Consistent and asymptotically effective signal source positioning method based on received signal strength difference
By employing regularization methods and Gauss-Newton iteration, the problems of biased estimation and high computational complexity in sensor signal source localization are solved, enabling fast, accurate, and consistent localization of signal source positions, adaptable to different noise environments.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ACAD OF MATHEMATICS & SYSTEMS SCIENCE - CHINESE ACAD OF SCI
- Filing Date
- 2025-12-11
- Publication Date
- 2026-05-01
AI Technical Summary
Existing sensor signal source localization methods suffer from problems such as biased signal source location estimation, inability of iterative algorithms to converge to the global optimum, high computational complexity, and inability to quickly locate the source.
Based on the regularization method, an explicit form of a consistent and asymptotically unbiased estimate of the signal source location is given, and a consistent and asymptotically effective estimate is obtained through a one-step Gauss-Newton iteration. A consistent and asymptotically effective positioning scheme is designed.
It achieves fast and accurate location of signal source, ensures that the estimation error converges to the true location, has low computational complexity, adapts to scenarios with known and unknown noise variance, and provides consistent and asymptotically effective estimation.
Smart Images
Figure CN121955876A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a method for locating a signal source using differential signal strength data received by a sensor. Based on regularized identification theory, this method adaptively provides an explicit form of a consistent and asymptotically unbiased estimate of the signal source location, regardless of whether the measurement noise is known or unknown. Furthermore, based on this explicit solution, a consistent and asymptotically effective estimate of the signal source location is provided, and a fast scheme for consistent and asymptotically effective estimation of the signal source location is designed. Background Technology
[0002] Differential signal strength data from a sensor refers to the difference between the signal strength received by the sensor from the signal source (either emitted or reflected) and the signal strength received by the reference sensor. Therefore, unlike active sensors, this type of sensor only measures distance to the signal source, making it impossible for a single sensor to locate the source. To obtain the signal source's location, it's necessary to combine measurement information from multiple sensors. Furthermore, in many scenarios, rapid localization of the measured signal source is required, meaning that using only signal source measurement information at a single moment is insufficient, and it's impossible to combine any signal source motion model. Additionally, the localization algorithm must have low computational complexity, run fast enough, and be as unaffected by noise as possible.
[0003] Meanwhile, the sensor's measurement of the signal source is also affected by noise. Even with multiple sensors measuring the signal source, it is still impossible to accurately calculate the signal source's position. Therefore, this type of localization problem belongs to the category of parameter estimation problems, that is, using the signal source position as the parameter of the sensor measurement model, and estimating this parameter using known measurement data. For parameter estimation problems, consistency and asymptotic validity are two crucial properties. For problems based on a sample size of... The data gives the estimate , called estimate Consistency refers to the estimation The estimation error converges in probability to . - Consistency indicates that the estimation error converges to... speed and Same level. (Called) Asymptotic validity means The variance converges to the Cramer-Rao lower bound, i.e. yes Among all asymptotically unbiased estimators, the one with the smallest asymptotic variance is the one with the smallest asymptotic variance. Asymptotic efficiency reflects the reliability and stability of the parameter estimate.
[0004] Existing sensor-based signal source localization methods mainly include least squares and improved least squares methods, iterative solution methods, etc. See: 1. Hu YC, Leus G. Robust Differential Received Signal Strength-Based Localization[J]. IEEE Transactions on Signal Processing, 2017, 65(12):3261-3276. 2. Chen YP, Li JJ, Yan Q L. Robust DRSS Based Localization in Sensor Networks With Generalized Gaussian Noise[J]. IEEE Communications Letters, 2022, 26(12): 2909-2913. 3. Li J, Doğançay K, Nguyen NH, et al. Reducing the Bias in DRSS-Based Localization: An Instrumental Variable Approach[C]. 2019 27th European Signal Processing Conference (EUSIPCO), 2019:1-5. Existing sensor-based measurement signal source localization methods have the following limitations: 1. Some existing methods provide biased estimates of the source location, meaning that they are not equal to or do not converge to the true source location in the mathematical expectation sense.
