CN115470913A - Method and device for reconstructing PIR sensor network behavior track based on quantum walk - Google Patents
Method and device for reconstructing PIR sensor network behavior track based on quantum walk Download PDFInfo
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Abstract
The invention discloses a reconstruction method and a device of a PIR sensor network behavior track based on quantum walk, wherein the method comprises the following steps: calculating the probability of the walker in each base state by a quantum walking state of a known initial state at given arbitrary time t, and simulating the probability of the walker in the base state corresponding to each position on the sensor network; simulating and generating a sensor network topological behavior mode according to the probability of each base state, and simulating different motion modes under the sensor network; matching and synchronization are performed based on the different generated motion patterns. The invention can well complete the matching and synchronization of the PIR sensor network track, the generated track can better express the actual motion situation in time and space, and all tracks under the constraint of the sensor network and the sensor response data can be generated.
Description
Technical Field
The invention relates to quantum physics and graph theory, in particular to a reconstruction method and a device of PIR sensor network behavior locus based on quantum walk.
Background
The method is based on a high-density and low-cost pyroelectric Infrared sensor (PIR) network to carry out positioning and reconstruction of the behavior track of people, and is an important means for indoor behavior analysis. The crowd behavior characteristic analysis is one of hot spots in the current data mining field, and is based on the crowd behavior characteristic analysis of the PIR sensor, and response data of crowd moving in a sensor network scene is obtained mainly by arranging a large number of sensor network nodes in a research environment. And analyzing and researching the response data by using methods such as a statistical analysis method, a target positioning and tracking algorithm, a behavior model and the like so as to analyze the behavior characteristics of the movement of the crowd in a specific scene. The existing analysis method such as a tracklet graph model can dynamically inquire and visualize a human motion mode on a space-time scale. In addition, human motion patterns are extracted in a statistical manner, such as Kalman filtering, hidden Markov chain models, and topic models. However, since the sensor data recorded to the behavioral trace map is not unique, i.e., the same sensor recording may be caused by different behavioral traces, the accuracy of these methods is left to be considered. A PIR sensor behavior track reconstruction method based on geometric algebra adopts a matrix outer product mode to reconstruct tracks of a sensor network, a time window is set, and response periods of the time window are used for replacing sensor response data with different response time lengths. The method can simulate the behavior track trend under the constraints of the sensor network and the response data, and compared with a statistical method, the method has a more complete structure. However, the method based on geometric algebra uses matrix outer product to reconstruct the track, which involves a large amount of matrix calculation and iteration, and when the matrix dimension is increased, the running time of the whole algorithm is increased sharply. Secondly, the method replaces the response state of the whole time window with the response state of the sensor in the time window, and the setting of the time window is based on experience or hypothesis, the setting is too large to ignore data of many sensor responses, and the setting is too small to increase the calculation amount obviously. Thirdly, the method only considers the motion tracks of people in adjacent time windows, can not extract the behavior characteristics of people, and can not obtain tracks with different speeds. Based on the method and the device for reconstructing the network behavior track of the PIR sensor based on quantum walk, the invention aims at solving the problem that the existing method for reconstructing the network behavior track of the PIR sensor cannot effectively distinguish different behavior modes.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problem that different behavior modes cannot be effectively distinguished by the existing PIR sensor network behavior track reconstruction method, a quantum walk-based PIR sensor network behavior track reconstruction method and device are provided, and sensor network track matching and synchronization are completed.
The technical scheme is as follows: the invention aims to provide a reconstruction method of a network behavior track of a PIR sensor based on quantum walking, which specifically comprises the following steps:
(1) Based on the quantum migration characteristic, constructing the operation environment of quantum migration: calculating the probability of the walker in each base state by a quantum walking state of a known initial state at given arbitrary time t, and simulating the probability of the walker in the base state corresponding to each position on the sensor network;
(2) Simulating and generating a sensor network topological behavior mode according to the probability of each base state, and simulating different motion modes under the sensor network;
(3) And (3) matching and synchronizing based on the different motion patterns generated in the step (2).
