Indoor positioning system based on empirical mode decomposition and spatial auto-regressive neural network

Abstract

The application discloses an indoor positioning system based on empirical mode decomposition and spatial autoregressive neural network, aiming at solving the problems of insufficient positioning accuracy and reliability of traditional ultra-wideband indoor positioning. The system is composed of a base station, a tag, a background server and a data processing terminal. The base station and the tag measure the distance through the ultra-wideband signal, the tag sends the positioning data to the server, and then the real-time positioning result is obtained through the data processing terminal. The main source of positioning error is the multipath effect of indoor signal. Empirical mode decomposition is used to reduce the noise in the signal, then spatial autoregressive neural network is used to model the multipath effect, and the multipath error is compensated, and finally the accurate position of the tag is calculated. Compared with the prior art, the application has higher positioning accuracy and robustness, the system network is easy to build, has strong portability, simple equipment, and is easy to popularize, and has great advantages and commercial prospects in the complex indoor positioning scene.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of high-precision indoor positioning, and is applied to the positioning data denoising optimization and solving process of indoor ultra-wideband positioning, and in particular to an indoor positioning system based on empirical mode decomposition and spatial autoregressive neural network. BACKGROUND

[0002] Nowadays, the society has begun to move from the Internet era to the Internet of Things era, and the importance of location information is obvious. At the same time, the role of location-based positioning technology in the Internet of Things has become a top priority. The positioning technology under the Internet is mainly outdoor positioning, which mainly relies on satellites in the sky and ground communication base stations to achieve accurate positioning. The positioning technology under the Internet of Things also involves high-precision indoor positioning, which is not the field that traditional GPS positioning technology is good at. Because of the sheltering of buildings and other factors, the GPS signal will be severely disturbed, so its positioning accuracy will also be sharply attenuated. In addition, the complex and variable environment in the room, the signal will be hindered by various objects, causing the signal to produce reflection, scattering and other phenomena, resulting in serious signal propagation. This is also the main reason affecting the accuracy of various indoor positioning technologies. There are mainly indoor positioning technologies based on Bluetooth, WIFI, inertial navigation and other technologies, which are widely used but have relatively low accuracy. In indoor positioning and spatial perception technology, ultra-wideband technology is a latecomer and is attracting more and more attention. Its large bandwidth characteristics make it have strong ability to penetrate obstacles, anti-interference ability and multi-path resolution ability. These characteristics make it have strong competitiveness in the field of indoor positioning.

[0003] In the field of ultra-wideband indoor positioning, time-based ultra-wideband positioning technology has broken through the meter-level precision that traditional positioning methods cannot break through, but due to the influence of multi-path factors in the indoor environment, the time-based positioning method has errors caused by multi-path, and is the main error source. Therefore, in the existing time-based ultra-wideband indoor positioning technology, the suppression of multi-path error has always been placed in a key position. Multi-path error can be modeled according to its regularity in time and space, and then the observed value is corrected to eliminate the interference of multi-path error on the positioning result. SUMMARY

[0004] The purpose of the present application is to address the deficiencies of the prior art due to the fact that indoor positioning signals are susceptible to multipath effects, proposing an indoor positioning system based on empirical mode decomposition and spatial autoregressive neural networks, which uses base stations, tags, a background server and a data processing terminal to build the positioning system, uses empirical mode decomposition to reduce noise in the signal, uses a spatial autoregressive neural network to model the multipath effect and compensate for multipath errors, and finally calculates the accurate position of the tag to eliminate the effects of multipath errors and improve positioning accuracy. Since the present application does not require the laying of a large number of additional hardware devices and does not require changes to existing hardware devices, it is easy to promote and has great advantages and commercial prospects in high-precision indoor positioning application scenarios.

[0005] The purpose of the present application is achieved as follows:

[0006] An indoor positioning system based on empirical mode decomposition and spatial autoregressive neural networks, the system comprising master base stations, slave base stations, switches, positioning tags, a background server and a data processing terminal, the master base stations and slave base stations being several; the switches are connected by optical fiber to the master base stations, slave base stations and background server, the background server is connected by optical fiber to the data processing terminal, and the positioning tags transmit signals to the master base stations and slave base stations in a wireless manner; the indoor positioning process is implemented and comprises the following steps:

[0007] Step 1: sample collection

[0008] The indoor site is divided into grid areas, and the TWR (Two-Way-Ranging) data at the intersection of the grid is collected as prior data information for training the spatial autoregressive neural network;

