CN112784963B - Indoor and outdoor seamless positioning method based on simulated annealing optimization BP neural network - Google Patents

Indoor and outdoor seamless positioning method based on simulated annealing optimization BP neural network Download PDF

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CN112784963B
CN112784963B CN202110087963.XA CN202110087963A CN112784963B CN 112784963 B CN112784963 B CN 112784963B CN 202110087963 A CN202110087963 A CN 202110087963A CN 112784963 B CN112784963 B CN 112784963B
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刘宇
王伟伟
路永乐
刘茄鑫
文丹丹
黎人溥
邹新海
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Chongqing University of Post and Telecommunications
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Abstract

The invention discloses an indoor and outdoor seamless positioning method based on simulated annealing optimization BP neural network, belonging to the navigation positioning field, and specifically comprising the following steps: firstly, an indoor and outdoor seamless positioning algorithm model based on a BP neural network is established, secondly, an indoor and outdoor seamless positioning algorithm model based on a simulated annealing optimization BP neural network is established according to the established indoor and outdoor seamless positioning algorithm model based on the BP neural network and combined with a simulated annealing algorithm, then, the BP neural network model after the simulated annealing optimization is used for training by utilizing collected samples, the optimal weight and threshold are determined, and finally, the trained BP neural network based on the simulated annealing optimization is used for indoor and outdoor seamless positioning. The experimental result shows that the average absolute error of the indoor and outdoor seamless positioning algorithm for optimizing the BP neural network by utilizing simulated annealing is reduced by about 69% compared with that of the BP neural network, and the positioning accuracy is improved by about 55.11% compared with that of PDR positioning.

Description

Indoor and outdoor seamless positioning method based on simulated annealing optimization BP neural network
Technical Field
The invention belongs to the field of navigation positioning, and particularly relates to an algorithm suitable for indoor and outdoor seamless positioning.
Background
With the rapid development of scientific technology, researchers have conducted many studies on pedestrian navigation positioning technology. The current mature pedestrian navigation positioning technology mainly comprises the following steps: GPS positioning technology, WiFi positioning technology, UWB positioning technology, geomagnetic positioning technology, PDR positioning technology, Bluetooth positioning technology and the like. Since the single positioning technology cannot realize indoor and outdoor seamless positioning of pedestrians, providing seamless positioning service capable of connecting indoor and outdoor environments has become a key issue.
At present, many researchers at home and abroad carry out related research aiming at an indoor and outdoor seamless positioning technology. A Positioning algorithm based on GPS/WiFi is proposed in the literature (Machaj, Brida P, Benikovsky J. scaling Optimization of Wireless Positioning Service [ J ]. Mobile Information Systems,2016, (2016-6-23),2016,2016(Pt.3):1-11.), the algorithm can reduce the time required for position estimation caused by frequent access to the indoor and outdoor, but the WiFi Positioning signal is unstable and is easily affected by the surrounding environment, and the WiFi Positioning needs to consume a large amount of acquisition work. A fused positioning Technology based on GPS/UWB is proposed in the literature (Belakbir A, Amghar M, Sbiti N, et al. an index-based positioning system of GPS and UWB sensors [ J ]. Journal of the Theoretical & Applied Information Technology,2014,25(3-4):301-303.), and the system can realize indoor and outdoor positioning, but needs to deploy base stations in advance, has high cost and is not easy to popularize in a large scale. The document (Liuxingcuan, Wuzhenfeng, Linxiaokang. WLAN/MARG/GPS combined positioning system [ J ] based on the adaptive weighting algorithm, Qinghua university school newspaper (Nature science edition), 2013(7):955 + 960) proposes a WLAN/MARG/GPS combined positioning system based on the adaptive weighting algorithm, although the indoor and outdoor seamless positioning can be realized, the algorithm complexity is too large. The document (Niuhua, Sunburgh-France, a GPS + PDR combined positioning method [ J ] based on improved UKF filtering, survey and drawing report, 2017(07):5-9.) proposes a GPS/PDR combined positioning filtering method, GPS and PDR data are fused by using an unscented Kalman filtering algorithm, but the filtering result is easy to deviate due to the fact that assumed signal noise adopted by the UKF filter is Gaussian white noise.
The BP neural network is a multi-layer feedforward network trained according to an error inverse propagation algorithm, and is one of the most widely applied neural network models at present. It can learn and store a large number of input-output pattern mappings without revealing the description in advance. Although the learning algorithm of the BP neural network has wide practical application due to the theoretical integrity, the BP neural network has the defects of slow convergence speed and easy falling into a local optimal solution. The simulated annealing algorithm can overcome the defect that the BP neural network is easy to fall into a local optimal solution through the similarity between the simulated solid annealing process and a general combinatorial optimization problem, and depends on the selection of an initial value like a genetic algorithm. Therefore, the invention provides an indoor and outdoor seamless positioning method for optimizing a BP neural network by using simulated annealing.
