Adaptive data-driven fractional derivative positioning optimization method

Abstract

This invention discloses an adaptive data-driven fractional derivative positioning optimization method, belonging to the field of radio positioning technology, comprising the following steps: S1. Receive signal strength indicators at actual locations using sensors within a target area to generate an RSSI dataset; S2. Generate and train a fractional derivative kernel adaptive filter based on the RSSI dataset; S3. Input the actual location and RSSI dataset into the trained fractional derivative kernel adaptive filter to obtain the target location. Compared to traditional classical kernel adaptive filtering methods, this invention utilizes a weight update strategy constructed using fractional derivatives, resulting in higher and more robust filtering accuracy. This invention is the first to incorporate fractional calculus combined with q-Laplacian kernel technology into kernel adaptive filters to construct a positioning system. Experiments have shown that this algorithm achieves better positioning accuracy than the most advanced positioning algorithms currently available.

Description

Technical Field

[0001] The present invention belongs to the technical field of radio positioning, and in particular relates to a fractional-order derivative positioning optimization method based on adaptive data driving. Background Art

[0002] The Internet of Things (IoT), a revolutionary technology that emerged in the early 21st century, has been widely adopted in both industrial and everyday life. The IoT connects people and objects through heterogeneous communication networks, enabling the exchange and sharing of information. Positioning technologies, such as GPS, provide users with personalized, location-based services such as navigation, weather forecasts, and social networking, significantly enhancing the practicality and convenience of these services.

[0003] Currently, there are a wide variety of indoor positioning technologies, each requiring different hardware and operating principles. Common indoor positioning technologies include wireless Wi-Fi, Bluetooth, ultra-wideband, infrared, and machine vision. These technologies each have their own advantages and disadvantages in terms of hardware complexity, positioning accuracy, and environmental sensitivity. Wi-Fi and Bluetooth positioning technologies emerged relatively early and are essential components of indoor wireless local area networks (WLANs). WLANs, with their large-scale deployment for communication purposes, have enabled a wide range of positioning tasks. Ultra-wideband technology, based on radar concepts, is currently used for high-speed, short-range communications and offers excellent positioning accuracy. Infrared signals, like radio waves, travel at the speed of light. Indoor time measurement with infrared signals is complex, requiring stringent clock requirements and resulting in high costs. Therefore, infrared technology is less widely used than Wi-Fi and Bluetooth. In practical applications, different positioning technologies should be selected based on the specific indoor environment.

[0004] Fingerprint matching algorithms use signal information generated by signal reflections to build a fingerprint signal database offline. They then calculate location distances online by measuring actual signal strength. The Naive Bayes algorithm and the K-nearest neighbor algorithm are classic fingerprint matching localization algorithms in the field of machine learning. While these two algorithms can achieve good localization results in indoor environments with simple noise, they struggle in complex and variable indoor environments, with positioning errors still in the meter range. Furthermore, in recent years, deep learning has surpassed traditional machine learning techniques in various fields, particularly computer vision and image processing, garnering significant attention and widespread application. Many researchers have also applied deep learning to indoor localization problems, achieving considerable success. However, the database construction process for deep learning is time-consuming and expensive, requiring advanced computing power. Furthermore, deep learning presents challenges in determining the optimal model type and structure for a specific task and evaluating the effectiveness of a particular architecture or algorithm. Therefore, finding lightweight online localization methods that can be used with a limited number of smart devices remains a pressing challenge.

[0005] In the field of indoor positioning technology, fingerprint recognition systems based on received signal strength indicators (RSS) are widely used due to their high positioning accuracy and relatively economical deployment costs. These systems are primarily divided into two phases: offline and online. In the offline phase, the system uses sensors to measure RSSI values ​​at pre-defined reference points and creates a fingerprint database based on these values. These reference points are pre-defined and evenly distributed, and serve as the baseline for the location fingerprint. By averaging multiple measurements, errors caused by fluctuations can be reduced, thereby improving the accuracy of the fingerprint database. In the online phase, RSSI measurements of user devices at unknown locations are used to generate new fingerprints, which are then compared with the data in the fingerprint database. Using trained prediction models such as the nearest neighbor algorithm, the K-nearest neighbor algorithm, and the weighted K-nearest neighbor algorithm, the system estimates the user's location. These algorithms compare the new fingerprint with the fingerprints in the database for similarity. The weighted K-nearest neighbor algorithm assigns different weights based on the similarity to improve positioning accuracy.