[0009] Step 2: model training

[0010] The collected TWR data is processed to obtain a data format that meets the network input, the network training parameters are adjusted, and the optimal model is trained;

[0011] Step 3: empirical mode decomposition filtering

[0012] The positioning tag communicates with the base stations using ultra-wideband signals and performs TWR ranging. After the tag obtains the distances to each base station, it sends the TWR data to the background server side through the Bluetooth GATT protocol, and uses the empirical mode decomposition algorithm to filter out the noise in the TWR data;

[0013] Step 4: model application

[0014] The Newton iteration algorithm is used to solve the preliminary tag coordinates, and the spatial autoregressive neural network is used to correct the obtained TWR data;

[0015] Step 5: coordinate calculation

[0016] The Newton iteration algorithm and the corrected TWR data are used to solve the coordinates of the tag, that is, the accurate tag coordinates.

[0017] The TWR is a bilateral two-way ranging, and its observation equation is calculated by the following formula (1):

[0018]

[0019] Where T f is the time for the signal flying in the air from the tag sending the signal to the base station receiving the signal, R a is the time experienced by the tag from sending the first data packet to receiving the second data packet returned by the base station; D b is the sending delay time from the base station receiving the first data packet to sending the second data packet; D a is the sending delay time from the tag receiving the second data packet to sending the third data packet; R b is the time experienced by the base station from sending the second data packet to receiving the third data packet returned by the base station; the flight time T f multiplied by the speed of light is the distance between the tag and the base station; when there is no obstruction, the error of ranging is the clock drift of the base station and the tag, and its calculation method is calculated by the following formula (2):

[0020]

[0021] Where is the estimated value of the flight time, T f is the true value of the flight time, and e is the deviation of the actual frequency value of the clock from the nominal frequency value, with a unit of ppm, that is, one millionth.

[0022] The empirical mode decomposition algorithm specifically includes:

[0023] Suppose that the signal is composed of a finite number of intrinsic mode functions (IMF) and residual signals, and each IMF is obtained by the following method:

[0024] Suppose that the original signal is x(t), all the maximum points of x(t) are found, the maximum envelope e max (t) is found by a cubic spline function, all the minimum points of x(t) are found, and the minimum envelope e min (t) is found by a cubic spline function; the average envelope m1(t) is obtained by averaging the two envelopes:

[0025]

[0026] Subtracting m1(t) from the original signal obtains a new signal removing low frequency components

[0027]

[0028] With Repeat the above steps as a new signal until The following conditions are met: (1) for the entire signal, the difference between the number of poles and zeros cannot exceed 1; (2) at any point, the average value of the maximum and minimum envelope lines is zero;

[0029] Then, the first IMF component of the original signal x(t) is obtained:

[0030]

[0031] By subtracting the first IMF imf1(t) component from the original signal x(t), a new signal r1(t) removing high frequency components is obtained:

[0032] r1(t) = x(t) - imf1(t) (6)

[0033] Repeat the above process for r1(C) to obtain the second IMF component imf2(t); then repeat the above process until the nth IMF component is less than the preset value, and finally x(t) is expressed as:

[0034]

[0035] Then the signal is decomposed into several high frequency components imf i (t) plus a stationary trend item c(t).

[0036] The Newton iteration algorithm is represented by the following equation (8):

[0037] Δx (k) = (F′(x (k) )) -1 (-F(x (k) )) (8)

[0038] The distance between the base station and the tag is represented by the following equation:

[0039]

[0040] Where (x, y, z) is the coordinate to be calculated for the tag, (x i , y i , z i ) is the coordinate of one of the base stations, d i is the distance between the two base stations and the tag; since there are a number of base stations in total, rewrite equation (9) to obtain the following equations:

[0041]

[0042] Let the coordinates (x, y, z) be a vector x, then the process of variable iteration is represented as:

[0043] x (k+1) = x (k) + Δx (k) (11)

[0044] Let equation (11) be a vector F(x), according to Newton iteration method, we have:

[0045] Δx (k) = (F'(x (k) )) -1 (-F(x (k) )) (12)

[0046] Where (F'(x (k) )) -1 is the inverse of the Jacobian matrix of F(x (k) ); calculate Δx (k) , then update the coordinate vector through formula (11) to complete one iteration; iteration stops when Δx meets the accuracy requirement.