[0005] 2. Some existing methods are based on iterative algorithms to solve for the location of the signal source. These methods cannot guarantee convergence to the global optimum and have high computational complexity, and cannot guarantee fast localization of the signal source.
[0006] 3. Existing methods cannot guarantee that the position estimation of the signal source is consistent and asymptotically effective. That is, they cannot guarantee that as the measurement data increases, the position estimation will quickly converge to the true position and the error variance will approach the theoretical minimum.
[0007] To address the aforementioned issues, this invention addresses the problem of locating measurement signal sources based on differential signal strength data received by sensors. Based on a regularization method, it provides an explicit form for a consistent and asymptotically unbiased estimate of the signal source's location. Using this estimate as an initial value, a consistent and asymptotically effective estimate of the signal source's location can be obtained with just one Gauss-Newton iteration, enabling rapid and accurate location of measurement signal sources based on sensors. Summary of the Invention
[0008] The technical problem solved by this invention is: how to locate a signal source based on differential data of the received signal strength from a sensor. Based on a regularization method, a consistent and asymptotically unbiased estimate of the signal source location is given in explicit form, and a consistent and asymptotically effective estimate of the signal source location is given. Furthermore, a scheme for consistent and asymptotically effective localization of the signal source location is designed, realizing consistent and asymptotically effective localization of the signal source based on sensor measurements.
[0009] The solution of this invention is as follows: For the differential data of the received signal strength of the sensor to the signal source, a consistent and asymptotically unbiased signal source position regularization estimator is designed; wherein, if the noise variance is unknown, the consistent estimate of the regularization coefficient is obtained by adaptive calculation of the measurement data; then, using the regularization estimate of the signal source position as the initial value, a Gauss-Newton iteration is performed to obtain a consistent and asymptotically effective signal source position estimate.
[0010] The specific steps proposed in this invention are explained below in response to the problem. Let the coordinates of the centroid position vector of the signal source be... ,in, They are respectively Components in the three coordinate axes of a three-dimensional coordinate system. Sensor The coordinates of the centroid position vector in the coordinate system are ,in, They are respectively The components in the three coordinate axes of the three-dimensional coordinate system, For the number of sensors, Let be the reference sensor. Assume that all sensors are not coplanar or spherical.
[0011] The measurement model for the differential signal strength received by the sensor is as follows: (1) Among them, the received signal strength difference component measurement noise For independent and identically distributed cells, the mean is The variance is Gaussian random variable, The path attenuation coefficient is a constant between 2 and 5. For the true distance from the sensor to the signal source, in particular, Reference sensor The actual distance to the signal source This is the measured value of the differential signal strength received.
[0012] Based on the differential measurement model of received signal strength (1), the specific steps for obtaining a consistent and asymptotically unbiased estimate of the signal source location using sensor measurements are as follows: Step 1: Establish a linear model for sensor measurement with the signal source location as a parameter. First, the measurement model (1) is simplified and linearized, which is equivalent to: (2) in, , These are the equivalent received signal strength difference component and noise, respectively.
[0013] If the noise variance is known, a linearized model is obtained based on model (2): (3) in, Indicates sensor The transpose of the coordinate vector. This represents the transpose of the coordinate vector of the reference sensor. Indicates sensor The magnitude of the coordinate vector, Indicates sensor The magnitude of the coordinate vector; centered equivalent exponential noise Equivalent exponential noise mean constant satisfy: (4) in, Represents the relationship between random variables Take the expected value. The base of the natural logarithm and the parameters to be identified in the linear model. .
[0014] Record the output of the linear model linear model regression vector Linear model equivalent noise Model (3) is equivalent to: (5) In summary Group measurements yielded an equivalent linear model: (6) in, The output vector of the equivalent linear model with known noise variance. The input matrix is the equivalent linear model with known noise variance. The noise vector of the equivalent linear model: (7) If the noise variance is unknown, without loss of generality, assume Based on model (2), the linearized model is obtained: (8) in, For sensors The negative of the square of the magnitude of the coordinate vector, the parameter to be identified in the linear model. .