[0006] While these indoor positioning data processing methods have achieved remarkable results in accuracy and efficiency, the widespread deployment of IoT devices necessitates lightweight, online assisted positioning methods for many resource-constrained smart devices. These methods must adapt to resource-constrained environments while addressing the high cost and time-consuming database construction. RSSI-based fingerprint recognition systems, however, continue to gain development and application due to their effectiveness in asset tracking, indoor navigation, and location-based services. With technological advancements and cost reductions, these systems are expected to play an even more important role in the future development of indoor positioning technology. Summary of the Invention

[0007] In order to solve the above problems, the present invention proposes a fractional-order derivative positioning optimization method based on adaptive data driving.

[0008] The technical solution of the present invention is: a fractional-order derivative positioning optimization method based on adaptive data driving comprises the following steps:

[0009] S1. Receive signal strength indicator values ​​at actual locations using sensors within the target area to generate an RSSI dataset.

[0010] S2. Generate and train a fractional-order derivative kernel adaptive filter based on the RSSI dataset;

[0011] S3. Input the actual position and RSSI data set into the trained fractional-order derivative kernel adaptive filter to obtain the target position.

[0012] Furthermore, S2 includes the following sub-steps:

[0013] S21, mapping the RSSI dataset into a high-dimensional reproducing kernel Hilbert space;

[0014] S22, using the RSSI data set in the high-dimensional reproducing kernel Hilbert space, updating the weight parameters of the fractional derivative kernel adaptive filter;

[0015] S23. Training the fractional-order derivative kernel adaptive filter after updating the weight parameters.

[0016] Furthermore, in S21, the calculation formula for mapping the RSSI data set to the high-dimensional reproducing kernel Hilbert space RKHS is:

[0017]

[0018] Where u(m) and u(n) represent any two input vectors in the original input space, and They represent the feature mapping amount after converting u(m) and u(n) into feature space, k q,λ (·) represents the Laplace kernel function.

[0019] Furthermore, the Laplace kernel function k q,λ The calculation formula of (·) is:

[0020]

[0021] Where u(m) and u(n) represent any two input vectors in the original input space, q represents the fractal dimension, and λ represents the distribution mean.

[0022] Furthermore, in S22, the expression for updating the weight parameter of the fractional-order derivative kernel adaptive filter is:

[0023]

[0024] Where D α J(ω i ) is the fractional order α derivative of the weight parameter update, J(ω i ) represents the loss function of the fractional-order derivative kernel adaptive filter, ω i represents the weight parameter in the kernel adaptive filter at the time of the i-th update, η represents the generalized gamma function ratio, represents the input vector of the ith update converted to RKHS, k q,λ (·) represents the Laplace kernel function, q represents the fractal dimension, λ represents the distribution mean, τ represents the regularization parameter, and a i represents the prediction error at the i-th update, j represents the index in the measurement sequence, sign(·) represents the sign function, and w iRepresents the weight factor at the i-th update.

[0025] Furthermore, in S22, the update expression of the weight parameter of the fractional-order derivative kernel adaptive filter is:

[0026]

[0027] Where, Ω i Represents the weight factor at the i-th update, Ω i-1 Indicates the weight factor for the i-1th update, a i represents the prediction error at the i-th update, r i Indicates the updated value at the i-th update, e i represents the prediction error at the i-th update, A i-1 Represents the feature weight matrix at the i-1th update, P i-1 represents the precision matrix at the time of the i-1th update, ψ i-1 Represents the high-dimensional RRSI data obtained by mapping the expansion of low-dimensional RRSI data in the high-dimensional reproducing kernel Hilbert space. represents high-dimensional RRSI data;

[0028] The prediction error e at the i-th update i The calculation formula is:

[0029] e i =d i -y i ;

[0030] Where, d i Indicates the true value of the i-th updated data, y i Represents the predicted value of the i-th updated data;

[0031] The prediction error a at the i-th update i The calculation formula is:

[0032]