[0047] The spatial autoregressive neural network can model the indoor multipath error, because in the indoor environment, the electromagnetic wave will cause the signal to have multipath effect due to the reflection and scattering of objects in the propagation process, therefore, the multipath error is correlated in space, the spatial correlation is considered as the nonlinear relationship between the spatial distance and the spatial weight, that is, the multipath error at any point in space can be modeled as follows:

[0048] e unkown = f(d)e T (13)

[0049] Where e unkown is the unknown multipath error at a point in space, f is a nonlinear mapping from distance to spatial weight, d is the distance vector, e is the observation error vector, and T is the transpose of the matrix;

[0050] The spatial distance is calculated by Euclidean distance:

[0051]

[0052] Where d i is the distance between the ith known point and the unknown point;

[0053] To build a model that relates the point multipath error and the unknown point multipath error, a nonlinear function between the spatial weight of the ith unknown point and the spatial distance is defined as follows:

[0054] w i =(w i1 , w i2 , …, w in ) = f(d i1 , d i2 , …, d in ) (15)

[0055] w i denotes the spatial weight vector of the ith point, w ij denotes the spatial weight between the ith point and the jth point, d ij is given by equation (15);

[0056] To characterize the complex relationship between the spatial weight and the distance, a spatial autoregressive neural network is constructed to fit w i ; the input of the network is the distance from the unknown point to the known points, and the output is the spatial weight; after multiplying the spatial weight with the observation vector, the predicted multipath error of the unknown point is obtained, i.e., e

[0057] e unkown = SANN(d i1 , d i2 , …, d in ) e T (16)

[0058] e unkown is the multipath error of the unknown point, d in is the distance from the ith unknown point to the nth known point, SANN denotes the spatial autoregressive neural network, and e is the error observation vector;

[0059] In the prediction, the unknown point and the known point are different, but in the training of the network, the unknown point will be the same as one of the known points, i.e., i equals j in equations (14) and (15), then d ii will be equal to zero, and w ii will denote the weight of the ith point itself; to prevent overfitting, this weight should be set to zero; therefore, the standard weight matrix should be multiplied by before obtaining the final spatial weight matrix to eliminate the above-mentioned effect:

[0060] w′ i = w i K (17)

[0061] K is the unit matrix, and the ith element on the diagonal is zero.

[0062] The base station and the tag communicate using ultra-wideband signals to exchange data, and then perform bilateral two-way ranging to obtain the required distance.

[0063] The positioning tag sends data packets containing the tag ID and TWR data to the backend server via Bluetooth at a frequency of 10Hz.

[0064] The actual coordinates of the base station and the intersection of the grid were measured and recorded using a millimeter-level laser rangefinder.

[0065] This invention utilizes prior information to train a neural network, and then uses the neural network to compensate for the TWR measurement value to improve positioning accuracy. Compared with existing technologies, this technology has higher stability and positioning accuracy, and the equipment is easy to deploy without the need for a large number of hardware devices. In addition, the system has good software environment compatibility and does not require too many changes to the corresponding software and hardware devices. Therefore, this system is easier to promote and has great advantages and commercial application prospects in complex indoor positioning application scenarios. Attached Figure Description

[0066] Figure 1 This is a schematic diagram of the system structure of the present invention;

[0067] Figure 2 This is a schematic diagram of the algorithm flow of the present invention;

[0068] Figure 3 This is a schematic diagram of the structure of a spatial autoregressive neural network;

[0069] Figure 4 This is a performance comparison chart of the positioning results of the present invention and the positioning results of the prior art. Detailed Implementation

[0070] See Figure 1 This invention constructs an ultra-wideband indoor positioning system based on several base stations, positioning tags, and a data processing terminal. The base stations and tags are battery-powered, and the tags transmit positioning data to the data processing terminal via Bluetooth. The data processing terminal first performs noise reduction filtering on the raw positioning data using empirical mode decomposition, then calculates coarse coordinates using Newton's iteration method. These coordinates are input into a spatial autoregressive neural network, and the output compensates for the positioning data. Finally, Newton's iteration method is used again to calculate the coordinates, outputting accurate positioning results, which are then visualized on the terminal screen.

[0071] The base station and the tag communicate using ultra-wideband signals to exchange data, and then perform bilateral, bidirectional ranging to obtain the required distance. The positioning tag sends data packets containing the tag ID and TWR data to the backend server via Bluetooth at a frequency of 10Hz. The actual coordinates of the base station and the grid intersection are measured and recorded using a millimeter-level laser rangefinder.

[0072] The application is further described in detail through specific examples.

