify the multi-sensor layout objective function;

[0080] S5. Use a greedy algorithm to solve the simplified multi-sensor layout objective function to obtain the optimal sensor layout.

[0081] Through research, it is found in the embodiments of the present invention that there are mainly two key points in multi-sensor layout optimization: (1) Spatio-temporal characteristics need to be fully considered in multi-sensor layout optimization. What sensors monitor is often a spatio-temporal process, and the data type is spatio-temporal data with spatio-temporal correlation. Since there are multiple variables, it is called multivariate spatio-temporal data. Multi-sensor layout optimization based on multivariate spatio-temporal data should fully consider spatio-temporal characteristics to effectively monitor spatio-temporal processes. (2) Modeling of spatio-temporal processes is required to solve the sensor layout optimization problem. The goal of sensor layout optimization is to effectively monitor the target area and accurately predict the value at a certain position in the target area. Therefore, it is necessary to accurately model the spatio-temporal process to minimize the prediction error. In the embodiments of the present invention, a spatio-temporal model is established using a Gaussian process, so that the complete data of the target area can be estimated using sensor monitoring values, and the optimal sensor layout is determined using a direct cost function that minimizes the prediction error. The obtained layout can minimize the prediction error of unmonitored positions to the greatest extent and is computationally efficient. At the same time, the use of a spatio-temporally separable covariance function significantly reduces the computational complexity. The following details a Gaussian process-based multi-sensor layout method (Multi Sensor Layout method based on Gaussian Process, MSL-GP) provided by the embodiments of the present invention:

[0082] S1. Based on a Gaussian process, use a univariate sensor spatio-temporal model to model the sensor monitoring situation;

[0083] Before performing multi-sensor layout optimization, it is necessary to first establish a multi-sensor spatio-temporal model, so that the complete data of the entire target area can be predicted using sensor monitoring data, and a sensor layout objective function is constructed based on the established spatio-temporal model for solution, and finally the optimal sensor layout is obtained. In the embodiments of the present invention, a univariate sensor is first modeled, and then the model is transitioned to the case of multivariate sensors.

[0084] Optionally, S1 specifically includes:

[0085] Let \(g\) be the number of all candidate positions of sensors in the target area, \(n\) be the number of positions of deployed sensors, and \(N\) be the number of positions of un-deployed sensors, \(g = n + N\); assume that there are \(n\) sensors of the same type located at positions The time when the sensor makes a measurement is defined as The measurement values collected by the sensor at all times are Among them represents the measured values at all positions at time t u ; represents the measured value at time t u and position s p ;

[0086] A univariate sensor spatio-temporal model is used to model the sensor monitoring situation:

[0087] Y t,s =X t,s β + W t,s + ε t,s (1-1)

[0088] In Equation (1-1): Y t,s is the measured value of the sensor; X t,s is the reference covariate; β is the coefficient of the covariate; W t,s is a latent random variable modeled by a zero-mean Gaussian process; ε t,s is an independent and uniformly distributed noise that follows a normal distribution with zero mean and variance τ 2 .

[0089] S2. Transition the univariate sensor model to the multivariate sensor case to obtain a multivariate sensor spatio-temporal model;

[0090] Optionally, S2 specifically includes:

[0091] Suppose there are k different types of sensors monitoring k different variables, and there are n of each type of sensor. All types of sensors are embedded on the same board, and different types of sensors are located at the same position s (in the embodiments of the present invention, for convenient layout and cost reduction during measurement, all types of sensors are embedded on the same board, so different types of sensors are located at the same position s). The collected measured values are expressed as:

[0092] Y t,s =X t,s β + W t,s + ε t,s (1-2)

[0093] In Equation (1-2): represents the measured values of k types of sensors at time t and position s, where is the measured value of the i-th type of sensor, and Y t,s follows a multivariate Gaussian distribution (Multivariate Gaussian Distribution, MGD), Y t,s ~ MGD(μ, Σ), μ = E(Y t,s) is the mean value, and Σ is the multivariate covariance matrix, expressed as:

[0094]

[0095]

[0096]

[0097] The covariance matrix represents the correlation of the observed values in time and space; where represents the coefficient corresponding to the i-th covariate; the covariate matrix X t,s is expressed as:

[0098]

[0099] where: represents the covariate value corresponding to the i-th variable;

[0100] W t,s is a process vector, modeled by a Multivariate Gaussian Process (MVGP), and W t,s ~MVGP(0, Ψ), with a mean of 0, and the covariance matrix Ψ is expressed as:

[0101]

[0102] In Equation (1-7): I is the identity matrix; represents the variance of the i-th variable; ε t,s ~N(0, τ 2 ) is the measurement error defined by Gaussian white noise.

[0103] S3. Based on the multivariate sensor spatio-temporal model, construct and simplify the multi-sensor layout objective function;

[0104] Optionally, the S3 specifically includes:

[0105] Let respectively represent the positions and moments in space and time that are not monitored and need to be predicted using the monitoring data of existing sensors. Generally, the number of positions to be predicted is much larger than the number of observed positions, N >> n. Let represent the potential random process of the required prediction time and position, which has a joint distribution with the observed value Y t,s Since Y t,s follows a multivariate Gaussian distribution, obtained from the multivariate Gaussian marginal distribution:

[0106]

[0107] In Equation (1-8): μ and Σ are the mean and covariance matrix of Y t,s respectively; μ Z and are the mean vector and covariance matrix of respectively; is the cross-covariance matrix representing the correlation between Y t,s and . According to Equation (1-8), given the observed value Y t,s , the conditional distribution of is derived as shown in Equation (1-9):

[0108]

[0109] where:

[0110]

[0111]

[0112] The key to sensor layout optimization lies in being able to minimize the prediction error at unmonitored locations to the greatest extent. It can be deduced from Equation (1-9) that, given the observed value Y t,s , the prediction uncertainty at the unobserved location time (t M , s N ) is related to the covariance matrix . Equation (1-11) shows that the diagonal elements of the covariance matrix represent the prediction variance values. Therefore, the sensor layout optimization problem is transformed into the problem of minimizing the diagonal element values of the covariance matrix ;

[0113] Let G be a set containing all possible placement positions of the sensors, the cardinality of G is g, and C is a subset of G, the cardinality of C is n. The goal of sensor layout optimization is to find a subset C in G such that when the sensors are located at the positions in C, the prediction error at unobserved locations can be reduced the most. Therefore, the objective function of sensor layout optimization is expressed as:

[0114]

[0115] where: C opt is the set of the best layout positions of the sensors. In Equation (1-11), since is the covariance matrix at the unobserved spatio-temporal location (t M , s N ), it does not depend on C. At the same time, since is, and The sign in front is negative, so Equation (1-12) is simplified to:

[0116]

[0117] Calculate The complexity of is O(kN 2 M 2 nm + kn 3 m 3 ).

[0118] Since tr(AB) = tr(BA), Equation (1-13) is simplified to:

[0119]

[0120] Calculate The complexity of is O(kNMn 2 m 2 + kn 3 m 3 ). Since N >> n, Equation (1-14) further reduces the computational complexity compared to Equation (1-13).

[0121] S4. Use a spatio-temporally separable covariance function to further simplify the multi-sensor layout objective function;

[0122] By solving Equation (1-14), the problem of how to determine the sensor positions can be solved. At the same time, by changing the number of sensors until the variance at the unobserved positions meets the proposed requirements, the problem of how to determine the number of sensors can be solved. Although Equation (1-14) can be solved in a small-scale sensor network with a small amount of data, in the case of a relatively large-scale sensor network (k, n are relatively large) and when collecting monitoring values over a long period of time (m is relatively large), the computational complexity and cost will increase significantly. Therefore, it is still necessary to further reduce the complexity of the sensor layout optimization problem. The embodiments of the present invention propose a method using a separable spatio-temporal covariance function to reduce the complexity of this problem.