Further, the step (1) is realized as follows:
quantum walk is represented as an evolution process on the graph, let G = (V, E) be a undirected weightless graph, where V = { V = { 1 ,v 2 ,…,v N Is a set of N vertices, E = { (v) r ,v c ),…}(v r ,v c E.g., V) is a set of edges; the adjacency matrix a of graph G is:
wherein A is rc ＝A cr ，A vv ＝0；
State vector
The evolution over time t can be expressed as
The form of the equation:
wherein, the Hamiltonian H is an N multiplied by N Hermitian matrix which is an adjacent matrix or a Laplacian matrix of the graph;
is a complex state vector;
quantum walking can solve from an initial state
Starting the evolution process; e.g. state vector at time t
Comprises the following steps:
wherein e is -iHt The time evolution operator is used for constructing quantum migration which dynamically evolves along with time;
state vector
Is the complex linear combination of each ground state in quantum migration at time t, and embodies the characteristic of coherent superposition of quantum system(ii) a Quantum walk computed on graph, using | v>Representing the state vector of the vertex V ∈ V corresponding to the ground state, the quantum wandering at any time t
Expressed as a complex superposition of the states at each vertex, the states at each vertex are the product of the ground state and its corresponding probability magnitude:
wherein, the first and the second end of the pipe are connected with each other,
representing the probability amplitude corresponding to the vertex v at the time t;
when the quantum system is observed, the quantum system collapses, and the probability that the quantum walker is positioned on the corresponding ground state | v > of each vertex can be obtained as follows:
and (3) calculating the probability of the walker in each base state by a quantum walking state of a known initial state at a given arbitrary time t, and simulating the probability of the walker in the base state corresponding to each position on the sensor network.
Further, the step (2) is realized as follows:
changing the observed change in the observed position of the rover on the network by different observation time differences; obtaining a sensor network abstract diagram through space constraint and time constraint, using an adjacent matrix to represent the topological relation of the diagram, and using the topological relation as an input parameter of quantum migration evolution;
determining the initial position of the quantum walker, namely determining the basic state corresponding to which vertex the walker is positioned at the initial moment; observing by utilizing a plurality of times to obtain a continuous moving path; using the interval of adjacent observation times to represent the difference of different motion modes;
observing the walker to obtain the change of the walker in the observation position at equal time intervals; observing by using a group of new time, and reflecting the difference of different motion modes by using the difference of the position change of the walker caused by different observation time sets; and (3) selecting a time scale by using a factor representing the observation time change as a time scale factor, setting the initial state of quantum migration, and observing the migrator respectively to obtain the observed position of the migrator, namely the motion trail corresponding to the behavior mode under the time scale factor.
Further, the step (3) is realized as follows:
carrying out space consistency judgment on the motion track of the walker, and obtaining a behavior track meeting the sensor response state through splitting and reconstructing; the sensing data in the sensor network is a 0-1 sequence related to time, the sensing state of the sensor is marked as '1', and the non-sensing state is marked as '0';
for each generated track, extracting the induction state corresponding to the corresponding time in the actual sensor response sequence; if the extracted response sequence contains a response state of 0, splitting the moving path of the walker according to the moment that the response state is 0; if the position distance of the sensors at the adjacent moments is too large, the path is also split; a series of behavior traces over time based on sensor response data are derived.
Based on the same inventive concept, the invention further provides a device for reconstructing the PIR sensor network behavior trace based on quantum walking, which comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the computer program realizes the method for reconstructing the PIR sensor network behavior trace based on quantum walking when being loaded into the processor.
Has the advantages that: compared with the prior art, the invention has the following beneficial effects: the invention can well complete the matching and synchronization of the network tracks of the PIR sensor, the quantum walker is a random model based on a graph, can represent the evolution process of the quantum walker on a specific space structure along with the time, and considers the time superposition and the space constraint; the behavior pattern generated by quantum walking can fully express the distribution condition of all possible tracks on the sensor network, the tracks meeting the given response data are obtained in the synchronous matching of the behavior pattern, and the result shows that the generated tracks can well express the actual motion situation in time and space, and all tracks under the constraint of the sensor network and the sensor response data can be generated; the method for reconstructing the track by using quantum walking is characterized in that the track is generated by using a probabilistic model randomly under the topological constraint of a sensor and the time constraint of actual induction data, the difference of the track and the completeness of track distribution can be fully considered, the reconstruction is evaluated from space and time, the adaptability and the stability of the reconstructed track can be well tested, the manpower and material resources are greatly saved, and the method has great application potential for the flow characteristics, the emergency response time and the like of random crowds in the future.
Drawings
FIG. 1 is a flow chart of a reconstruction method of a PIR sensor network behavior track based on quantum walking;
FIG. 2 is a diagram of sensor distribution and network representation; wherein (a) is a sensor profile and (b) is a network profile;
FIG. 3 is a graph of the trace frequency distribution for each time segment;
fig. 4 is a quantum walking reconstruction trajectory distribution diagram.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The invention provides a reconstruction method of a PIR sensor network behavior track based on quantum walking, which is a method for generating a topological structure behavior mode based on a sensor network by using the quantum walking and completing reconstruction of the sensor network track by means of matching and synchronization of actual sensing data of a sensor, and specifically comprises the following steps:
step 1: and (5) quantum walking construction and observation.
