A hybrid positioning optimal configuration solving method, system and device

Abstract

The application provides a hybrid positioning optimal configuration solving method, system and device, and relates to the technical field of target positioning. The method mainly comprises the following steps: constructing an AOA-RSS hybrid positioning mathematical model; constructing an FIM matrix of the AOA-RSS hybrid positioning based on the AOA-RSS hybrid positioning mathematical model and solving the determinant of the FIM matrix; and solving the maximum value of the determinant based on the determinant, platform system state information, AOA sensor measurement values and RSS sensor measurement values to obtain an optimal positioning configuration. The FIM matrix of the AOA-RSS hybrid positioning and the determinant thereof are solved and calculated, the optimal configuration of the AOA-RSS hybrid positioning can be quickly and effectively obtained, and the method has the advantages of high positioning accuracy, simple operation and low cost.

Description

Technical Field

[0001] This invention relates to the field of target positioning technology, and in particular to a method, system and apparatus for solving the optimal configuration of hybrid positioning. Background Technology

[0002] Currently, wireless sensor networks (WSNs) are widely used in environmental monitoring and protection, target localization, and other fields. Wireless sensor network localization systems can be categorized according to their localization methods, including: Angle of Arrival (AOA), Received Signal Strength (RSS), Time Difference of Arrival (TDOA), and Frequency Difference of Arrival (FDOA). Different localization methods correspond to different parameters in the target signal. In practical applications, different localization methods need to be selected based on different signal types.

[0003] Compared to other positioning systems, RSS-based ranging methods have advantages such as low hardware requirements, low information synchronization accuracy requirements, simple implementation, and low positioning cost. However, their positioning accuracy is not high. Generally, there are two main approaches to improving the positioning accuracy of RSS methods: one is to improve the accuracy of RSS or distance estimation, such as averaging multiple measurements and optimizing the RSS estimation model; the other is to add angle, position fingerprint, and other information to the RSS measurement, using the contained position information for hybrid positioning.

[0004] Among them, the AOA-RSS hybrid positioning method can fully leverage the advantages of both AOA angle measurement and RSS signal strength measurement, combining high positioning accuracy, ease of implementation, and low hardware requirements, and has attracted widespread attention in the industry. However, in practical positioning applications, the different relative configurations between multiple sensor positioning platforms and the target to be positioned can directly affect positioning accuracy. Finding the optimal configuration to obtain the best positioning accuracy has become a major issue that urgently needs to be addressed. Summary of the Invention

[0005] The purpose of this invention is to provide a method, system, and apparatus for solving the optimal configuration of hybrid positioning, so as to solve at least one of the above-mentioned technical problems existing in the prior art.

[0006] Firstly, to solve the above-mentioned technical problems, the present invention provides a method for solving the optimal hybrid positioning configuration, comprising:

[0007] Step 1: Construct a hybrid AOA-RSS localization mathematical model;

[0008] Step 2: Based on the AOA-RSS hybrid positioning mathematical model, construct the FIM matrix of AOA-RSS hybrid positioning and solve its determinant;

[0009] Step 3: Based on the determinant, platform system status information, AOA sensor measurement value and RSS sensor measurement value, solve for the maximum value of the determinant to obtain the optimal positioning configuration.

[0010] Using the above method, the target can be located using the AOA-RSS hybrid positioning method. The positioning accuracy is high and the scheme is simple and reliable. By solving for the maximum value of the determinant of the FIM matrix of the AOA-RSS hybrid positioning, the optimal positioning configuration can be obtained quickly and the positioning accuracy can be further improved.

[0011] In one feasible embodiment, step 1 includes:

[0012] Step 11: Construct the motion state equation of the AOA-RSS hybrid sensor:

[0013] The target is located and tracked by M platforms, each platform including a set of AOA-RSS hybrid sensors, so there are M AOA-RSS hybrid sensors;

[0014] The motion state of the AOA-RSS hybrid sensor can be represented as:

[0015]

[0016] Where, x i =[x i y i ] T Indicates the sensor position; Indicates sensor speed;

[0017] The position of the target can be represented as: x t =[x t y t ] T ;

[0018] r i Let r represent the distance from the i-th sensor to the target. i =||x t -x i ||.