[0123] Currently, there are mainly two spatio-temporal covariance functions, namely separable and non-separable. Non-separable covariance functions mainly include the Gneiting model, the Porcu and Mateu mixture model, etc. Theoretically, spatio-temporally non-separable covariance functions are considered to be able to better capture spatio-temporal interactions. However, such covariance functions have excessive computational complexity, especially when applied to relatively large-scale data sets. Therefore, the embodiments of the present invention use a spatio-temporally separable covariance function.

[0124] Optionally, the S4 specifically includes:

[0125] If the correlation between data is separable in space and time, its covariance matrix Σ is expressed as:

[0126]

[0127] Where: Σ (s) is a pure spatial covariance matrix that only contains spatial covariance values; Σ (t) is a pure temporal covariance matrix that only contains temporal covariance values;

[0128] Because the spatio-temporal covariance function is separable, the cross-covariance matrix Σ YZ is rewritten as:

[0129]

[0130] Where: and respectively represent the pure spatial and pure temporal cross-covariance matrices between Y t,s and According to the Kronecker product, the expression of the trace in Equation (1-14) is rewritten as:

[0131]

[0132] Therefore, we get:

[0133]

[0134] Because is a pure temporal covariance matrix, when the positions of the sensors change spatially, will not change. Therefore, the sensor layout optimization problem only depends on spatial changes and has nothing to do with temporal changes. Thus, the objective function of the sensor layout optimization problem is further rewritten as:

[0135]

[0136] Calculating has a complexity of O(kNn 2 + kn 3 ), which is significantly reduced compared to Equation (1-14).

[0137] S5. Use the greedy algorithm to solve the simplified multi-sensor layout objective function to obtain the optimal sensor layout.

[0138] As can be seen from Equation (1-19), solving the sensor layout problem is a combinatorial optimization problem. Selecting a subset C from the universal set G in a combinatorial optimization problem is an NP-hard problem. Generally, an NP-hard problem can be approximately solved with a greedy algorithm to obtain an approximate optimal solution. Additionally, for the convenience of layout and cost reduction in the embodiments of the present invention, all types of sensors are embedded on the same board, that is, different types of sensors are located at the same position. Therefore, the obtained results are different position points, and multiple types of sensors are deployed at each position point. The following describes how the greedy algorithm approximately optimally solves the problem of Equation (1-19).

[0139] Optionally, S5 specifically includes:

[0140] Define the approximate optimal subset of the sensor layout optimization problem as Assume that the optimal subset is an empty set under the initial condition,

[0141] Randomly select a position s from the set G of candidate sensor positions i , i = 1,..., g. Substitute each position s i , i = 1,..., g into in Equation (1-19), and a return value can be obtained for each substitution. The position s corresponding to the maximum value among all the return values i is the first candidate best sensor position, denoted as s1. At this time, the optimal subset

[0142] Remove the selected position s1 from G, and randomly select a new position s from the updated set G i , i = 1,..., g - 1, and temporarily add it to the optimal subset At this time Substitute each position s i , i = 1,..., g - 1 into in Equation (1-19), and a return value can be obtained for each substitution. The position s corresponding to the maximum value among all the return values i is the second candidate best sensor position, denoted as s2. At this time, the optimal subset

[0143] The algorithm iteratively runs. In each iteration, the newly obtained candidate best sensor position is added to until has a cardinality of n, and the set of best sensor positions

[0144] The specific implementation steps of this greedy algorithm are as follows:

[0145] Input: Set G of candidate sensor positions, number n of sensors, and number k of candidate optimal sensor positions.