The quantum walk can be represented as an evolution process on a graph, and for an undirected weightless graph, the adjacency matrix thereof can be represented by a set of points and edges. Let G = (V, E) be a undirected weightless graph, where V = V 1 ,v 2 ,…,v N Is a set of N vertices, E = { (v) r ,v c ),…}(v r ,v c E.v) is the set of edges. The adjacency matrix a of the graph G may be represented by formula (1):
wherein A is rc ＝A cr ，A vv ＝0。
Unlike classical random walk, quantum walk is not a Markov process. State vector
The evolution over time t can be expressed as
The equation is in the form of equation (2), and the problem is usually solved by converting the equation into a Hamiltonian H:
the hamiltonian H is an N × N Hermitian matrix, which may be an adjacency matrix or Laplacian matrix of the graph.
Is a complex-valued state vector.
Quantum walking can solve from the initial state
The process of evolution begins. E.g. state vector at time t
Can be expressed as shown in formula (3):
wherein e -iHt The time evolution operator is used for constructing quantum migration which dynamically evolves along with time.
State vector
The method is a complex linear combination of all ground states in quantum migration at time t, and embodies the coherent superposition characteristic of a quantum system. Quantum walk computed on graph, using | v>Indicating the ground state to which the vertex V ∈ V corresponds. Then the state vector of the quantum walk at any time t
Can be expressed as a complex superposition of the states at each vertex, the state at each vertex is the product of the ground state and its corresponding probability amplitude, expressed as formula (4):
wherein
The probability amplitude corresponding to the vertex v at the time t is shown.
When the quantum system is observed, the quantum system collapses, and the probability that the quantum walker is positioned on the corresponding ground state | V > (V ∈ V) of each vertex can be obtained. The solving method of the probability is the module of the probability amplitude corresponding to the current vertex. Therefore, at time t, the probability that a quantum walker is observed in the | v > state can be expressed as equation (5):
since the sum of the probabilities in all cases is 1, it is expressed as formula (6):
therefore, for a quantum walker system with a known initial state, the probability of the walker being in each of the fundamental states can be known given a time t.
And 2, step: and generating based on the topological behavior pattern of the sensor network.
Given the position of the graph and the quantum walker at time t =0, the wave function of the quantum walker is determined and the dynamic position of the walker is observed at different times. In order to simulate different movement modes in a sensor network, observed position changes of a walker on the network are changed through different observation time differences. Given that the sensor response time interval is deterministic, the observation of unequal time intervals of the walker is reflected in different scales of evolution relative to the sensor.
For example, a sensor network distributed indoors, as shown in fig. 2 (a), is a relatively simple spatial structure, and is subject to spatial constraints that limit movement by channels and the like, thereby easily abstracting the sensor network as shown in fig. 2 (b).
And after obtaining the sensor network abstract graph, using the adjacency matrix to represent the topological relation of the graph and using the adjacency matrix as an input parameter of quantum migration evolution. The adjacency matrix in fig. 2 (b) is represented by equation (7):
the initial position of the quantum walker is determined, i.e. the base state to which vertex the walker is at time 0 is determined. For example, if the walker exists in the state of the vertex a, the initial state can be expressed by equation (8):
use A instead of e in formula (3) -iHt H in (3) can obtain the quantum walking evolution equation on fig. 1, and given any t, the state of the walker at the moment can be calculated. For example, the state obtained at time t is formula (9):
indicating that the walker was observed to be at vertex b at time t. To obtain a continuous moving path, observation is performed using only a plurality of t. To fit the behavior embodying the different motion patterns, the interval of adjacent observation times is used to embody the difference of the different motion patterns. For example, using equation (10) as:
T＝{1k,2k,…,ik,…},(k≠0) (10)
and observing the walker to obtain the change of the observed position of the walker at equal time intervals. To obtain a set of paths with diversity, the method uses a new set of times for observation, such as equation (11):
T'＝{1k',2k',…,ik',…},(k'≠0,k'≠k) (11)
the difference of different movement modes is reflected by the difference of the position change of the walker caused by different observation time sets. The method refers to factors such as k, k' and the like representing the change of the observation time as time scale factors.
Selecting a time scale k (k is not equal to 0), setting the initial state of quantum migration, observing the migrator according to {1k,2k, …, ik, … and Nk } respectively, and obtaining the observed position { l } of the migrator 1 ,l 2 ,…,l i ,…,l N This is the trajectory of the corresponding behavior pattern at the time scale factor k.
