Fractional derivative positioning optimization method based on adaptive data driving

Abstract

The invention discloses a fractional derivative positioning optimization method based on adaptive data driving, which belongs to the technical field of radio positioning, and comprises the following steps: S1, receiving a signal strength indication value at an actual position by using a sensor in a target area, and generating an RSSI data set; s2, according to the RSSI data set, generating and training a fractional derivative kernel adaptive filter; and S3, inputting the actual position and the RSSI data set into the trained fractional derivative kernel adaptive filter to obtain a target position. Compared with a traditional classical kernel adaptive filtering method, the method has the advantages that a fractional order derivative is adopted to construct a weight updating strategy, and higher and more stable filtering precision is achieved; according to the method, the fractional calculus is combined with the q Laplacian kernel technology to be introduced into the kernel adaptive filter to construct the positioning system for the first time, and experiments show that the algorithm can obtain better positioning precision compared with the current most advanced positioning algorithm.

Description

Technical Field

[0001] The 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] As a revolutionary technology that emerged in the early 21st century, the Internet of Things has been widely used in industrial and daily life scenarios. The Internet of Things connects people and objects through heterogeneous communication networks to achieve information exchange and sharing. Among them, positioning technology, such as GPS, provides users with location-based personalized services such as navigation, weather forecasts and social networks, greatly improving the practicality and convenience of services.

[0003] At present, there are many indoor positioning technologies, and the required hardware and supporting principles are different. Common indoor positioning technologies include wireless WIFI technology, Bluetooth technology, ultra-wideband technology, infrared technology, and machine vision positioning. These technologies have their own advantages and disadvantages in terms of hardware structure complexity, positioning accuracy, and environmental sensitivity. WIFI and Bluetooth positioning technologies appeared earlier and are important components of indoor wireless LANs. WLAN has been deployed on a large scale with communication as the goal, and has achieved a large number of positioning tasks. Ultra-wideband technology is based on the concept of radar and is now used for high-speed short-range communication. It is a positioning technology with good accuracy. Infrared signals are electromagnetic waves that propagate at the speed of light, just like radio waves. It is quite complicated to measure time indoors with infrared signals, and the clock requirements are very strict and the cost is high. Therefore, infrared technology is less used than WIFI and Bluetooth technologies. In practical applications, different positioning technologies should be selected according to the specific indoor environment.

[0004] The fingerprint matching algorithm uses the signal information formed by signal reflection to establish a fingerprint signal database offline, and then calculates the position distance online by actually measuring the signal strength. The Naive Bayes algorithm and the K nearest neighbor algorithm are classic fingerprint matching positioning algorithms in the field of machine learning. Although these two algorithms can achieve good positioning results in indoor environments with simple noise composition, the positioning effect of the above two methods in complex and changeable indoor environments is not ideal, and the positioning error is still at the meter level. In addition, in recent years, deep learning has surpassed traditional machine learning techniques in various fields, especially in computer vision and image fields, and has received great attention and wide application. Many researchers have also applied deep learning to indoor positioning problems and achieved certain results. However, the process of building a database for deep learning is time-consuming and expensive, so it requires advanced computing power. In addition, deep learning has certain challenges in determining the best model type and structure for a specific task and evaluating the effectiveness of a specific architecture or algorithm in the task. Therefore, finding a lightweight online positioning method that uses a limited number of smart devices is still an urgent problem that people need to solve.

[0005] In the field of indoor positioning technology, fingerprint recognition systems based on received signal strength indication are widely used due to their high positioning accuracy and relatively economical deployment cost. This system is mainly divided into two stages: offline stage and online stage. In the offline stage, the system creates a fingerprint database by measuring RSSI values ​​using sensors at preset reference points. These reference points are pre-defined and evenly distributed, and they serve as the benchmark for location fingerprints. By taking the average value of multiple measurements, the error caused by fluctuations can be reduced, thereby improving the accuracy of the fingerprint database. In the online stage, the RSSI measurement value of the user's device at an unknown location is used to generate a new fingerprint, which is then compared with the data in the fingerprint database. By using well-trained prediction models such as the nearest neighbor algorithm, the K nearest neighbor algorithm, and the weighted K nearest neighbor algorithm, the system is able to estimate the user's location. These algorithms match the new fingerprint by comparing the similarity with the fingerprints in the database, among which the weighted K nearest neighbor algorithm gives different weights according to the similarity to improve positioning accuracy.