[0015] Record the output of the linear model and linear model regression vector Model (8) is equivalent to: (9) In summary The equivalent linear model was obtained from the measurements of each group: (10) in, This is the input matrix of the equivalent linear model with unknown noise variance; This is the output vector of the equivalent linear model with unknown noise variance; (11) Step 2: Calculate the regularization coefficient estimate When subsequently calculating a consistent and asymptotically unbiased estimate of the signal source location based on regularization methods, regularization coefficients are required. The regularization coefficient depends on the mean constant of the equivalent exponential noise. Therefore, this regularization coefficient needs to be obtained before calculating a consistent and asymptotically unbiased estimate of the signal source location.
[0016] If the variance of the noise is measured by the difference in received signal strength... Given that, the constant can be directly calculated using equation (4). Then calculate the regularization coefficient. .
[0017] For scenarios where the variance of measurement noise is unknown, the regularization coefficient needs to be calculated adaptively, meaning the regularization coefficient needs to be directly adjusted based on existing data. Estimation is performed. Let the input-output stacked matrix of the equivalent linear model with unknown noise variance be denoted as... Equivalent linear model with unknown noise variance and regular stacked matrix : (12) in, express OK All of the columns matrix, express OK All of the columns Matrix, matrix Input the regularization matrix into the equivalent linear model with unknown noise variance: (13) Indicates 1 row All of the columns Matrix, matrix For matrix transpose, They are respectively The transpose of .
[0018] Then, by the central limit theorem, the following holds: (14) Among them, matrix The noise-free input matrix of the equivalent linear model with unknown noise variance is: (15) Divide by Small quantities that are then bounded by probability.
[0019] Furthermore: (16) in, For matrix inverse and matrix The largest eigenvalue of the product matrix.
[0020] Therefore, the regularization coefficient The estimate is: (17) in, It is the regularization coefficient in scenarios where the variance of measurement noise is unknown. Consistent estimates.
[0021] Step 3: Calculate the asymptotically unbiased and consistent estimate of the signal source location. For scenarios where the noise variance is known, due to the data matrix Including noise, the parameters of model (6) Least squares estimation : (18) Least squares estimation It is biased. Naturally, the least squares estimate of the signal source location obtained from this estimation is the first three components of the estimator (18), namely: (19) in, Least squares estimation of the signal source location using existing methods; subscript This represents the first three components of the vector. Existing methods use least squares estimation. This is a biased estimate of the signal source location.
[0022] This method proposes that the parameters of model (6) of - Consistent and asymptotically unbiased estimation for: (20) Among them, matrix Input the regularization matrix and vectors into the equivalent linear model with known noise variance. Output a regularization vector for an equivalent linear model with known noise variance. For matrix transpose, Let be the regularization coefficient, satisfying ,matrix satisfy: (twenty one) According to the parameter structure And estimator (21), the location of the signal source - A consistent and asymptotically unbiased estimate is The first three components, namely (twenty two) in, It is a consistent and asymptotically unbiased estimate of the signal source location.
[0023] Consistent and asymptotically unbiased estimation of signal source location The asymptotic unbiasedness refers to: (twenty three) in, express The mathematical expectation, Divide by Small quantities that are bounded afterward.
[0024] For scenarios where the noise variance is unknown, similarly, due to the data matrix... Including noise, the parameters of model (10) Existing methods for least squares estimation : (twenty four) It is biased. Naturally, the least squares estimate of the signal source location obtained from this estimation is the first three components of the estimator (24), namely: (25) This is a biased estimate of the signal source location.
[0025] This method proposes that the parameters of model (10) of - A consistent and asymptotically unbiased estimate is: (26) Among them, the estimation of regularization parameters The result is obtained from the second step, and the matrix. Defined by equation (13).