[0073] Examples

[0074] Referring to Figure 1 , the test site of the application is a 6x5m rectangular conference room, and the experimental area is divided into a 1x1m grid in advance. The base stations are located at the four corners of the rectangular area, and the heights of the four base stations are 1.8m, 1.8m, 2m, and 2m, respectively.

[0075] An ultra-wideband indoor positioning system is formed by using a plurality of base stations 1, positioning tags 2, and a data processing terminal 3. The base stations and the tags use ultra-wideband signals to communicate, complete TWR ranging, and the tags send the TWR ranging data to the data processing terminal through Bluetooth. First, the TWR data of a plurality of grid points is collected and saved to the data processing terminal, and the data is used to train the spatial autoregressive neural network.

[0076] Referring to Figure 2 , during real-time positioning, the received TWR data is first filtered by using empirical mode decomposition 4 for noise reduction, and then a Newton iteration method 5 is used to solve a rough coordinate value. The coordinate value is input into the spatial autoregressive neural network 6 (as shown in the accompanying drawings) to correct the data, and finally a Newton iteration method 5 is used again to obtain an accurate coordinate value. The coordinate value can be visually displayed on the data processing terminal. Figure 3

[0077] Referring to Figure 4 , the cumulative distribution function of the traditional positioning technology has a positioning error of 150mm at the 80% quantile point, and the cumulative distribution function of the positioning technology of the application has a positioning error of 80mm at the 80% quantile point. It can be seen that the ultra-wideband indoor positioning method of the application based on empirical mode decomposition and spatial autoregressive neural network can effectively alleviate various positioning errors, and the positioning accuracy and robustness of the system are better than those of existing positioning technologies. The above is only a further description of the application and is not intended to limit the application. Equivalent implementations without departing from the spirit and scope of the application should be included in the scope of the claims of the application.​

Claims

1. An indoor positioning system based on empirical mode decomposition and spatial autoregressive neural network, characterized in that, The system includes a main base station, slave base stations, switches, positioning tags, a back-end server, and a data processing terminal. There are several main base stations and slave base stations. The switches are connected to the main base stations, slave base stations, and the back-end server via fiber optic cables. The back-end server is connected to the data processing terminal via fiber optic cables. The positioning tags transmit signals wirelessly to the main base stations and slave base stations. The indoor positioning process specifically includes the following steps: Step 1: Sample Collection The indoor space was divided into grid areas, and TWR (Two-Way-Ranging) data at the intersections of the grids were collected as prior data for training the spatial autoregressive neural network. Step 2: Train the model The collected TWR data is processed to obtain a data format that conforms to the network input, the network training parameters are adjusted, and the optimal model is trained. Step 3: Empirical Mode Decomposition Filtering The positioning tag uses ultra-wideband signals to communicate with base stations and perform TWR ranging. After obtaining the distance to each base station, the tag sends the TWR data to the back-end server via Bluetooth GATT protocol, and uses empirical mode decomposition algorithm to filter out noise in the TWR data. Step 4: Model Application The initial label coordinates were obtained using the Newton-Raphson iterative algorithm, and the obtained TWR data was corrected using a spatial autoregressive neural network. Step 5: Coordinate Calculation The coordinates of the label are obtained by using Newton's iterative algorithm and the corrected TWR data, which are the accurate label coordinates.

2. The indoor positioning system based on empirical mode decomposition and spatial autoregressive neural network according to claim 1, characterized in that, The TWR is a two-way, two-sided ranging system, and its observation equation is calculated by the following equation (1): (1)； in This refers to the time it takes for a signal to travel through the air from when the tag sends the signal to when the base station receives it. The time elapsed from when the tag sends the first data packet to the base station until it receives the second data packet back from the base station; The transmission delay time is from when the base station receives the first data packet to when it sends the second data packet. The transmission delay time is from when the tag receives the second data packet until it sends the third data packet; Time of flight: The time elapsed from when the base station sends the second data packet to the tag until it receives the third data packet returned by the base station. Multiplying by the speed of light gives the distance between the tag and the base station; when there is no obstruction, the ranging error is the clock drift of the base station and the tag, which is calculated by the following formula (2): (2)； in This is an estimate of the flight time. This is the actual value of the flight time. This represents the deviation between the actual frequency value and the nominal frequency value of the clock, expressed in ppm (parts per million).