[0033] Where η represents the generalized gamma function ratio, k q,λ (·) represents the Laplace kernel function, p represents the error loss factor, q represents the fractal dimension, λ represents the distribution mean, and α represents the order;

[0034] The calculation formula of the feature weight matrix at the i-1th update is:

[0035]

[0036] Where A i-1 Represents the feature weight matrix at the i-1th update, A i-2Represents the feature weight matrix at the i-2th update, a i-1 Represents the prediction error at the i-1th update, diag represents the diagonal matrix;

[0037] The updated value r at the i-th update i The expression is:

[0038]

[0039] Where, represents the i-th input vector converted to RKHS, v i and v i-1 Respectively represent the α-power of the opposite value of the input vector after being mapped to the high-dimensional space during the i-th and i-1-th updates; i represents the difference value at the time of the i-th update.

[0040] The beneficial effects of the present invention are: compared with the traditional classical kernel adaptive filtering method, the present invention adopts fractional-order derivatives to construct a weight update strategy, which has higher and more robust filtering accuracy; the present invention is the first to introduce fractional-order calculus combined with q Laplace kernel technology into the kernel adaptive filter to construct a positioning system. Experiments show that this algorithm can achieve better positioning accuracy than the most advanced positioning algorithm currently. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 Flowchart of the adaptive data-driven fractional derivative positioning optimization method;

[0042] Figure 2 This is the principle diagram of the kernel adaptive filtering algorithm based on fractional derivatives;

[0043] Figure 3 This is a diagram of classroom indoor positioning training data;

[0044] Figure 4 This is a schematic diagram of laboratory indoor positioning test data;

[0045] Figure 5 This is a diagram of classroom indoor positioning training data;

[0046] Figure 6 This is a diagram of classroom indoor positioning test data;

[0047] Figure 7 This is the prediction performance diagram of each algorithm for classroom indoor positioning X coordinate;

[0048] Figure 8 This is the prediction performance diagram of each algorithm for classroom indoor positioning Y coordinate;

[0049] Figure 9 This is the predicted performance diagram of each algorithm for laboratory indoor positioning X coordinate;

[0050] Figure 10 This is the predicted performance diagram of each algorithm for laboratory indoor positioning Y coordinate. DETAILED DESCRIPTION

[0051] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0052] like Figure 1 As shown, the present invention provides a fractional-order derivative positioning optimization method based on adaptive data driving, comprising the following steps:

[0053] S1. Receive signal strength indicator values ​​at actual locations using sensors within the target area to generate an RSSI dataset.

[0054] S2. Generate and train a fractional-order derivative kernel adaptive filter based on the RSSI dataset;

[0055] S3. Input the actual position and RSSI data set into the trained fractional-order derivative kernel adaptive filter to obtain the target position.

[0056] The present invention uses a mobile sensor to receive the signal strength indicator (RSSI) value at the actual location within the target area, generating RSSI data. An advanced kernel adaptive filter is then trained based on the actual location and RSSI data, specifically for precise positioning. In practical applications, RSSI data of the target to be located is collected and then input into the trained kernel adaptive filter to obtain the target location. Compared to traditional kernel adaptive filtering methods, the present invention is unique in that it cleverly integrates fractional-order derivatives with q-Laplacian kernel technology to construct a weight update strategy, which not only improves filtering accuracy but also enables stable performance in changing environments. This invention is the first to introduce fractional-order calculus into the q-Laplacian kernel adaptive filter to construct a positioning system, ensuring the accuracy of the positioning results. Experimental results demonstrate that the present algorithm surpasses the most advanced positioning technologies currently available in the market in terms of positioning accuracy, demonstrating its potential and application value in the field of high-precision positioning.

[0057] In this embodiment of the present invention, S2 includes the following sub-steps:

[0058] S21, mapping the RSSI dataset into a high-dimensional reproducing kernel Hilbert space;

[0059] S22, using the RSSI data set in the high-dimensional reproducing kernel Hilbert space, updating the weight parameters of the fractional derivative kernel adaptive filter;

[0060] S23. Training the fractional-order derivative kernel adaptive filter after updating the weight parameters.