[0026] According to the parameter structure And estimator (26), the location of the signal source - A consistent and asymptotically unbiased estimate is The first three components are: (27) Consistent and asymptotically unbiased estimation of signal source location The asymptotic unbiasedness refers to: (28) Step 4: Using a consistent and asymptotically unbiased estimate of the signal source location as the initial value, perform a Gauss-Newton iteration to obtain a consistent and asymptotically effective estimate. by Using the initial value, a single Gaussian-Newton iteration yields a consistent and asymptotically efficient estimate. : (29) in, It is a vector composed of the equivalent received signal strength differential measurements of model (2), where the matrix Let Jacobian matrix be the maximum likelihood function, satisfying: (30) matrix For matrix The transpose of a vector. For consistent and asymptotically unbiased estimation The prediction vector of the equivalent received signal strength difference satisfies: (31) The advantages of this invention compared to the prior art are: First, it provides a consistent and asymptotically unbiased estimate of the location of the signal source in an explicit form, which can be directly calculated using measurement data and is very easy to implement. Furthermore, the algorithm can adaptively handle scenarios where the noise variance is known or unknown. Second, only one Gauss-Newton iteration is needed to ensure a consistent and asymptotically effective estimate of the signal source location, with extremely low computational complexity. Third, it provides a theoretical guarantee that the estimated position of the signal source converges to the true position of the signal source, gives the convergence rate, and ensures that it is the best estimate in the asymptotic sense. Attached image description: Figure 1 This is a flowchart of a consistent and asymptotically effective signal source localization method based on differential data of sensor-received signal strength.
[0027] Figure 2 yes , and The sum of the absolute values of the mean deviations of each coordinate component varies with the sample size. The change graph.
[0028] Figure 3 yes , and Root mean square error varies with sample size The change graph. Detailed Implementation
[0029] The following simulations illustrate the specific implementation of a sensor-based, consistent, and asymptotically effective signal source localization method for scenarios with known and unknown measurement noise variance. In the simulations, [the following conditions are set up / previously defined]. There are 1 sensor location, which are:
[0030] Each site was placed with There are one sensor, and the reference sensor position is... The location of the signal source is The sensor measurement model is given by equation (1), where the standard deviation of the measurement noise is... dB, total number of sensors .
[0031] If the noise variance is known, the method first rewrites the sensor measurement model as an equivalent linear model whose parameters include the location of the signal source, according to equations (3) and (5)-(7), and then calculates the input of the linear model based on the measurement data. and output Then, the equivalent exponential noise mean constant is calculated according to equation (4). Then calculate the regularization coefficient. Subsequently, according to equations (20)-(22), a consistent and asymptotically unbiased estimate of the signal source location is calculated. Finally, according to Equations (30) and (31) are used to calculate process quantities. and Then, according to equation (29), a consistent and asymptotically effective estimate of the signal source location is calculated. .
[0032] If the noise variance is unknown, the algorithm first writes the sensor measurement model into an equivalent linear model whose parameters include the location of the signal source, according to equations (8)-(11), and then calculates the input of the linear model based on the measurement data. and output Then, the process quantities are calculated according to equations (12)-(13). and Then, a consistent estimate of the regularization coefficient is calculated according to equation (17). Subsequently, according to equations (26) and (27), a consistent and asymptotically unbiased estimate of the signal source location is calculated. Finally, according to Equations (30) and (31) are used to calculate process quantities. and Then, according to equation (29), a consistent and asymptotically effective estimate of the signal source location is calculated. .
[0033] According to the simulation scenario of the present invention, for (i.e., sample size) ), respectively This experiment. Table 1 shows the estimates of the regularization coefficients. The root mean square error varies with sample size The changes. Figure 1 This shows the location estimate given by existing least-squares-based localization methods when the noise variance is unknown. This invention provides a consistent and asymptotically efficient position estimation. And the consistent and asymptotically effective position estimation ultimately provided by this invention. The sum of the absolute values of the mean deviations of each coordinate component varies with the sample size. The changes, Figure 2 It was explicitly stated that the noise variance was unknown. , ,as well as The root mean square error varies with sample size The changes.