[0019] Step 12: Based on the measurement equation of the AOA sensor, derive the measurement vector and its probability density function of the AOA sensor:

[0020] For an AOA sensor, its measurement equation can be expressed as:

[0021]

[0022] Among them, e i Indicates measurement error, and φ i (x t φ represents the angle between the sensor and the target. i (x t ) = arctan2(y t -y i ,x t -x i );

[0023] Indicates the variance of the error:

[0024] Where β≥0 represents the path loss factor; This indicates the magnitude of the error variance per unit distance;

[0025] The set of measurements from M AOA sensors can be represented as:

[0026] Among them, the measurement vector set Φ(x) t )=[φ1(x t ),L,φ M (x t )] T The measurement error set e = [e1,L,e] M ] T ;

[0027] Assuming that the measurement errors of different sensors are independent of each other, and that the error variance can be expressed as:

[0028]

[0029] The probability density function of the AOA measurement vector can then be expressed as:

[0030]

[0031] Step 13: Based on the measurement equation of the RSS sensor, derive the measurement vector and its probability distribution function of the RSS sensor:

[0032] For an RSS sensor, its measurement equation can be expressed as:

[0033]

[0034] Where, p i p represents the true strength of the signal received by sensor i; s γ represents the intensity of the target radiated signal, in dB; iIndicates path loss intensity, n i Indicates conformity to variance Gaussian distribution

[0035] Since the measurement error is related to the signal-to-noise ratio (SNR) of the received signal when the bandwidth of the sensor's received signal is constant, and the SNR is mainly determined by the distance between the sensor and the target when the power and frequency of the radiation source are constant, the relationship between the error and distance for the i-th sensor can be expressed as:

[0036] Where α≥0 represents the path loss factor; This indicates the magnitude of the RSS measurement error variance per unit distance;

[0037] For M RSS sensors, their measurement vectors can be represented as:

[0038]

[0039] Assuming that the measurement errors between different sensors are completely independent, their covariance distance can be expressed as: The probability distribution function of the RSS measurement vector can then be expressed as:

[0040] In one feasible embodiment, step 2 includes:

[0041] Step 21: Based on the probability distribution function of the RSS sensor measurement vector, derive the FIM matrix J corresponding to RSS positioning. RSS :

[0042] For RSS sensors, the FIM standard solution matrix is:

[0043]

[0044] in, express The probability density function;

[0045] Substituting the probability distribution function of the RSS measurement vector into the standard FIM solution matrix yields the FIM matrix of noise variance as a function of distance:

[0046]

[0047] definition Substituting the probability distribution function of the RSS measurement vector, we obtain the FIM matrix J corresponding to RSS positioning. RSS Simplified representation:

[0048]

[0049] Step 22: Based on the probability density function of the AOA sensor measurement vector, derive the FIM matrix J corresponding to AOA positioning using the same method. AOA Simplified representation:

[0050]

[0051] in, It represents the magnitude of the AOA measurement error variance per unit distance.

[0052] Step 23: Based on the RSS positioning, the corresponding FIM matrix J RSS and the FIM matrix J corresponding to AOA positioning AOA Construct the FIM matrix for AOA-RSS hybrid positioning. Since the two matrices mentioned above are similar in form and differ only in coefficients, J... AOARSS It can be represented as:

[0053]

[0054] Where, η i =b i +c i μ i =b i +d i .

[0055] Thus, the AOA-RSS hybrid positioning J is obtained. AOARSS The determinant is:

[0056]

[0057] The FIM matrix is ​​the Fisher Information Matrix, which is a prior art technology. Since the FIM matrix can represent the area of ​​the confidence region corresponding to the minimized estimated parameters and is not easily affected by changes in the objective function parameters and nonlinear transformations, the larger the determinant value of the FIM matrix, the higher the positioning accuracy.

[0058] In one feasible embodiment, step 3 specifically includes:

[0059] Based on J AOARSS From the determinant of the matrix, we can know that det((J) AOARSS The size of the angle φ between the lines connecting each sensor and the target is related to the value of the sensor. i Directly related, and based on the platform system status information, AOA sensor measurements, and RSS sensor measurements, the φ corresponding to the maximum solution of the determinant is calculated according to different numbers of sensors. i The optimal positioning configuration is obtained by calculating the value.