Disclosure of Invention
The present invention is directed to solving the above problems of the prior art. An indoor and outdoor seamless positioning method based on simulated annealing optimization BP neural network is provided. The technical scheme of the invention is as follows:
an indoor and outdoor seamless positioning method based on simulated annealing optimization BP neural network comprises the following steps:
step1, firstly, establishing an indoor and outdoor seamless positioning algorithm model based on a BP neural network;
step2, establishing an indoor and outdoor seamless positioning algorithm model based on a simulated annealing optimized BP neural network according to the established indoor and outdoor seamless positioning algorithm model based on the BP neural network and combining the simulated annealing algorithm;
step3, training the BP neural network model optimized by simulated annealing by using the collected samples, and determining the optimal weight and threshold;
and 4, finally, using the trained BP neural network based on simulated annealing optimization for indoor and outdoor seamless positioning.
Further, the step1 of establishing an indoor and outdoor seamless positioning algorithm model based on the BP neural network specifically includes:
a1 first sets the activation function of each level node in the neural network as the ReLU function:
Figure BDA0002911588430000031
a2, capital letters I, J, L respectively represent an input layer, a hidden layer and an output layer, superscripts in and out respectively represent input and output, subscripts i, j and l respectively represent ith, j and l nodes of the input layer, the hidden layer and the output layer, and input and output of each layer are respectively:
Figure BDA0002911588430000032
Figure BDA0002911588430000033
Figure BDA0002911588430000034
Figure BDA0002911588430000035
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002911588430000036
the activation function of the hidden layer is represented,
Figure BDA0002911588430000037
representing the activation function of the output layer, WijFor the weight vector of the input layer to the hidden layer, WjlA weight vector from the hidden layer to the output layer;
a3 defines the difference between the training output and the expected output as the error of the network, then
Figure BDA0002911588430000038
If the output layer has n nodes, the square error of the training output and the expected output is:
Figure BDA0002911588430000039
wherein the content of the first and second substances,
Figure BDA00029115884300000310
is the desired output of the sample point;
a4 determining the number of nodes of each layer of BP neurons; the algorithm calculates the coordinate (x) of the positioning result of the PDR (Pedestrian dead reckoning) in the indoor and outdoor seamless positioningpi,ypi) And GPS positioning result coordinates (x)gi,ygi) The fused coordinates are used as an input layer of the neural network, the fused coordinates are used as an output layer of the neural network, the number of neurons of the input layer of the neural network is 4, the number of neurons of the output layer is 2, and the number of neurons of the hidden layer is determined according to an empirical formula (10);
Figure BDA00029115884300000311
in the formula, m is the number of neurons in the hidden layer, n is the number of neurons in the input layer, l is the number of neurons in the output layer, and a is a constant between 1 and 10. Therefore, the number of neurons of the neural network hidden layer is set to 8.
Further, the step2 is combined with a simulated annealing algorithm to establish an indoor and outdoor seamless positioning algorithm model based on a simulated annealing optimized BP neural network, and specifically comprises the following steps:
b1 initializes the algorithm: setting the initial temperature T0Establishing a BP neural network according to the length L of the Markov chain, randomly setting the weight of the neural network and obtaining an initial solution vector S0；
B2 sets the perturbation function: the perturbation function is used to solve the vector S from the previous one at the k-th stepkGenerating a new solution Sk+1The perturbation function is set as follows:
f(k+1)＝f(k)+ηξ (11)
wherein eta is a disturbance amplitude, and xi is a random disturbance variable;
b3 calculates the delta: calculating Sk+1E (S) is equal tok+1)-E(Sk) Wherein E (S)k) Is E (S)k) The corresponding squared error;
b4 sets the Metropolis reception decision function: and judging whether to accept the new solution according to the Metropolis criterion shown as the formula (12), and if the increment dE is less than 0, receiving the new solution with the probability of 1. Otherwise, firstly generating a uniformly distributed random number epsilon in the interval [0,1], if epsilon is less than P, receiving the solution, otherwise refusing to accept, and entering the next step.