[0061] In this embodiment of the present invention, in S21, the calculation formula for mapping the RSSI data set to the high-dimensional reproducing kernel Hilbert space RKHS is:

[0062]

[0063] Where u(m) and u(n) represent any two input vectors in the original input space, and They represent the feature mapping amount after converting u(m) and u(n) into feature space, k q,λ (·) represents the Laplace kernel function.

[0064] In the embodiment of the present invention, the Laplace kernel function k q,λ The calculation formula of (·) is:

[0065]

[0066] Where u(m) and u(n) represent any two input vectors in the original input space, q represents the fractal dimension, and λ represents the mean of the distribution.

[0067] In the embodiment of the present invention, in S22, the loss function J(ω i ) is:

[0068]

[0069] In the formula, p represents the error loss factor, τ represents the regularization parameter, and k q,λ (·) represents the Laplace kernel function, e j represents the position error at the i-th update, ω i Denotes the weight parameter in the kernel adaptive filter at the i-th update, D α represents the α-order differential operator, and j represents the index in the measurement sequence.

[0070] In the embodiment of the present invention, in S22, the expression for updating the weight parameter of the fractional-order derivative kernel adaptive filter is:

[0071]

[0072] Where D α J(ω i ) is the fractional order α derivative of the weight parameter update, J(ω i ) represents the loss function of the fractional-order derivative kernel adaptive filter, ω i represents the weight parameter in the kernel adaptive filter at the time of the i-th update, η represents the generalized gamma function ratio, represents the input vector of the ith update converted to RKHS, k q,λ (·) represents the Laplace kernel function, q represents the fractal dimension, λ represents the distribution mean, τ represents the regularization parameter, and a i represents the prediction error at the i-th update, j represents the index in the measurement sequence, sign(·) represents the sign function, and w i Represents the weight factor at the i-th update.

[0073] In the embodiment of the present invention, in S22, the update expression of the weight parameter of the fractional-order derivative kernel adaptive filter is:

[0074]

[0075] Where, Ω i Represents the weight factor at the i-th update, Ω i-1 Indicates the weight factor for the i-1th update, a i represents the prediction error at the i-th update, r i Indicates the updated value at the i-th update, e i represents the prediction error at the i-th update, A i-1 Represents the feature weight matrix at the i-1th update, P i-1 represents the precision matrix at the time of the i-1th update, ψ i-1 Represents the high-dimensional RRSI data obtained by mapping the expansion of low-dimensional RRSI data in the high-dimensional reproducing kernel Hilbert space. represents high-dimensional RRSI data;

[0076] The prediction error e at the i-th update i The calculation formula is:

[0077] e i =d i -y i ;

[0078] Where, d i Indicates the true value of the i-th updated data, y i Represents the predicted value of the i-th updated data;

[0079] The prediction error a at the i-th update i The calculation formula is:

[0080]

[0081] Where η represents the generalized gamma function ratio, k q,λ (·) represents the Laplace kernel function, p represents the error loss factor, q represents the fractal dimension, λ represents the distribution mean, and α represents the order;

[0082] The calculation formula of the feature weight matrix at the i-1th update is:

[0083]

[0084] Where A i-1 Represents the feature weight matrix at the i-1th update, A i-2 Represents the feature weight matrix at the i-2th update, a i-1 Represents the prediction error at the i-1th update, diag represents the diagonal matrix;

[0085] The updated value r at the i-th update i The expression is:

[0086]

[0087] Where, represents the i-th input vector converted to RKHS, v i and v i-1 Respectively represent the α-power of the opposite value of the input vector after being mapped to the high-dimensional space during the i-th and i-1-th updates; i represents the difference value at the time of the i-th update.

[0088] In the embodiment of the present invention, the principle of the q Laplace kernel adaptive filtering algorithm based on fractional calculus is as follows: Figure 2 As shown. Define a sequence sample set {u(i), d(i)}, where u(i) represents the input RSSI data at time i to be filtered, and d(i) represents the corresponding actual position; k q,λ (·) represents the kernel function, which can map the input RRSI data u(i) into the high-dimensional reproducing kernel Hilbert space, thereby using data processing in the high-dimensional space to learn the nonlinear relationship of the input RRSI data u(i); define The high-dimensional input RRSI data u(i) is mapped to the reproducing kernel Hilbert space based on the kernel function.