3. The indoor positioning system based on empirical mode decomposition and spatial autoregressive neural network according to claim 1, characterized in that, The empirical mode decomposition algorithm specifically includes: Suppose the signal consists of a finite number of intrinsic mode functions (IMFs) and residual signals, and each IMF is obtained by the following method: Let the original signal be Find Find the maximum envelope of all maximum points using a cubic spline function. Then, calculate Find all the minimum points and find the minimum envelope using a cubic spline function. The average envelope is obtained by averaging the two envelopes. : (3)； Subtract from the original signal Obtain a new signal with low-frequency components removed. : (4)； use Repeat the above steps as a new signal until... The following conditions must be met: (1) For the entire signal, the difference between the number of poles and the number of zero crossings must not exceed 1; (2) At any point, the average value of the envelope of the maximum and minimum values ​​is zero; Then, the original signal is obtained. First-order IMF components: (5)； By from the original signal Subtract the first-order IMF from the middle The components are used to obtain a new signal with high-frequency components removed. : (6) right Repeat the above process to obtain the second-order IMF components. Then repeat the above process until the nth IMF component is less than the preset value, and finally... Represented as: (7) The signal is then decomposed into several high-frequency components. Adding a stable trend item .

4. The indoor positioning system based on empirical mode decomposition and spatial autoregressive neural network according to claim 1, characterized in that, The Newton iteration algorithm is represented by the following equation (8): (8)； The distance between the base station and the tag is represented by the following equation: (9)； in These are the coordinates to be calculated for the label. These are the coordinates of one of the base stations. This is the distance between the two base stations and the tag; since there are a total of several base stations, rewriting equation (9) yields the following equations: (10)； coordinates Let it be a vector Then the process of variable iteration can be represented as: (11)； Let equation (11) be a vector. According to Newton's iteration method, we obtain: (12)； in yes Find the inverse of the Jacobian matrix; calculate Then, the coordinate vector is updated using formula (11) to complete one iteration; the iteration occurs in... Stop when the accuracy requirements are met.

5. The indoor positioning system based on empirical mode decomposition and spatial autoregressive neural network according to claim 1, characterized in that, The described spatial autoregressive neural network can model indoor multipath errors because, in an indoor environment, electromagnetic waves undergo multipath effects due to reflection and scattering by objects during propagation. Therefore, multipath errors are spatially correlated, and spatial correlation is considered to be a nonlinear relationship between spatial distance and spatial weight. In other words, the multipath error at any point in space is modeled as follows: (13) in, It is the unknown multipath error at a point in space. It is a nonlinear mapping from distance to spatial weights. It is a distance vector. It is the observation error vector. It is the transpose of the matrix; Spatial distance is calculated using Euclidean distance: (14)； in It is the first The distance between the i-th known point and the i-th unknown point; To establish a model of the relationship between multipath error at known points and multipath error at unknown points, the nonlinear function between the spatial weight and spatial distance of the i-th unknown point is defined as follows: (15)； This represents the spatial weight vector of the i-th point. This represents the spatial weight between point i and point j. Given by equation (14); To characterize the complex relationship between spatial weights and distance, a spatial autoregressive neural network was constructed to fit the data. The input to the network is the distance from the unknown point to the known point, and the output is the spatial weight. After multiplying the spatial weight with the observation vector, the prediction multipath error of the unknown point is obtained, which is expressed as equation (16). (16) ； For multipath error at unknown points, Let be the distance from the i-th unknown point to the n-th known point. Representational autoregressive neural network, This is the error observation vector; When making predictions, the unknown points and known points are different, but when training the network, the unknown points will be the same as one of the known points, that is, i equals j in equations (14) and (15). It will equal zero. Let represent the weight of the i-th point; to prevent overfitting, this weight should be set to zero; therefore, it should be multiplied by the standard weight matrix before obtaining the final spatial weight matrix to eliminate the above effects. (17)； K is the identity matrix, and the i-th element on its diagonal is zero.

6. The indoor positioning system based on empirical mode decomposition and spatial autoregressive neural network according to claim 1, characterized in that, The base station and the tag communicate using ultra-wideband signals to exchange data, and then perform bilateral two-way ranging to obtain the required distance.

7. The indoor positioning system based on empirical mode decomposition and spatial autoregressive neural network according to claim 1, characterized in that, The positioning tag sends data packets containing the tag ID and TWR data to the backend server via Bluetooth at a frequency of 10Hz.

8. The indoor positioning system based on empirical mode decomposition and spatial autoregressive neural network according to claim 1, characterized in that, The actual coordinates of the base station and the intersection of the grid were measured and recorded using a millimeter-level laser rangefinder.

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