Figure BDA0002911588430000041
B5: setting an internal circulation termination judgment condition; selecting a time-aligned simulation as a judgment condition of the internal circulation, namely performing cooling operation when the length L of the Markov chain at each temperature is traversed;
b6: setting a cooling function: and (3) selecting a temperature decay function as shown in the formula (13) to perform cooling operation:
Tk+1＝αTk(k＝0,1,2,3...) (13)
wherein, TkTemperature at which the temperature decreases K times, Tk+1The temperature is the temperature after primary cooling; α ∈ (any constant of 0.5, 0.99;
b7: and setting an external circulation termination judgment condition, selecting a total circulation control method as the external circulation judgment condition, namely setting the total number of times of temperature reduction, finishing the algorithm when the number of times of circulation reaches the total number of times, and otherwise, jumping back to Step 2.
Further, step3, a designed indoor and outdoor seamless positioning algorithm model based on simulated annealing optimization BP neural network is used, training samples are collected according to the sampling rules shown in the following table, and the algorithm is trained;
TABLE 1 sampling rules
Figure BDA0002911588430000042
Figure BDA0002911588430000051
。
The invention has the following advantages and beneficial effects:
the invention aims to provide an effective solution for indoor and outdoor seamless positioning, which comprises the following steps: the invention considers the problem of discontinuous positioning caused by environmental influence and the problem of inaccurate positioning caused by error accumulation along with time in the GPS positioning technology, but can correct the accumulated error of the PDR by using the GPS and make up the problem of discontinuous positioning caused by GPS deficiency by using the PDR; the invention does not use the traditional Kalman filtering or a variant method based on the Kalman filtering to fuse PDR positioning and GPS positioning, but adopts a brand-new fusion mode BP neural network to fuse and train the PDR positioning and the GPS positioning, in order to optimize the weight of the BP neural network, accelerate the convergence speed of the neural network and avoid the convergence speed from falling into the local optimal solution, the invention provides an indoor and outdoor seamless positioning method based on the simulated annealing optimization BP neural network, and the problem that the BP neural network cannot ensure the global optimal solution due to self factors is solved by optimizing the weight of the BP neural network by using the global optimization capability of the simulated annealing; experiments show that the average absolute error of the BP neural network optimized by simulated annealing is reduced by about 69% compared with that before optimization, the positioning accuracy is improved by about 55.11% compared with that of PDR positioning, and high-accuracy indoor and outdoor seamless positioning can be realized.
Drawings
FIG. 1 is a diagram of a preferred embodiment BP neural network model provided by the present invention.
Fig. 2 is a flow chart of the algorithm of the present invention.
FIG. 3 is a graph of the simulation results of the BP neural network algorithm without optimization using the simulated annealing algorithm.
FIG. 4 is a graph of the error of the simulation result of the BP neural network algorithm which is not optimized by using the simulated annealing algorithm.
FIG. 5 is a graph of simulation results of the BP neural network algorithm optimized using the simulated annealing algorithm.
FIG. 6 is an error diagram of a simulation result of the BP neural network algorithm optimized by using a simulated annealing algorithm.
FIG. 7 is a roadmap for the validation algorithm.
FIG. 8 is a graph showing the results of different positioning modes
Detailed Description
The technical solutions in the embodiments of the present invention will be described in detail and clearly with reference to the accompanying drawings. The described embodiments are only some of the embodiments of the present invention.
The technical scheme for solving the technical problems is as follows:
1. and (3) establishing a BP neural network model by combining the attached figure 1. Wherein, WijFor the weight vector of the input layer to the hidden layer, WjlIs a weight vector from the hidden layer to the output layer. The specific implementation process for establishing the BP neural network model is as follows:
step1 first sets the activation function of each level node in the neural network as the most commonly used relu (rectified Linear unit) function:
Figure BDA0002911588430000061
step2 represents the input layer, hidden layer and output layer with capital letters I, J, L, the input and output with superscripts in, out, respectively, and the i, j, l nodes of the input layer, hidden layer and output layer with subscripts i, j, l, respectively. The input and output of each layer are respectively:
Figure BDA0002911588430000062
Figure BDA0002911588430000068
Figure BDA0002911588430000063
Figure BDA0002911588430000064
step3 defines the difference between the training output and the expected output as the error of the net, then
Figure BDA0002911588430000065
If the output layer has n nodes, the square error of the training output and the expected output is:
Figure BDA0002911588430000066
wherein the content of the first and second substances,
Figure BDA0002911588430000067
is the desired output of the sample point.
Step4 determines the number of nodes on each layer of the BP neuron. The algorithm maps (x) of PDR positioning results in indoor and outdoor seamless positioningpi,ypi) And GPS positioning result coordinates (x)gi,ygi) And the fused coordinates are used as an input layer of the neural network, and the fused coordinates are used as an output layer of the neural network. Therefore, the number of input layer neurons of the neural network is 4, and the number of output layer neurons is 2. The number of neurons in the hidden layer is determined according to the empirical formula (10).