[0089] This paper demonstrates the superiority of the proposed high-precision positioning adaptive data processing method through indoor positioning experiments. The experiments used two real-world indoor positioning datasets: a classroom with high levels of interference and a laboratory with moderate interference, to demonstrate the performance of the present invention.

[0090] In the experiment, FrqLaKMPE was adopted as a specific implementation of the data processing method proposed in this invention. It uses the principle of fractional calculus to optimize the filtering process through kernel adaptation, thereby achieving high-precision positioning effects in complex indoor environments.

[0091] The experiment follows the steps of the high-precision positioning adaptive data processing method. First, the signal receiver is placed Figure 3 and Figure 4 The signal receivers were placed on the training points marked in the figure to capture and record the RSSI signal strength value at each point, forming the training data sets of the two experimental scenarios. Figure 5 and Figure 6 The RSSI values ​​of each point are recorded at a series of random test points as shown in the figure to create the test data sets for the two experiments. The training data set and the test data set contain data sequences. The input RSSI data and the corresponding actual positions of the two data sets are known. First, the signal receivers are placed as follows: Figure 3 and Figure 4 At the training data reference point shown in , the RSSI value of each position is recorded to generate input RSSI data, and then the training data sets corresponding to the two experiments are generated respectively. Subsequently, in order to test the performance of the proposed data processing method, the signal receivers are placed as follows Figure 5 and Figure 6 At the randomly generated test points shown, the RSSI value at each location is recorded to generate input RSSI data and test datasets corresponding to the two experiments. The training and test datasets contain the data sequence {u(i), d(i)}. For both datasets, the input RSSI data u(i) and the corresponding actual location information d(i) are known.

[0092] During the experiment, the input RSSI data u(i) and the corresponding actual location d(i) of the training dataset were first fed into the FrqLaKMPE filter for learning. Subsequently, only the input RSSI data u(i) of the test dataset was fed into the kernel adaptive filter of the present invention to obtain the corresponding estimated location y(i), thereby achieving online application functionality. Finally, the mean squared error (MSE) was used to measure the difference between the actual location d(i) of the test dataset and the estimated location y(i) obtained during the test, reflecting the accuracy of the positioning data processing.

[0093] The experiments were conducted in the two representative indoor positioning experimental scenarios described above, and compared with the classic kernel adaptive filtering algorithms (KRLS, KLMS, KLMP, KRGMC, KGMC, KMPE), fractional-order Gaussian kernel adaptive filter (FrgKMPE), classic indoor positioning algorithms (K nearest neighbor, trilateration, naive Bayes) and machine learning-based algorithms (transfer learning).

[0094] The performance of the high-precision positioning adaptive data processing method proposed in this invention is compared with other kernel adaptive filtering algorithms. Figure 7-10As shown. The results show that the proposed FrqLaKMPE uses the least squares method to update the weights, has a lower mean square error during the iteration process, and is better than methods such as KLMS that use stochastic gradient descent to update the weights. In addition, FrqLaKMPE has a better convergence speed than methods such as KLMS and KRLS. In summary, the high-precision positioning adaptive data processing method proposed in the present invention shows significant advantages in the performance comparison with other kernel adaptive filtering algorithms, and its steady-state filtering accuracy is the highest. Compared with the classical kernel adaptive filtering method and the Gaussian kernel adaptive filtering method based on fractional calculus, this method can also maintain high positioning accuracy and stability.

[0095] The indoor positioning prediction errors and variances of the proposed method and the comparison algorithms are shown in Tables 1 and 2. The results show that the proposed method has the highest filtering accuracy and higher robustness compared with the classic kernel adaptive filtering algorithm, the classic indoor positioning method, and the indoor positioning algorithm based on machine learning.

[0096] In summary, compared with the classical kernel adaptive filtering algorithm, the classical indoor positioning method and the indoor positioning algorithm based on machine learning, the invented adaptive data processing method for high-precision positioning has significant advantages in positioning prediction accuracy.