[0006] Although these indoor positioning data processing methods have achieved remarkable achievements in accuracy and efficiency, in the context of widespread deployment of IoT devices, many resource-constrained smart devices require lightweight online auxiliary positioning methods. These methods need to adapt to resource-constrained environments while solving the problem of high cost and time-consuming database construction. RSSI-based fingerprint recognition systems continue to be developed and applied due to their effectiveness in asset tracking, indoor navigation, and location-based services. With the advancement of technology and the reduction of costs, it is expected that such systems will play a more important role in the development of indoor positioning technology in the future. 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, using the sensor to receive the signal strength indicator value at the actual position in the target area to generate an RSSI data set;

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

[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 data set 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] In the formula, 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, and 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] Further, 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 α-order derivative of the weight parameter update, J(ω i ) represents the loss function of the fractional derivative kernel adaptive filter, ω i represents the weight parameter in the kernel adaptive filter at 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] In the formula, Ω i represents the weight factor at the i-th update, Ω i-1 represents the weight factor for the i-1th update, a i represents the prediction error at the i-th update, r i represents 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 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] In the formula, 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, and diag represents the diagonal matrix;

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

[0038]

[0039] In the formula, represents the i-th input vector converted to RKHS, v i and v i-1 Respectively represent the α-th 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; z i Represents the difference value at 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, and 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 A 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 schematic 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 schematic 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] Fig. 9 This is the predicted performance diagram of each algorithm for laboratory indoor positioning X coordinate;

[0050] Fig.10 This is the prediction 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 in conjunction with 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, using the sensor to receive the signal strength indicator value at the actual position in the target area to generate an RSSI data set;

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

[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 indication RSSI value at the actual position in the target area to form RSSI data; then an advanced kernel adaptive filter is trained based on the actual position and RSSI data, and the filter is dedicated to precise positioning; in practical applications, the RSSI data of the target to be positioned is collected and then input into the trained kernel adaptive filter to obtain the target position. Compared with the traditional kernel adaptive filtering method, the uniqueness of the present invention lies in the clever fusion of fractional-order derivatives and q Laplace kernel technology to construct a weight update strategy, which not only improves the filtering accuracy, but also enables it to maintain stable performance in a changing environment. The present invention introduces fractional-order calculus into the q Laplace kernel adaptive filter for the first time to construct a positioning system, ensuring the accuracy of the positioning results. Experimental results show that the algorithm of the present invention surpasses the most advanced positioning technology on the current market in terms of positioning accuracy, showing 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 data set 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 the 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] In the formula, 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, and 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] In the formula, 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.

[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 represents 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 α-order derivative of the weight parameter update, J(ω i ) represents the loss function of the fractional derivative kernel adaptive filter, ω i represents the weight parameter in the kernel adaptive filter at 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] In the formula, Ω i represents the weight factor at the i-th update, Ω i-1 represents the weight factor for the i-1th update, a i represents the prediction error at the i-th update, r i represents 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 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] In the formula, 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, and diag represents the diagonal matrix;

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

[0086]

[0087] In the formula, represents the i-th input vector converted to RKHS, v i and v i-1 Respectively represent the α-th 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; z i Represents the difference value at 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 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] The present invention verifies the superiority of the proposed high-precision positioning adaptive data processing method through indoor positioning experiments. The experiment uses two real-scene indoor positioning data sets, one in a classroom with a lot of interference and the other in a laboratory with a moderate interference level, to demonstrate the performance of the present invention.