Figure BDA0002911588430000071
In the formula, m is the number of neurons in the hidden layer, n is the number of neurons in the input layer, l is the number of neurons in the output layer, and a is a constant between 1 and 10. Therefore, the number of neurons of the neural network hidden layer is set to 8.
2. And (3) optimizing the established BP neural network algorithm model by using simulated annealing in combination with the attached figure 2. The optimization is realized by the following specific steps:
step1 initializes the algorithm. Setting the initial temperature T0Establishing a BP neural network according to the length L of the Markov chain, randomly setting the weight of the neural network and obtaining an initial solution vector S0。
Step2 sets the perturbation function. The perturbation function is used to solve the vector S from the previous one at the k-th stepkProducing a new solution Sk+1. The perturbation function is set as follows:
f(k+1)＝f(k)+ηξ (11)
wherein eta is the disturbance amplitude, and xi is the random disturbance variable.
Step3 calculates the increment. Calculating Sk+1E (S) is equal tok+1)-E(Sk) Wherein E (S)k) Is E (S)k) The corresponding squared error.
Step4 sets the Metropolis reception decision function. Whether to accept a new solution is determined according to the Metropolis criterion as shown in equation (12). If the increment dE < 0, a new solution is received with probability 1. Otherwise, firstly generating a uniformly distributed random number epsilon in the interval [0,1], if epsilon is less than P, receiving the solution, otherwise refusing to accept, and entering the next step.
Figure BDA0002911588430000072
Step 5: and setting an inner loop termination judgment condition. And selecting the time-aligned simulation as a judgment condition of the internal circulation. Namely, the temperature reduction operation is carried out when the Markov chain length L at each temperature is traversed.
Step 6: and setting a cooling function. And selecting a temperature decay function shown in the formula (13) which is more applied to carry out cooling operation.
Tk+1＝αTk(k＝0,1,2,3...) (13)
Wherein, TkTemperature at which the temperature decreases K times, Tk+1The temperature is the temperature after primary cooling; α ∈ (0.5, 0.99).
Step 7: and setting an outer loop termination judgment condition. And selecting a total circulation control method as a judgment condition of the outer circulation. I.e., the total number of temperature drops is set, and the algorithm ends when the number of cycles reaches the total number, otherwise it jumps back to Step 2.
3. And (3) collecting training samples by using a designed algorithm according to the sampling rule shown in the following table, and training the algorithm. Fig. 3 and 4 are Y-axis coordinate training outputs and training error curves obtained using an unoptimized BP neural network, respectively. Fig. 5 and 6 are Y-axis coordinate training outputs and training error curves obtained using simulated annealing optimized BP neural networks, respectively. As can be seen from the attached FIGS. 4 and 6, the BP neural network prediction after simulated annealing optimization is more accurate, the average absolute error after optimization is 0.568m, the average absolute error before optimization is 1.837m, the predicted average absolute error is reduced by about 69%, and the feasibility of the fusion algorithm is verified.
TABLE 1 sampling rules
Figure BDA0002911588430000081
4. And (3) introducing the trained indoor and outdoor seamless positioning algorithm for simulating the annealing optimization BP neural network into navigation equipment, carrying out experimental verification according to the route shown in the attached figure 7, and finally obtaining the results of all the positioning modes as shown in the attached figure 8. By analyzing and processing the data, the average error of different positioning modes can be obtained as shown in table 2. As can be seen from the table, the positioning accuracy obtained after the SA-BP algorithm is fused is improved by about 55.11 percent compared with the positioning accuracy of the PDR.
TABLE 2 mean error for different positioning modes
Figure BDA0002911588430000082
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The above examples are to be construed as merely illustrative and not limitative of the remainder of the disclosure. After reading the description of the invention, the skilled person can make various changes or modifications to the invention, and these equivalent changes and modifications also fall into the scope of the invention defined by the claims.