[0146] Output: Set of optimal sensor positions

[0147] Step1: Initialize the set of optimal sensor positions Let be an empty set, and let k = 1;

[0148] Step2: Substitute all positions s in the set G of candidate sensor positions i , i = 1,..., g into Calculate the return value;

[0149] Step3: Denote the position corresponding to the maximum value in the return value as s1, add it to the set of candidate optimal sensor positions remove s1 from G, and k = k + 1;

[0150] Step4: Substitute all positions in the new set G of candidate sensors into Calculate the return value;

[0151] Step5: Denote the position corresponding to the maximum value in the return value as s k , add it to the set of candidate optimal sensor positions and k = k + 1;

[0152] Step6: If the cardinality of the set of optimal sensor positions is n, i.e., k = n, go to Step7; otherwise, go to Step4;

[0153] Step7: Obtain the set of optimal sensor positions

[0154] In the embodiments of the present invention, a data acquisition system is established, which can better obtain the relevant data to be mined and applied to the multi-sensor layout method MSL-GP based on Gaussian process. It can effectively optimize the multi-sensor layout, has the best prediction effect on unmonitored positions, requires fewer sensors, and significantly reduces the calculation time required to obtain the layout result. The embodiments of the present invention also construct a monitoring system APP for convenient real-time monitoring. The three parts of the data acquisition system, the multi-sensor layout method based on Gaussian process, and the monitoring APP in the embodiments of the present invention are interconnected to form a complete system. The embodiments of the present invention verify this method on the collected Beijing air quality dataset and the Nanyang Technological University test room dataset respectively. The experimental results show that this method can effectively and reasonably layout the sensors and reduce the prediction error at unmonitored positions. Experiments show that, compared with the existing methods, the prediction error of the multi-sensor layout method MSL-GP in the embodiments of the present invention is reduced by 16% - 31.5%.

[0155] As Figure 2 shown, the embodiments of the present invention also provide a multi-sensor layout device based on Gaussian process, and the device includes:

[0156] The first modeling module 210 is used to model the sensor monitoring situation based on the Gaussian process using the univariate sensor spatio-temporal model;

[0157] The second modeling module 220 is used to transition the univariate sensor model to the multivariate sensor situation to obtain a multivariate sensor spatio-temporal model;

[0158] The construction module 230 is used to construct and simplify the multi-sensor layout objective function based on the multivariate sensor spatio-temporal model;

[0159] The simplification module 240 is used to further simplify the multi-sensor layout objective function using the spatio-temporally separable covariance function;

[0160] The solution module 250 is used to solve the simplified multi-sensor layout objective function using the greedy algorithm to obtain the optimal sensor layout.

[0161] The function structure of the multi-sensor layout device based on Gaussian process provided by the embodiments of the present invention corresponds to the multi-sensor layout method based on Gaussian process provided by the embodiments of the present invention, and will not be elaborated here.

[0162] Figure 3It is a schematic structural diagram of an electronic device 300 provided by an embodiment of the present invention. The electronic device 300 may vary greatly due to different configurations or performances, and may include one or more central processing units (CPUs) 301 and one or more memories 302. Among them, at least one instruction is stored in the memory 302, and the at least one instruction is loaded and executed by the processor 301 to implement the steps of the above-mentioned multi-sensor layout method based on Gaussian process.

[0163] In an exemplary embodiment, a computer-readable storage medium is also provided, such as a memory including instructions. The above instructions can be executed by a processor in a terminal to complete the above-mentioned multi-sensor layout method based on Gaussian process. For example, the computer-readable storage medium can be a ROM, a random access memory (RAM), a CD-ROM, a magnetic tape, a floppy disk, and an optical data storage device, etc.

[0164] Those of ordinary skill in the art can understand that all or part of the steps of implementing the above embodiments can be completed by hardware, or can be completed by instructing relevant hardware through a program. The program can be stored in a computer-readable storage medium. The above-mentioned storage medium can be a read-only memory, a magnetic disk, or an optical disc, etc.