[0060] Furthermore, due to φ in the determinant i Replace with -φ i Since the objective function value remains unchanged, for any positioning configuration, the positioning configuration obtained by mirroring the sensor with any straight line passing through the target as a reference has the same positioning accuracy as the original positioning configuration. This allows for the expansion of the already obtained optimal configuration, quickly yielding several other feasible solutions for the optimal configuration.

[0061] Furthermore, the platform system status information includes the number, position, direction, and speed of the platforms; because the platform includes a set of AOA-RSS hybrid sensors, which includes one AOA sensor and one RSS sensor; therefore, the number of platforms is equal to the number of AOA sensors and also equal to the number of RSS sensors; the position of the platform is equal to the position of the AOA sensor and also equal to the position of the RSS sensor; the direction of the platform is equal to the direction of the AOA sensor and also equal to the direction of the RSS sensor; the speed of the platform is equal to the speed of the AOA sensor and also equal to the speed of the RSS sensor.

[0062] Furthermore, the AOA sensor measurement includes the angle of arrival, which refers to the relative angle between the AOA sensor and the target.

[0063] Furthermore, the RSS sensor measurement includes the target radiation signal intensity.

[0064] Furthermore, step 3 also includes constraints, which include: an upper limit constraint on the distance between the platform and the target, a lower limit constraint on the distance between the platform and the target, an upper limit constraint on the distance between platforms, and a lower limit constraint on the distance between platforms.

[0065] Furthermore, step 3 also includes an optimization algorithm, based on the constraints, using J... AOARSS The determinant is used as the objective function. The optimal solution with the maximum value is obtained through optimization algorithms, such as differential evolution algorithm. The optimal angle between the line connecting each sensor and the target is obtained, and the optimal positioning configuration image is generated.

[0066] Secondly, based on the same inventive concept, this invention also provides a hybrid positioning optimal configuration solution system, including a data acquisition module, a data processing module, and a result generation module:

[0067] The data acquisition module is used to collect AOA sensor measurement values, RSS sensor measurement values, and platform system status information;

[0068] The data processing module includes a FIM unit and a solution unit:

[0069] The FIM unit is used to store the FIM matrix and its determinant of AOA-RSS hybrid positioning;

[0070] The solution unit is used to receive the AOA sensor measurement value, the RSS sensor measurement value and the platform system status information, call the FIM matrix and its determinant of the AOA-RSS hybrid positioning, perform optimization calculation of the maximum value of the determinant, and obtain the optimal positioning configuration.

[0071] The result generation unit is used to output the optimal positioning configuration to the outside world.

[0072] Thirdly, based on the same inventive concept, the present invention also provides a hybrid positioning optimal configuration solving device, including a processor, a memory and a bus. The memory stores instructions and data that can be read by the processor. The processor is used to call the instructions and data in the memory to execute the hybrid positioning optimal configuration solving method as described above. The bus connects the functional components to transmit information.

[0073] By adopting the above technical solution, the present invention has the following beneficial effects:

[0074] The method, system, and apparatus for solving the optimal configuration of hybrid positioning provided by this invention, based on the FIM matrix and determinant of AOA-RSS hybrid positioning, can quickly and effectively obtain the optimal configuration of AOA-RSS hybrid positioning, and has the advantages of high positioning accuracy, simple operation, and low cost. Attached Figure Description

[0075] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0076] Figure 1 This is a flowchart of the hybrid positioning optimal configuration solution method provided in an embodiment of the present invention;

[0077] Figure 2 This is a schematic diagram of AOA-RSS hybrid positioning provided in an embodiment of the present invention;

[0078] Figure 3 A diagram of the hybrid positioning optimal configuration solution system provided in this embodiment of the invention;

[0079] Figure 4 This is an example diagram of the optimal configuration for AOA-RSS hybrid positioning on two platforms provided in this embodiment of the invention;

[0080] Figure 5 Example diagrams of the optimal configuration regularization for AOA-RSS hybrid positioning on three platforms provided in this embodiment of the invention;

[0081] Figure 6 Example diagrams of non-regular cases for the optimal configuration of AOA-RSS hybrid positioning on three platforms provided in the embodiments of the present invention;

[0082] Figure 7 Example diagrams of the optimal configuration regularization of AOA-RSS hybrid positioning for four platforms provided in the embodiments of the present invention;

[0083] Figure 8 Example diagrams of non-regular cases for the optimal AOA-RSS hybrid positioning configuration on four platforms provided in this embodiment of the invention;

[0084] Figure 9 Example diagrams of the optimal configuration regularization of AOA-RSS hybrid positioning for five platforms provided in this embodiment of the invention;

[0085] Figure 10 Example diagrams of non-regular cases for the optimal AOA-RSS hybrid positioning configuration on five platforms provided in the embodiments of the present invention. Detailed Implementation

[0086] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0087] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0088] The present invention will be further explained below with reference to specific embodiments.