[0097] Table 1

[0098] algorithm Prediction error (m) <![CDATA[Variance (m 2 )]]> The present invention 1.84 0.85 KRLS 1.91 0.89 KLMP 2.25 0.86 KLMS 2.34 0.91 KRGMC 1.84 1.37 KGMC 1.91 0.91 KMPE 2.01 0.98 FrgKMPE 1.87 0.90 K-nearest neighbor algorithm 1.94 1.14 Naive Bayes algorithm 2.42 2.84 Trilateration 4.79 1.46 Transfer learning algorithm 2.06 1.80

[0099] Table 2

[0100]

[0101]

[0102] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.

Claims

1. A fractional-order derivative positioning optimization method based on adaptive data driving, characterized in that: The following steps are involved: S1. Receive signal strength indicator values ​​at actual locations using sensors within the target area to generate an RSSI dataset. S2. Generate and train a fractional-order derivative kernel adaptive filter based on the RSSI dataset; S3, input the actual position and RSSI data set into the trained fractional derivative kernel adaptive filter to obtain the target position; The S2 includes the following sub-steps: S21, mapping the RSSI dataset into a high-dimensional reproducing kernel Hilbert space; S22, using the RSSI data set in the high-dimensional reproducing kernel Hilbert space, updating the weight parameters of the fractional derivative kernel adaptive filter; S23, training the fractional-order derivative kernel adaptive filter after updating the weight parameters; In the S22, the expression for updating the weight parameter of the fractional-order derivative kernel adaptive filter is: ； Where, is the fractional order of weight parameter update Second derivative, represents the loss function of the fractional derivative kernel adaptive filter, Indicates the The weight parameters in the kernel adaptive filter are updated. represents the generalized gamma function ratio, Indicates the first updated input vector, represents the Laplace kernel function, represents the fractal dimension, represents the mean of the distribution, represents the regularization parameter, Indicates the The prediction error at the update time is represents the index in the measurement sequence, represents the symbolic function, Indicates the The weight factor at the time of the update; In S22, the update expression of the weight parameter of the fractional-order derivative kernel adaptive filter is: ； Where, Indicates the The weight factor for the update, Indicates the The weight factor for the update, Indicates the The prediction error at the update time is Indicates the The updated value at the time of update, e i Indicates the The prediction error at the update time, A i-1 Represents the feature weight matrix at the i-1th update, P i-1 represents the precision matrix at the time of the i-1th update, Represents the high-dimensional RRSI data obtained by mapping the expansion of low-dimensional RRSI data in the high-dimensional reproducing kernel Hilbert space. represents high-dimensional RRSI data; The said The prediction error at update The calculation formula is: ； Where, Indicates the The true value of the updated data, Indicates the The predicted value of the updated data; The said The prediction error at update The calculation formula is: ； Where, represents the generalized gamma function ratio, represents the Laplace kernel function, represents the error loss factor, represents the fractal dimension, represents the mean of the distribution, Indicates the order; The calculation formula of the feature weight matrix during the i-1th update is: Where A i-1 Represents the feature weight matrix at the i-1th and i-2th updates, Represents the prediction error at the i-1th update, diag represents the diagonal matrix; The updated value r at the i-th update i The expression is: ； ； Where, Indicates the first input vector, v i and v i-1 Respectively represent Second and The input vector at the time of the update is mapped to the opposite value of the high-dimensional space Power; z i Indicates the The difference value when updating.

2. The adaptive data-driven fractional derivative positioning optimization method according to claim 1, characterized in that: In S21, the calculation formula for mapping the RSSI data set to the high-dimensional reproducing kernel Hilbert space RKHS is: ； Where, and Represent any two input vectors in the original input space, and Respectively indicate and The feature mapping amount after conversion to feature space, represents the Laplace kernel function.

3. The adaptive data-driven fractional derivative positioning optimization method according to claim 2, characterized in that: The Laplace kernel function The calculation formula is: ； Where, and Represent any two input vectors in the original input space, represents the fractal dimension, Represents the mean of the distribution.

4. The adaptive data-driven fractional derivative positioning optimization method according to claim 1, characterized in that: In S22, the loss function of the fractional-order derivative kernel adaptive filter is The expression is: ； Where, represents the error loss factor, represents the regularization parameter, represents the Laplace kernel function, Indicates the The position error at the update time is Indicates the The weight parameters in the kernel adaptive filter are updated. express order differential operators, Represents an index into the measurement sequence.

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