[0034] Table 1
[0035] As can be seen from Table 1, the estimation error of the regularization coefficients given in this invention is small, providing a reliable basis for subsequent calculation of signal source location estimation using the method proposed in this invention. Figure 2 It can be seen that the deviation of the signal source location estimation provided by this invention is significantly smaller than that of existing methods. This indicates that the expected value of the signal source location estimation given by the method proposed in this invention is approximately close to the true value of the signal source, with extremely small error. Figure 3 It can be seen that the root mean square error of the signal source location estimation provided by this invention is significantly smaller than that of existing methods. This indicates that the signal source location estimation method proposed in this invention has extremely small and more stable errors. Furthermore, from... Figure 2 and Figure 3 It can be seen that the signal source position estimation given by the method proposed in this invention converges rapidly to the true value of the signal source position as the number of sensors increases, while existing methods cannot be improved as the number of sensors increases.
[0036] In summary, this invention addresses the problem of locating measurement signal sources based on sensors by transforming the measurement model, proposing a display format for a consistent and asymptotically unbiased estimate of the regularization coefficient and the signal source position, further proposing a consistent and asymptotically effective estimate of the signal source position, and providing a reasonable scheme for consistent and asymptotically effective rapid location of measurement signal sources based on sensors.
Claims
1. A consistent and asymptotically effective signal source localization method based on received signal strength difference, characterized in that: Let the coordinates of the centroid position vector of the signal source be... ,in, They are respectively Components in the three coordinate axes of a three-dimensional coordinate system; sensor The coordinates of the centroid position vector in the coordinate system are ,in, They are respectively The components in the three coordinate axes of the three-dimensional coordinate system, For the number of sensors, Assume that all sensors are not coplanar or spherical. The measurement model for the differential signal strength received by the sensor is as follows: (1) Among them, the received signal strength difference component measurement noise For independent and identically distributed cells, the mean is The variance is Gaussian random variable, The path attenuation coefficient is a constant between 2 and 5. This represents the actual distance from the sensor to the signal source. Reference sensor The actual distance to the signal source The measured value is the differential component of the received signal strength. Based on the differential measurement formula (1) for received signal strength, the specific steps for obtaining a consistent and asymptotically unbiased estimate of the signal source location using sensor measurements are as follows: Step 1: Establish a linear sensor measurement model with the signal source location as a parameter. First, the measurement formula (1) is simplified and linearized, which is equivalent to: (2) in, , These are the equivalent received signal strength differential measurement and noise, respectively; Step 2: Calculate the estimated regularization coefficient. When calculating a consistent and asymptotically unbiased estimate of the signal source location using regularization methods, regularization coefficients are required. The regularization coefficient depends on the mean constant of the equivalent exponential noise. ; Step 3: Calculate the asymptotically unbiased and consistent estimate of the signal source location; Step 4: Using a consistent and asymptotically unbiased estimate of the signal source location as the initial value, perform a Gauss-Newton iteration to obtain a consistent and asymptotically effective estimate.
2. The consistent and asymptotically effective signal source localization method based on received signal strength difference according to claim 1, characterized in that: In step one, if the noise variance is known, the linearized model is obtained based on formula (2): (3) in, Indicates sensor The transpose of the coordinate vector. This represents the transpose of the coordinate vector of the reference sensor. Indicates sensor The magnitude of the coordinate vector, Indicates sensor The magnitude of the coordinate vector; centered equivalent exponential noise Equivalent exponential noise mean constant satisfy: (4) in, Represents the relationship between random variables Take the expected value. The base of the natural logarithm and the parameters to be identified in the linear model. .