[0165] The above are only the preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

Claims

1. A multi-sensor layout method based on Gaussian process, characterized in that, The method includes: S1. Using a univariate sensor spatio-temporal model based on Gaussian process to model the sensor monitoring situation; S2. Transitioning the univariate sensor model to the multivariate sensor situation to obtain a multivariate sensor spatio-temporal model; S3. Based on the multivariate sensor spatio-temporal model, constructing and simplifying the multi-sensor layout objective function; S4. Using a spatio-temporally separable covariance function to further simplify the multi-sensor layout objective function; S5. Using a greedy algorithm to solve the simplified multi-sensor layout objective function to obtain the optimal sensor layout; The S1 specifically includes: Let be the number of all candidate positions of sensors in the target area, be the number of positions of deployed sensors, be the number of positions of undeployed sensors, ; Suppose there are sensors of the same type located at the position , the time when the sensors make measurements is defined as , the measurement values collected by the sensors at all times are , where represents the measurement values at all positions at time , represents the measurement value at time and position ; Using a univariate sensor spatio-temporal model to model the sensor monitoring situation: （1-1） In Equation (1-1): is the measured value of the sensor; is the reference covariate; is the coefficient of the covariate; is a latent random variable modeled by a zero-mean Gaussian process; is an independent and uniformly distributed noise that follows a normal distribution with zero mean and variance ; The S2 specifically includes: Suppose there is different types of sensors to monitor different variables, and each type of sensor has pieces. All types of sensors are embedded on the same board, and different types of sensors are located at the same position , and the collected measurements are expressed as: （1-2） In formula (1-2): express Type of sensor at time and location The measured value at For the The measured values ​​of the sensors of different types, Obey multivariate Gaussian distribution MGD, , is the mean, is the multivariate covariance matrix, expressed as: （1-3） （1-4） （1-5） The covariance matrix represents the correlation of the observed values in time and space; , where represents the coefficient corresponding to the -th covariate; the covariate matrix is expressed as: （1-6） Wherein: represents the covariate value corresponding to the th variable; is a process vector, modeled by a multi-variate Gaussian process (MVGP), with a mean of 0 and a covariance matrix expressed as: （1-7） In formula (1-7): is the identity matrix; represents the variance of the th variable; is the measurement error defined by Gaussian white noise.

2. The method according to claim 1, characterized in that, The S3 specifically includes: Let , , respectively represent the unmonitored positions and times in space and time that need to be predicted using the monitoring data of existing sensors. Generally, the number of positions to be predicted is much larger than the number of observed positions. Let represent the latent stochastic process of the required prediction time and position, which has a joint distribution with the observed value . Since obeys a multivariate Gaussian distribution, it is obtained from the multivariate Gaussian marginal distribution: （1-8） In Equation (1-8): and are respectively the mean value and covariance matrix of; and are respectively the mean vector and covariance matrix of; is the cross-covariance matrix representing the correlation between and . According to Equation (1-8), given the observed value , the conditional distribution of is derived as shown in Equation (1-9): （1-9） Wherein: （1-10） （1-11） The key to sensor layout optimization lies in minimizing the prediction error at unmonitored locations as much as possible. It can be deduced from Equation (1-9) that, given the observed value , the prediction uncertainty at the unobserved location time is related to the covariance matrix . Equation (1-11) shows that the diagonal elements of the covariance matrix represent the prediction variance values. Therefore, the sensor layout optimization problem is transformed into the problem of minimizing the diagonal element values of the covariance matrix . Let be a set that contains all possible placement positions of the sensors, The cardinality of is which is a subset of , The cardinality of is The goal of sensor layout optimization is to find a subset in such that when the sensors are located at the positions in , the prediction error at the unobserved positions can be reduced the most. Therefore, the objective function of sensor layout optimization is expressed as: （1-12） Wherein: is the set of the optimal layout positions of the sensors. In Equation (1-11), since is the unobserved spatio-temporal position at the covariance matrix of which does not depend on , and since there is a negative sign before , Equation (1-12) is simplified to: （1-13） Because , Equation (1-13) simplifies to: （1-14）。 3. The method according to claim 2, characterized in that, The S4 specifically includes: If the correlation between data is separable in space and time, its covariance matrix is expressed as: （1-15） Wherein: is a pure spatial covariance matrix containing only spatial covariance values; is a pure temporal covariance matrix containing only temporal covariance values; Because the spatio-temporal covariance function is separable, the cross-covariance matrix is rewritten as: （1-16） Wherein: and respectively represent and the pure spatial and pure temporal cross-covariance matrices between, and rewrite the expression of the trace in Equation (1-14) according to the Kronecker product: （1-17） Thus, it is obtained that: （1-18） Because is a pure time covariance matrix, when the positions of the sensors change spatially, it will not change. Therefore, the sensor layout optimization problem only depends on spatial changes and has nothing to do with time changes. Thus, the objective function of the sensor layout optimization problem is further rewritten as: （1-19）。 4. The method according to claim 3, characterized in that, The S5 specifically includes: Define the approximate optimal subset for the sensor layout optimization problem as , assuming that the optimal subset is an empty set under the initial condition, ; Randomly select a position from the set of candidate sensor positions and substitute each position into the formula (1-19) at to obtain a return value. The position corresponding to the maximum value among all return values is the first candidate optimal sensor position, denoted as and at this time the optimal subset ; ​ Remove the selected position from and re - select a position from the latest set and temporarily add it to the optimal subset . At this time , substitute each position into in formula (1 - 19), and a return value can be obtained. The position corresponding to the maximum value among all return values is the second candidate best sensor position, denoted as , and at this time the optimal subset ; ; The algorithm runs iteratively. In each iteration, the newly obtained candidate best sensor positions are added to until has a cardinality of , obtaining the set of best sensor positions .