[0089] Firstly, to solve the above-mentioned technical problems, the hybrid positioning optimal configuration solution method provided by the embodiments of the present invention, such as... Figure 1 As shown, it includes:

[0090] Step 1: Construct a hybrid AOA-RSS localization mathematical model:

[0091] First, the target is located and tracked using M platforms. Each platform includes a set of AOA-RSS hybrid sensors, resulting in M ​​AOA-RSS hybrid sensors, such as... Figure 2 As shown;

[0092] The circular marker in the figure represents the AOA-RSS hybrid sensor, whose motion state can be represented as follows:

[0093] Where, x i =[x i y i ] T Indicates the sensor position; Indicates sensor speed;

[0094] The square marker in the diagram represents the target, and the target's position can be represented as: x t =[x t y t ] T ;r i Let r represent the distance from the i-th sensor to the target. i =||x t -x i ||.

[0095] Then, for the AOA sensor, its measurement equation can be expressed as:

[0096] Among them, e i Indicates measurement error, and φ i (x t φ represents the angle between the sensor and the target. i (x t ) = arctan2(y t -y i ,x t -x i );

[0097] Indicates the variance of the error:

[0098] Where β≥0 represents the path loss factor; This indicates the magnitude of the error variance per unit distance;

[0099] The set of measurements from M AOA sensors can be represented as:

[0100] Wherein, Φ(x) t)=[φ1(x t ),L,φ M (x t )] T e = [e1,L,e] M ] T ;

[0101] Assuming that the measurement errors of different sensors are independent of each other, and that the error variance can be expressed as:

[0102]

[0103] The probability density function of the AOA measurement vector can then be expressed as:

[0104]

[0105] Finally, for the RSS sensor, its measurement equation can be expressed as:

[0106]

[0107] Where, p i p represents the true strength of the signal received by sensor i; s γ represents the intensity of the target radiated signal, in dB; i Indicates path loss intensity, n i Indicates conformity to variance Gaussian distribution

[0108] Since the measurement error is related to the signal-to-noise ratio (SNR) of the received signal when the bandwidth of the sensor's received signal is constant, and the SNR is mainly determined by the distance between the sensor and the target when the power and frequency of the radiation source are constant, the relationship between the error and distance for the i-th sensor can be expressed as:

[0109] Where α≥0 represents the path loss factor; This indicates the magnitude of the RSS measurement error variance per unit distance;

[0110] For M RSS sensors, their measurement vectors can be represented as:

[0111]

[0112] Assuming that the measurement errors between different sensors are completely independent, their covariance distance can be expressed as: The probability distribution function of the RSS measurement vector can then be expressed as:

[0113] Step 2: Based on the AOA-RSS hybrid positioning mathematical model, construct the FIM matrix J.AOARSS And solve its determinant:

[0114] First, for an RSS sensor, the FIM standard solution matrix is:

[0115]

[0116] in, express The probability density function;

[0117] Substituting the probability distribution function of the RSS measurement vector into the standard FIM solution matrix yields the FIM matrix of noise variance as a function of distance:

[0118]

[0119] definition Substituting the probability distribution function of the RSS measurement vector, we obtain the FIM matrix J corresponding to RSS positioning. RSS Simplified representation:

[0120]

[0121] Then, following the same method, the FIM matrix J corresponding to AOA positioning is derived. AOA Simplified representation:

[0122]

[0123] in, It represents the magnitude of the AOA measurement error variance per unit distance.

[0124] Finally, the FIM matrix for AOA-RSS hybrid localization is constructed. Since the two matrices mentioned above are similar in form and differ only in coefficients, J... AOARSS It can be represented as:

[0125]

[0126] Where, η i =b i +c i μ i =b i +d i .