Claims (2)

1. An indoor and outdoor seamless positioning method based on simulated annealing optimization BP neural network is characterized by comprising the following steps:
step1, firstly, establishing an indoor and outdoor seamless positioning algorithm model based on a BP neural network;
step2, establishing an indoor and outdoor seamless positioning algorithm model based on a simulated annealing optimized BP neural network according to the established indoor and outdoor seamless positioning algorithm model based on the BP neural network and combining the simulated annealing algorithm;
step3, training the BP neural network model optimized by using simulated annealing by using the collected samples, and determining the optimal weight and threshold;
step4, finally, the trained BP neural network based on simulated annealing optimization is used for indoor and outdoor seamless positioning;
the step1 of establishing an indoor and outdoor seamless positioning algorithm model based on the BP neural network specifically comprises the following steps:
a1 first sets the activation function of each level node in the neural network as the ReLU function:
Figure FDA0003648984850000011
a2, capital letters I, J, L respectively represent an input layer, a hidden layer and an output layer, superscripts in and out respectively represent input and output, subscripts i, j and l respectively represent ith, j and l nodes of the input layer, the hidden layer and the output layer, and input and output of each layer are respectively:
Figure FDA0003648984850000012
Figure FDA0003648984850000013
Figure FDA0003648984850000014
Figure FDA0003648984850000015
wherein the content of the first and second substances,
Figure FDA0003648984850000016
the activation function of the hidden layer is represented,
Figure FDA0003648984850000017
representing the activation function of the output layer, WijFor the weight vector of the input layer to the hidden layer, WjlIs a weight vector from the hidden layer to the output layer;
a3 defines the difference between the training output and the expected output as the error of the network, then
Figure FDA0003648984850000018
If the output layer has n nodes, the square error of the training output and the expected output is:
Figure FDA0003648984850000019
wherein the content of the first and second substances,
Figure FDA00036489848500000110
is the desired output of the sample point;
a4 determining the number of nodes of each layer of BP neurons; the algorithm calculates and positions the PDR pedestrian track dead reckoning result coordinate (x) in indoor and outdoor seamless positioningpi,ypi) And GPS positioning result coordinates (x)gi,ygi) The fused coordinates are used as an input layer of the neural network, the fused coordinates are used as an output layer of the neural network, the number of neurons of the input layer of the neural network is 4, the number of neurons of the output layer is 2, and the number of neurons of the hidden layer is determined according to an empirical formula (10);
Figure FDA0003648984850000021
in the formula, m is the number of neurons in the hidden layer, n is the number of neurons in the input layer, l is the number of neurons in the output layer, and a is a constant between 1 and 10, so that the number of neurons in the hidden layer of the neural network is set to be 8;
the step2 is combined with a simulated annealing algorithm to establish an indoor and outdoor seamless positioning algorithm model based on a simulated annealing optimization BP neural network, and the method specifically comprises the following steps:
b1 initializes the algorithm: setting the initial temperature T0Establishing a BP neural network according to the length L of the Markov chain, randomly setting the weight of the neural network and obtaining an initial solution vector S0；
B2 sets the perturbation function: the perturbation function is used to solve the vector S from the previous solution in the k stepkGenerating a new solution Sk+1The perturbation function is set as follows:
f(k+1)＝f(k)+ηξ (11)
wherein eta is the disturbance amplitude, and xi is the random disturbance variable;
b3 calculates the delta: calculating Sk+1E (S) is equal tok+1)-E(Sk) Wherein E (S)k) Is a solution vector SkCorresponding planeSquare error;
b4 sets the Metropolis reception decision function: judging whether to accept a new solution according to Metropolis criterion shown in a formula (12), if the increment dE is less than 0, receiving the new solution by using the probability 1, otherwise, firstly generating a uniformly distributed random number epsilon in an interval [0,1], if epsilon is less than P, receiving the solution, otherwise, refusing to accept, and entering the next step;
Figure FDA0003648984850000022
b5: setting an internal circulation termination judgment condition; selecting a time-aligned simulation as a judgment condition of the internal circulation, namely performing cooling operation when the length L of the Markov chain at each temperature is traversed;
b6: setting a cooling function: and (3) selecting a temperature decay function as shown in the formula (13) to perform cooling operation:
Tk+1＝αTk(k＝0,1,2,3...) (13)
wherein, TkTemperature, T, at which the temperature decreases K timesk+1The temperature is the temperature after primary cooling; α ∈ (0.5, 0.99);
b7: and setting an external circulation termination judgment condition, selecting a total circulation control method as the external circulation judgment condition, namely setting the total number of times of temperature reduction, finishing the algorithm when the number of times of circulation reaches the total number of times, and otherwise, jumping back to B2.
2. The indoor and outdoor seamless positioning method based on simulated annealing optimization BP neural network according to claim 1, characterized in that step3 uses a designed indoor and outdoor seamless positioning algorithm model based on simulated annealing optimization BP neural network, collects training samples according to sampling rules, and trains the algorithm;
the adopted rule is as follows: the sampling length is 550m, the sampling interval is 1.1m, the total number of samples is 500 groups, the number of training samples is 400 groups, and the number of testing samples is 100 groups.
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