3. The consistent and asymptotically effective signal source localization method based on received signal strength difference according to claim 2, characterized in that: Record the output of the linear model linear model regression vector Linear model equivalent noise Formula (3) is equivalent to: (5) In summary Group measurements yielded an equivalent linear model: (6) in, The output vector of the equivalent linear model with known noise variance. The input matrix is the equivalent linear model with known noise variance. The noise vector of the equivalent linear model: (7)。 4. The consistent and asymptotically effective signal source localization method based on received signal strength difference according to claim 3, characterized in that: If the noise variance is unknown, without loss of generality, assume Based on formula (2), the linearized model is obtained: (8) in, For sensors The negative of the square of the magnitude of the coordinate vector, the parameter to be identified in the linear model. ; Record the output of the linear model and linear model regression vector Formula (8) is equivalent to: (9) In summary The equivalent linear model was obtained from the measurements of each group: (10) in, This is the input matrix of the equivalent linear model with unknown noise variance; This is the output vector of the equivalent linear model with unknown noise variance; (11)。 5. The consistent and asymptotically effective signal source localization method based on received signal strength difference according to claim 1, characterized in that: In step three, if the variance of the received signal strength difference component is measured... Given, directly calculate the constant. Then calculate the regularization coefficient. ; For scenarios where the variance of measurement noise is unknown, the regularization coefficient needs to be calculated adaptively, meaning the regularization coefficient needs to be directly adjusted based on existing data. Perform estimation; denote the input-output stacked matrix of the equivalent linear model with unknown noise variance. Equivalent linear model with unknown noise variance and regular stacked matrix : (12) in, express OK All of the columns matrix, express OK All of the columns Matrix, matrix Input the regularization matrix into the equivalent linear model with unknown noise variance: (13) Indicates 1 row All of the columns Matrix, matrix For matrix transpose, They are respectively The transpose of .
6. The consistent and asymptotically effective signal source localization method based on received signal strength difference according to claim 5, characterized in that: By the central limit theorem, the following holds: (14) Among them, matrix The noise-free input matrix of the equivalent linear model with unknown noise variance is: (15) Divide by Small quantities that are then bounded by probability.
7. The consistent and asymptotically effective signal source localization method based on received signal strength difference according to claim 6, characterized in that: Furthermore: (16) in, For matrix inverse and matrix The largest eigenvalue of the product matrix; Therefore, the regularization coefficient The estimate is: (17) in, It is the regularization coefficient in scenarios where the variance of measurement noise is unknown. Consistent estimates.
8. The consistent and asymptotically effective signal source localization method based on received signal strength difference according to claim 1, characterized in that: In step three, for scenarios where the noise variance is known, due to the data matrix... Includes noise, parameters Least squares estimation for: (18) Least squares estimation It is biased; the least squares estimate of the signal source location is the first three components of formula (18), that is: (19) in, Least squares estimate of the signal source location; subscript Represents the first three components of a vector; least squares estimation This is a biased estimate of the signal source location; parameter of - Consistent and asymptotically unbiased estimation for: (20) Among them, matrix Input the regularization matrix and vectors into the equivalent linear model with known noise variance. Output a regularization vector for an equivalent linear model with known noise variance. For matrix transpose, Let be the regularization coefficient, satisfying ,matrix satisfy: (21) signal source location - A consistent and asymptotically unbiased estimate is The first three components, namely (22) in, It is a consistent and asymptotically unbiased estimate of the signal source location; Consistent and asymptotically unbiased estimation of signal source location The asymptotic unbiasedness is: (23) in, express The mathematical expectation, Divide by Small quantities that are bounded afterward.
9. The consistent and asymptotically effective signal source localization method based on received signal strength difference according to claim 8, characterized in that: For scenarios where the noise variance is unknown, due to the data matrix Includes noise, parameters Least squares estimation : (24) It is biased; the least squares estimate of the signal source location is the first 3 components of the estimator (24), namely: (25) This is a biased estimate of the signal source location; parameter of - A consistent and asymptotically unbiased estimate is: (26) signal source location - A consistent and asymptotically unbiased estimate is The first three components are: (27) Consistent and asymptotically unbiased estimation of signal source location The asymptotic unbiasedness is: (28)。 10. The consistent and asymptotically effective signal source localization method based on received signal strength difference according to claim 1, characterized in that: In step four, with Using the initial value, perform one Gaussian-Newton iteration to obtain a consistent and asymptotically efficient estimate. : (29) in, It is a vector composed of the equivalent received signal strength differential measurements of model (2), where the matrix Let Jacobian matrix be the maximum likelihood function, satisfying: (30) matrix For matrix transpose of vector; For consistent and asymptotically unbiased estimation The prediction vector of the equivalent received signal strength difference satisfies: (31)。