[0127] Thus, the AOA-RSS hybrid positioning J is obtained. AOARSS The determinant is:

[0128]

[0129] Step 3: Based on the determinant, platform system status information, AOA sensor measurements, and RSS sensor measurements, solve for the maximum value of the determinant to obtain the optimal positioning configuration:

[0130] The FIM matrix is ​​the Fisher Information Matrix, which is a prior art technology. Since the FIM matrix can represent the area of ​​the confidence region corresponding to the minimized estimated parameters and is not easily affected by changes in the objective function parameters and nonlinear transformations, the larger the determinant value of the FIM matrix, the higher the positioning accuracy.

[0131] Based on J AOARSS From the determinant of J, we can know that det(J) AOARSS The size of the angle φ between the lines connecting each sensor and the target is related to the value of the sensor. i Directly related, the φ corresponding to the maximum solution is calculated according to different numbers of sensors. i The optimal positioning configuration is obtained by calculating the value.

[0132] Furthermore, due to φ in the determinant i Replace with -φ i Since the objective function value remains unchanged, for any positioning configuration, the positioning configuration obtained by mirroring the sensor with any straight line passing through the target as a reference has the same positioning accuracy as the original positioning configuration. This allows for the expansion of the already obtained optimal configuration, quickly yielding several other feasible solutions for the optimal configuration.

[0133] Furthermore, the platform system status information includes the number, position, direction, and speed of the platforms; because the platform includes a set of AOA-RSS hybrid sensors, which includes one AOA sensor and one RSS sensor; therefore, the number of platforms is equal to the number of AOA sensors and also equal to the number of RSS sensors; the position of the platform is equal to the position of the AOA sensor and also equal to the position of the RSS sensor; the direction of the platform is equal to the direction of the AOA sensor and also equal to the direction of the RSS sensor; the speed of the platform is equal to the speed of the AOA sensor and also equal to the speed of the RSS sensor.

[0134] Furthermore, the AOA sensor measurement includes the angle of arrival, which refers to the relative angle between the AOA sensor and the target.

[0135] Furthermore, the RSS sensor measurement includes the target radiation signal intensity.

[0136] Furthermore, step 3 also includes constraints, which include: an upper limit constraint on the distance between the platform and the target, a lower limit constraint on the distance between the platform and the target, an upper limit constraint on the distance between platforms, and a lower limit constraint on the distance between platforms.

[0137] Furthermore, step 3 also includes an optimization algorithm, based on the constraints, using J... AOARSS The determinant of the matrix is ​​used as the objective function. An optimization algorithm, such as the differential evolution algorithm, is used to find the optimal solution that maximizes the value, thus obtaining the optimal angle between the lines connecting each sensor and the target, and generating the optimal positioning configuration image. The differential evolution algorithm is a highly efficient global optimization algorithm, belonging to existing technology. In short, it is a population-based heuristic search algorithm where each individual in the population corresponds to a solution vector. The evolutionary process of the differential evolution algorithm is similar to that of the genetic algorithm, including mutation, crossover, and selection operations.

[0138] Secondly, such as Figure 3 As shown, this embodiment of the invention also provides a hybrid positioning optimal configuration solution system, including a data acquisition module, a data processing module, and a result generation module:

[0139] The data acquisition module is used to collect AOA sensor measurement values, RSS sensor measurement values, and platform system status information;

[0140] The data processing module includes a FIM unit and a solution unit:

[0141] The FIM unit is used to store the FIM matrix and its determinant of AOA-RSS hybrid positioning;

[0142] The solution unit is used to receive the AOA sensor measurement value, the RSS sensor measurement value and the platform system status information, call the FIM matrix and its determinant of the AOA-RSS hybrid positioning, perform optimization calculation of the maximum value of the determinant, and obtain the optimal positioning configuration.

[0143] The result generation unit is used to output the optimal positioning configuration to the outside world.

[0144] Thirdly, embodiments of the present invention also provide a hybrid positioning optimal configuration solving device, including a processor, a memory, and a bus. The memory stores instructions and data that can be read by the processor. The processor is used to call the instructions and data in the memory to execute the hybrid positioning optimal configuration solving method as described above. The bus connects the functional components to transmit information.

[0145] In another embodiment, this solution can also be implemented by means of a device, which may include corresponding modules that perform one or more steps in the various embodiments described above. A module may be one or more hardware modules specifically configured to perform the corresponding step, or implemented by a processor configured to perform the corresponding step, or stored in a computer-readable medium for implementation by a processor, or implemented by some combination thereof.