5. A multi-sensor layout device based on Gaussian process, characterized in that, The device includes: A first modeling module, configured to use a univariate sensor spatio-temporal model based on Gaussian process to model the sensor monitoring situation; A second modeling module, configured to transition the univariate sensor model to the multivariate sensor situation to obtain a multivariate sensor spatio-temporal model; A construction module, configured to construct and simplify the multi-sensor layout objective function based on the multivariate sensor spatio-temporal model; A simplification module, configured to use a spatio-temporally separable covariance function to further simplify the multi-sensor layout objective function; A solution module, configured to use a greedy algorithm to solve the simplified multi-sensor layout objective function to obtain the optimal sensor layout; The first modeling module is specifically configured to: Let be the number of all candidate positions of sensors in the target area, be the number of positions of deployed sensors, be the number of positions of undeployed sensors, ; Suppose there are sensors of the same type located at position , the time when the sensor makes a measurement is defined as , the measurement values collected by the sensor at all times are , where represents the measurement values at all positions at time , represents the measurement value at time and position ; Use a univariate sensor spatio-temporal model to model the sensor monitoring situation: （1-1） In Equation (1-1): is the measured value of the sensor; is the reference covariate; is the coefficient of the covariate; is a latent random variable modeled by a zero-mean Gaussian process; is an independent and uniformly distributed noise that follows a normal distribution with zero mean and variance ; The second modeling module is specifically configured to: Suppose there is different types of sensors for monitoring different variables, and each type of sensor has pieces. All types of sensors are embedded on the same board, and different types of sensors are located at the same position , and the collected measurements are expressed as: （1-2） In formula (1-2): represents the measured value of the th type of sensor at time and position where is the measured value of the th type of sensor, , is the mean value, is the multivariate covariance matrix, expressed as: （1-3） （1-4） （1-5） The covariance matrix represents the correlation of the observed values in time and space; , where represents the coefficient corresponding to the -th covariate; the covariate matrix is expressed as: （1-6） Wherein: represents the covariate value corresponding to the th variable; is a process vector, modeled by a multi-variate Gaussian process (MVGP), with a mean of 0 and a covariance matrix represented as: （1-7） In formula (1-7): is the identity matrix; represents the variance of the th variable; the measurement error defined by Gaussian white noise.

6. An electronic device, the electronic device includes a processor and a memory, and at least one instruction is stored in the memory, wherein, The at least one instruction is loaded and executed by the processor to implement the Gaussian process-based multi-sensor layout method according to any one of claims 1-4.

7. A computer-readable storage medium, at least one instruction is stored in the storage medium, wherein, The at least one instruction is loaded and executed by the processor to implement the Gaussian process-based multi-sensor layout method according to any one of claims 1-4.

Images