And step 3: behavior pattern matching and synchronization.
Because data observed randomly according to quantum walking do not always accord with the actual response sequence of the sensor, the motion trail of the walker needs to be judged according to the space consistency, and the behavior trail meeting the response state of the sensor is obtained through splitting and reconstructing. The sensing data in the sensor network is a series of 0-1 sequences related to time, the sensing state of the sensor is marked as '1', and the non-sensing state is marked as '0'. For a sensor network as shown in fig. 1, the response sequence of each sensor is represented by equation (12):
wherein b is vt ,v∈[1,8],t∈[1,N]Indicating the response state of the v vertex in the sensor at the time t.
For each behavior trace, e.g. { l } 1 ,l 2 ,…,l i ,…,l N Extracting the induction states of the corresponding sensors in the actual sensor response sequence according to time sequence, namely
If the extracted response sequence includes a response state of "0", the moving path of the walker is split according to the time when the response state is "0", for example
{1,1,0,1,1}→{1,1},{1,1}
In addition, if the position distance of the sensors at the adjacent moments is too large, the path is also split, for example, a path { v } satisfying the response state of the sensors is provided 1 ,v 3 ,v 7 ,v 6 v 8 But v is 3 And v 7 The actual distance is too large and can be split into
{v 1 ,v 3 ,v 7 ,v 6 v 8 }→{v 1 ,v 3 },{v 7 ,v 6 ,v 8 }
Therefore, each generated random track is processed, and a series of behavior tracks meeting the sensor network topological structure and the sensor response data can be obtained.
Based on the same inventive concept, the invention further provides a device for reconstructing the PIR sensor network behavior trace based on quantum walking, which comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the computer program realizes the method for reconstructing the PIR sensor network behavior trace based on quantum walking when being loaded into the processor.
The method is characterized in that non-contact sensor monitoring data issued by Mitsubishi Electric Research Labs (MERL) is selected as a basis, 11 sensors are selected as Research objects, path reconstruction is carried out on the basis of response data in 12 hours, 40 minutes and 13 hours, 13 days, 4 months and 13 days, 2006, and fire alarm simulation evacuation is carried out in 54 minutes at 12 hours. The data provided by the MERL is the starting and stopping time of the response when the response state of the sensor is '1', the sensor response data of the selected research period is converted into a response sequence with the interval of 1s, and each sensor corresponds to a group of 0-1 sequences with the length of 3000. Assuming that the walking speed range of the ordinary people is 1-2m/s, the sensing areas of each sensor are adjacent, and dead zones hardly exist between the sensing areas. When a person walks, the sensor can respond in the sensing area of the person. Each sensor has a sensing area with a side length of 2m, the time for a person to pass one sensor and enter another sensor is approximately 0-2s. Therefore, in the case of taking 1s as the sensing period of the sensor, the pedestrian can span 1 sensor at most in two adjacent sensing periods.
In order to enable the quantum walking to simulate the tracks of different behavior modes, the range of a time scale factor k is set to be 0.5-2.0, the behavior modes are respectively generated by 0.01 increment, namely the tracks are simulated by the time scale factors of {0.5,0.51, … and 1.99,2.0}, and all possible behavior tracks are simulated by taking each sensor induction position as a starting point. And splitting the track meeting the network topology and response time constraint from the generated track according to the response sequence of the sensor. Within the selected 50 minutes, the tracks of different behavior patterns generated by using the method reach 8000, and in order to reveal the time characteristics of the track distribution, the distribution of the tracks in each minute is counted, and the result shown in fig. 3 is obtained.
From the time distribution of the trajectories shown in fig. 3, it can be seen that the time distribution rule of the trajectories is extracted by the method, and the trajectory distribution is increased after 54 minutes of the evacuation time 12. Within the selected 50 minutes, the distribution of the traces exhibits a certain periodicity, with periods of no human movement occurring in the hallway of the sensor distribution at approximately every 5 minutes. Furthermore, we picked the distribution of the trajectory display trajectory over the various sensors generated at 55 minutes during evacuation 12, as shown in fig. 4.
FIG. 4 is a graph of the trace distribution on the sensor generated by the quantum walking method using multiple time scale factors, which reflects the direction of movement of the group of 12 th 55 th group of people, approximately 6 → 2 → 11 → 5. From the aspect of time complexity, the method provided by the patent can obtain the track of the walker starting to move from each vertex under the condition that the time complexity and the sensor response data length N are related to the number M of sensors under the condition of a time scale factor, and the time complexity is O (W × N).