[0146] The processor executes the various methods and processes described above. For example, the method implementations in this scheme can be implemented as software programs tangibly contained in a machine-readable medium, such as memory. In some implementations, part or all of the software program can be loaded and / or installed via memory and / or a communication interface. When the software program is loaded into memory and executed by the processor, one or more steps of the methods described above can be performed. Alternatively, in other implementations, the processor can be configured to execute one of the methods described above by any other suitable means (e.g., by means of firmware).

[0147] This device can be implemented using a bus architecture. A bus architecture can include any number of interconnect buses and bridges, depending on the specific application of the hardware and overall design constraints. The bus connects various circuits, including one or more processors, memory, and / or hardware modules. The bus can also connect various other circuits such as peripherals, voltage regulators, power management circuitry, external antennas, etc.

[0148] Buses can be Industry Standard Architecture (ISA) buses, Peripheral Component Interconnect (PCI) buses, or Extended Industry Standard Component (EISA) buses, etc. Buses can be divided into address buses, data buses, control buses, etc.

[0149] By adopting the above technical solution, the present invention has the following beneficial effects:

[0150] The method, system, and apparatus for solving the optimal configuration of hybrid positioning provided by this invention, based on the FIM matrix and determinant of AOA-RSS hybrid positioning, can quickly and effectively obtain the optimal configuration of AOA-RSS hybrid positioning, and has the advantages of high positioning accuracy, simple operation, and low cost.

[0151] Example 1:

[0152] For both platforms, steps 1 and 2 remain unchanged, and details are unnecessary to elaborate on. In step 3, J... AOARSS The objective function obtained from the determinant can be simplified to:

[0153]

[0154] From this objective function, we can obtain: when When the optimal solution is obtained;

[0155] That is, the error variance is minimized when the angles connecting the two platforms to the target are orthogonal; for example, when φ1-φ2=π / 2, the objective function f(Φ) reaches its maximum value, resulting in an optimal configuration diagram for AOA-RSS hybrid positioning, such as... Figure 4 As shown.

[0156] Example 2:

[0157] Steps 1 and 2 remain unchanged across the three platforms, and details are unnecessary to elaborate on. In step 3, let M = 3. and The objective function can be expressed as:

[0158]

[0159] Find φ in the above equation i Taking the partial derivatives of (i = 1, 2, 3) and setting them equal to 0, we get:

[0160]

[0161] The solution can be obtained from the following formula:

[0162]

[0163] Because of the domain of arccos(·), it is necessary to distinguish between regular and non-regular cases:

[0164] Case 1: For regular expressions:

[0165] when At this time, the domain of arccos(·) is satisfied. and The values ​​of all can be obtained from the above formula, resulting in four optimal configuration diagrams under the three-platform canonical case, such as... Figure 5 As shown;

[0166] Case 2: For cases without regular expressions:

[0167] when It is easy to prove that f(Φ) reaches its maximum value if and only if the following equation is satisfied between the platforms:

[0168]

[0169] For example, when φ1-φ2=π / 2, the objective function f(Φ) reaches its maximum value. This yields two optimal configuration diagrams for the non-regular three-platform case, such as... Figure 6 As shown.

[0170] Example 3:

[0171] Steps 1 and 2 remain unchanged across all four platforms, and details are unnecessary to elaborate on. Step 3 also includes two scenarios:

[0172] Case 1: For regular expressions:

[0173] when At that time, the distance r i Given any i ∈ {1, ..., M ≥ 4}, we can obtain:

[0174]

[0175] The condition for the above formula to hold true is:

[0176]

[0177] when When the above equation satisfies the regularity condition, the optimal configuration diagram can be obtained by solving this system of equations.

[0178] Preferably, the platform set can be divided into several subsets, the optimal configuration of each subset can be solved, and then the optimal configurations of the subsets can be combined to obtain the optimal configuration of the platform set.

[0179] For example, the four platforms can be divided into two platform subsets. As shown in Example 1, the optimal configuration with two platforms is when the lines connecting each platform to the target form right angles. This quickly yields two optimal configurations, such as... Figure 7 As shown, Rx4 and Rx3 form one platform subset, and Rx1 and Rx2 form another platform subset.