[0090] In the experiment, FrqLaKMPE was used as a specific implementation of the data processing method proposed in the present invention. It uses the principle of fractional calculus to optimize the filtering process through kernel adaptation, thereby achieving high-precision positioning effect 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 at the training points marked in the figure to capture and record the RSSI signal strength value at each point, forming the training data set for the two experimental scenarios. Subsequently, in order to evaluate the performance of the proposed method, the signal receivers were placed at Figure 5 and Figure 6 The RSSI value of each point is also recorded at a series of random test points depicted in Figure 1 to create 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 The RSSI value of each position is recorded at the training data reference point shown in Figure 1, and the input RSSI data is generated, thereby generating the training data sets corresponding to the two experiments. 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 in the figure, the RSSI value of each position is recorded, the input RSSI data is generated, and the test data sets corresponding to the two experiments are generated. The training data set and the test data set contain the data sequence {u(i), d(i)}, and the input RSSI data u(i) and the corresponding actual location information d(i) of the two data sets are known.

[0092] During the experiment, the input RSSI data u(i) and the corresponding actual position d(i) of the training data set are first input into FrqLaKMPE for filtering learning. Then, only the input RSSI data u(i) of the test data set is input into the kernel adaptive filter of the present invention to obtain the corresponding estimated position y(i), thereby realizing the function of online application. Finally, the mean square error (MSE) is used to measure the difference between the actual position d(i) of the test data set and the estimated position y(i) obtained by the test, reflecting the accuracy of positioning data processing.

[0093] The experiments were compared with 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) in the two representative indoor positioning experimental scenarios described above.

[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 updates the weights based on the least squares method, has a lower mean square error in the iterative 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 method of the present invention and the comparison algorithm are shown in Table 1 and Table 2. The results show that the method proposed by the present invention 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 FrKMPE 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 Algorithms 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 should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope 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, using the sensor to receive the signal strength indicator value at the actual position in the target area to generate an RSSI data set; S2. Generate and train a fractional-order derivative kernel adaptive filter based on the RSSI data set; S3. Input the actual position and RSSI data set into the trained fractional-order derivative kernel adaptive filter to obtain the target position.

2. The adaptive data-driven fractional-order derivative positioning optimization method according to claim 1 is characterized in that: The S2 comprises the following sub-steps: S21, mapping the RSSI data set 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.

3. The adaptive data-driven fractional-order derivative positioning optimization method according to claim 2 is characterized in that: In S21, the calculation formula for mapping the RSSI data set to the high-dimensional reproducing kernel Hilbert space RKHS is: In the formula, 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, and k q,λ (·) represents the Laplace kernel function.

4. The adaptive data-driven fractional-order derivative positioning optimization method according to claim 3 is characterized in that: The Laplace kernel function k q,λ The calculation formula of (·) is: 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.

5. The adaptive data-driven fractional-order derivative positioning optimization method according to claim 2 is characterized in that: In S22, the loss function J(ω i ) is: 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 represents 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.

6. The adaptive data-driven fractional-order derivative positioning optimization method according to claim 3 is characterized in that: In S22, the expression for updating the weight parameter of the fractional-order derivative kernel adaptive filter is: Where D α J(ω i ) is the fractional α-order derivative of the weight parameter update, J(ω i ) represents the loss function of the fractional derivative kernel adaptive filter, ω i represents the weight parameter in the kernel adaptive filter at 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.

7. The adaptive data-driven fractional-order derivative positioning optimization method according to claim 2 is characterized in that: In S22, the update expression of the weight parameter of the fractional-order derivative kernel adaptive filter is: In the formula, Ω i represents the weight factor at the i-th update, Ω i-1 represents the weight factor for the i-1th update, a i represents the prediction error at the i-th update, r i represents 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 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; The prediction error e at the i-th update i The calculation formula is: e i =d i -y i ; 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; The prediction error a during the i-th update i The calculation formula is: 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; The calculation formula of the feature weight matrix during the i-1th update is: In the formula, 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, and diag represents the diagonal matrix; The update value r at the i-th update i The expression is: In the formula, represents the i-th input vector converted to RKHS, v i and v i-1 Respectively represent the α-th 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; z i Represents the difference value at the i-th update.

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