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and improvements can be made without departing from the principle of the present invention, and such modifications and improvements should also be considered within the scope of the present invention.
Claims (5)
1. A reconstruction method of a PIR sensor network behavior track based on quantum walk is characterized by comprising the following steps:
(1) Based on the quantum migration characteristic, constructing the operation environment of quantum migration: calculating the probability of the walker in each base state by a quantum walking state of a known initial state at given arbitrary time t, and simulating the probability of the walker in the base state corresponding to each position on the sensor network;
(2) Simulating and generating a sensor network topological behavior mode according to the probability of each base state, and simulating different motion modes under the sensor network;
(3) And (3) matching and synchronizing based on the different motion patterns generated in the step (2).
2. A reconstruction method of a PIR sensor network behavior track based on quantum walking according to claim 1, characterized in that the step (1) is realized by the following steps:
quantum walk is represented as an evolution process on a graph, and G = (V, E) is a undirected weightless graph, wherein V = { V = { 1 ，v 2 ，...，v N Is a set of N vertices, E = { (v) r ，v c )，...}(v r ，v c E.g., V) is a set of edges; the adjacency matrix a of graph G is:
wherein A is rc ＝A cr ，A vv ＝0；
State vector
The evolution over time t can be expressed as
The form of the equation:
wherein, the Hamiltonian H is an N multiplied by N Hermitian matrix which is an adjacent matrix or a Laplacian matrix of the graph;
is a complex state vector;
quantum walking can solve from the initial state
Starting the evolution process; e.g. state vector at time t
Comprises the following steps:
wherein e is -iHt The time evolution operator is used for constructing quantum migration which dynamically evolves along with time;
state vector
The method is a complex linear combination of each ground state in quantum walking at time t, and embodies the coherent superposition characteristic of a quantum system; quantum walk computed on graph, using | v>State vector representing the corresponding ground state of vertex V e V, the quantum wandering at any time t
Expressed as a complex superposition of the states at each vertex, the states at each vertex are the product of the ground state and its corresponding probability magnitude:
wherein the content of the first and second substances,
representing the probability amplitude corresponding to the vertex v at the time t;
when the quantum system is observed, the quantum system collapses, and the probability that the quantum walker is positioned on the corresponding ground state | v > of each vertex can be obtained as follows:
and (3) calculating the probability of the walker in each base state by a quantum walking state of a known initial state at a given arbitrary time t, and simulating the probability of the walker in the base state corresponding to each position on the sensor network.
3. A reconstruction method of a PIR sensor network behavior track based on quantum walking as claimed in claim 1, wherein the step (2) is implemented as follows:
changing the observed change in the observed position of the rover on the network by different observation time differences; obtaining a sensor network abstract diagram through space constraint and time constraint, using an adjacent matrix to represent the topological relation of the diagram, and using the topological relation as an input parameter of quantum migration evolution;
determining the initial position of the quantum walker, namely determining the basic state corresponding to which vertex the walker is positioned at the initial moment; observing by utilizing a plurality of times to obtain a continuous moving path; using the interval of adjacent observation times to represent the difference of different motion modes;
observing the walker to obtain the change of the walker in the observation position at equal time intervals; observing by using a group of new time, and reflecting the difference of different motion modes by using the difference of the position change of the walker caused by different observation time sets; and (3) selecting a time scale by using a factor representing the observation time change as a time scale factor, setting the initial state of quantum migration, and observing the migrator respectively to obtain the observed position of the migrator, namely the motion trail corresponding to the behavior mode under the time scale factor.
4. A reconstruction method of a PIR sensor network behavior track based on quantum walking as claimed in claim 1, characterized in that the step (3) is implemented as follows:
carrying out space consistency judgment on the motion track of the walker, and obtaining a behavior track meeting the sensor response state through splitting and reconstructing; the sensing data in the sensor network is a 0-1 sequence related to time, the sensing state of the sensor is marked as '1', and the non-sensing state is marked as '0';
for each generated track, extracting the induction state corresponding to the corresponding time in the actual sensor response sequence; if the extracted response sequence contains a response state of 0, splitting the moving path of the walker according to the moment that the response state is 0; if the position distance of the sensors at the adjacent moments is too large, the path is also split; a series of behavior traces over time based on sensor response data are derived.
5. An apparatus for reconstructing a quantum walk based PIR sensor network behavior trace, comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the computer program, when loaded into the processor, implements a method for reconstructing a quantum walk based PIR sensor network behavior trace according to any of claims 1-4.
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| WO2024065644A1 (en) | 2024-04-04 |
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