[0180] Case 2: For cases without regular expressions:

[0181] when It is easy to prove that the maximum value is obtained if and only if the following equation is satisfied between the platforms:

[0182]

[0183] The maximum value of the corresponding objective function f(Φ) is The optimal configuration at this point is to place one platform on the normal to the line connecting the other three collinear platforms and the target, such as... Figure 8 The two optimal configurations are shown.

[0184] Example 4:

[0185] For all five platforms, steps 1 and 2 remain unchanged, and details are unnecessary to elaborate on. Step 3 also includes two scenarios, with the specific formulas being the same as in Example 3, and need not be repeated:

[0186] Specifically, in Case 1, for the regular case, the five platforms can be divided into two platform subsets: one subset has two platforms, and the other subset has three platforms. The optimal configuration for two platforms can be obtained through Example 1, and the optimal configuration for three platforms can be obtained through Example 2. Combining these optimal configurations quickly yields four optimal configurations for the five platforms, such as... Figure 9 As shown, Rx4 and Rx5 form one platform subset, while Rx1, Rx2, and Rx3 form another platform subset.

[0187] In case 2, for the non-regular case, similar to Example 3, the optimal configuration is to place one platform on the normal line connecting the other four collinear platforms and the target, thus quickly obtaining two optimal configurations for the five platforms, such as... Figure 10 As shown.

[0188] In addition, when the number of platforms is greater than 5, the solution can be found by referring to Example 4, which will not be repeated here.

[0189] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for solving the optimal configuration of hybrid positioning, characterized in that, include: Step 1: Construct a hybrid AOA-RSS localization mathematical model; Step 2: Based on the AOA-RSS hybrid positioning mathematical model, construct the FIM matrix of AOA-RSS hybrid positioning and solve its determinant; Step 3: Based on the determinant, platform system status information, AOA sensor measurement values, and RSS sensor measurement values, solve for the maximum value of the determinant to obtain the optimal positioning configuration; Step 2 includes: Step 21: Based on the probability distribution function of the RSS sensor measurement vector, derive the FIM matrix corresponding to RSS positioning. ; Step 22: Based on the probability density function of the AOA sensor measurement vector, derive the FIM matrix corresponding to AOA positioning. ; Step 23: Based on RSS positioning, obtain the corresponding FIM matrix. and the FIM matrix corresponding to AOA positioning Constructing an AOA-RSS hybrid positioning FIM matrix and its determinant; Specifically: ； in, ; Indicates the angle between the sensor and the target; Indicates path loss intensity; Indicates the path loss factor; This indicates the magnitude of the RSS measurement error variance per unit distance; Indicates the first The distance from each sensor to the target; Indicates the number of sensors; Specifically: ； in, ; ; This indicates the magnitude of the variance in AOA measurement error per unit distance; Specifically: ； in, ; ; The determinant is: 。 2. The method according to claim 1, characterized in that, Step 1 includes: Step 11: Construct the motion state equation of the AOA-RSS hybrid sensor; Step 12: Based on the measurement equation of the AOA sensor, derive the measurement vector and its probability density function of the AOA sensor; Step 13: Based on the measurement equation of the RSS sensor, derive the measurement vector of the RSS sensor and its probability distribution function.

3. The method according to claim 2, characterized in that, The motion state equation of the AOA-RSS hybrid sensor is: ； in, Indicates the sensor position; Indicates the sensor speed.

4. A hybrid positioning optimal configuration solution system employing the method described in any one of claims 1 to 3, characterized in that, It includes a data acquisition module, a data processing module, and a result generation module: The data acquisition module is used to collect AOA sensor measurement values, RSS sensor measurement values, and platform system status information; The data processing module includes a FIM unit and a solution unit: The FIM unit is used to store the FIM matrix and its determinant for AOA-RSS hybrid positioning; The solution unit is used to receive the AOA sensor measurement value, the RSS sensor measurement value and the platform system status information, call the FIM matrix and its determinant of the AOA-RSS hybrid positioning, perform optimization calculation of the maximum value of the determinant, and obtain the optimal positioning configuration. The result generation module is used to output the optimal positioning configuration to the outside world.

5. A hybrid positioning optimal configuration solving device, characterized in that, It includes a processor, a memory, and a bus. The memory stores instructions and data that can be read by the processor. The processor is used to call the instructions and data in the memory to execute the method as described in any one of claims 1 to 3. The bus connects the functional components to transmit information.

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