A node dynamic cooperative sensing and positioning method of air-based navigation enhancement ad hoc network

Abstract

The application relates to a node dynamic cooperative sensing and positioning method of an air-based navigation enhancement ad hoc network, which comprises the following steps: S1, a redundant distribution cooperative relationship between nodes is established in the navigation enhancement ad hoc network arranged in the near space, and dynamic cooperative sensing between the nodes is carried out based on an evolution game cooperative mechanism; S2, a cooperative positioning information state space model is established according to node information of the dynamic cooperative sensing; and S3, recursive filtering is carried out on the cooperative positioning information state space model to realize cooperative positioning between the sensing nodes. The application can realize accurate and complete dynamic sensing between network nodes of the proposed air-based navigation enhancement ad hoc network, and can realize cooperative positioning to improve positioning precision.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of navigation enhanced ad hoc network, and particularly relates to a node dynamic cooperative sensing and positioning method for space-based navigation enhanced ad hoc network. BACKGROUND

[0002] Due to the natural vulnerability of the signal system of GNSS, GNSS may be subjected to shadowing, suppression, interference and deception, and service interruption may occur. In order to solve the navigation problem under the condition of reduced availability or even failure of GNSS, the service performance of satellite navigation can be improved through information enhancement and signal enhancement. The sky-ground integrated navigation enhancement network composed of space-based satellites, space-based aircraft and ground-based pseudolites can realize the cooperation among the enhancement platforms, and improve the navigation service quality and reliability through multi-source and multi-layer navigation enhancement.

[0003] However, for the space-based navigation enhanced ad hoc network, the aircraft nodes dynamically fly, and due to the limitation of the types, number and measurement accuracy of the sensors carried, it is difficult to obtain high-precision space-time reference; the running environment of the nodes is complex, and the dynamic drift of the trajectory affects the stability of the network geometry configuration; the coupling relationship between the nodes easily causes the propagation and accumulation of errors; and the failure of part of the nodes may cause the decrease of the network geometry precision and affect the navigation service performance. SUMMARY

[0004] In view of the above analysis, the application aims to disclose a node dynamic cooperative sensing and positioning method for space-based navigation enhanced ad hoc network, which is used to solve the problem of cooperative sensing and positioning among network nodes.

[0005] The application discloses a node dynamic cooperative sensing and positioning method for space-based navigation enhanced ad hoc network, characterized in that it comprises the following steps:

[0006] Step S1, establishing a redundant distributed cooperative relationship among nodes in the navigation enhanced ad hoc network arranged in the near space, and performing dynamic cooperative sensing among the nodes based on the cooperative mechanism of evolutionary game;

[0007] Step S2, establishing a cooperative positioning information state space model according to the node information of the dynamic cooperative sensing;

[0008] Step S3, performing recursive filtering on the cooperative positioning information state space model to realize cooperative positioning among the sensing nodes.

[0009] Further, the recursive filtering is improved particle filtering; in the recursive calculation process of the improved particle filtering, the support vector regression is used to estimate the posterior probability density, and new particles are obtained through resampling.

[0010] Further, the air-based navigation-enhanced ad hoc network comprises upper and lower layers of networks; any three neighboring nodes in the lower layer network form an equilateral triangle; each node in the upper layer network is located directly above the centroid of the equilateral triangle formed by the neighboring nodes in the lower layer; and one upper layer node and the corresponding three lower layer nodes form a triangular pyramid.

[0011] Each node in the air-based navigation-enhanced ad hoc network is a space vehicle carrying the same navigation sensor and having independent navigation capability; the nodes are connected by establishing point-to-point connections for bidirectional ranging; and each node dynamically senses the state including the positions of the surrounding nodes and the formation configuration.

[0012] A circular cooperation region is drawn with any node as the center and a set maximum cooperation distance as the radius; the nodes in the upper and lower layers of networks covered by the circular region are the nodes that establish a redundant distributed cooperation relationship with the center node.

[0013] Further, in the nodes of the navigation-enhanced ad hoc network that establish a redundant distributed cooperation relationship, an evolution game-based cooperation mechanism is used for distributed cooperation, a public goods game theory is used for node sensing in cooperation, the optimal neighboring nodes are selected for cooperation, and the sensing information including the node state, ranging information and network structure is exchanged; thereby achieving dynamic cooperative sensing between the nodes.

[0014] Further, in the dynamic cooperative sensing between the nodes, a triple G(A, S, Q) is used to define a game interaction behavior model of a cooperation group.

[0015] Wherein,

[0016] A is an adjacency matrix, used to represent the interaction relationship between the individuals participating in the game;

[0017] The elements in the adjacency matrix A are:

[0018]

[0019] Wherein, N is the total number of nodes in the network;

[0020] S is a strategy space matrix, used to represent the strategy relationship between the individuals;

[0021] The elements in the strategy space matrix S are:

[0022]

[0023] Q is the collaborative revenue function, which represents the collaborative revenue of this collaborative group. The collaborative revenue includes the total revenue obtained by the central node of the collaborative group and the revenue obtained by the neighboring nodes. The total revenue obtained by the central node includes the unilateral total revenue obtained by the central node in this collaborative group and the revenue obtained by the central node in the game when the neighboring nodes are the central nodes of other collaborative groups.

[0024] Furthermore, the distributed collaborative sensing process based on the evolutionary game theory collaborative mechanism includes the following steps:

[0025] 1) At the start of perception time k, initialize the network node state information and the game model G(A) k S k Q k );

[0026] 2) k = k + 1, the central node x of the cooperative group i choose neighbor node y j The central node and selected neighboring nodes perform bidirectional ranging;

[0027] 3) Central node x i In a game, if the neighbor node y after the game... j strategy Then the central node x i To neighbor node y j Send an inquiry signal;

[0028] 4) Each neighbor node y that receives the query signal j If a game is played and the result is that the central node x... i Strategy Then towards the central node x i Send neighbor node y j The state information is used as the response signal; if the node strategy after the game... Then it will not respond;

[0029] 5) Central node x i Received neighbor node y j After receiving the response signal, coordination is performed, and a message containing the information of the central node x is sent. i A secondary response signal for status information;

[0030] 6) Neighbor node y j Using the central node x i The secondary response signal is coordinated;

[0031] 7) Calculate the node payoff Q in the game theory model. k+1 Update the policy space S k+1 ;

[0032] Returning to step 2), steps 2)-7) are repeated until the end of perception time.

[0033] Further, the state equation of the node motion model included in the cooperative positioning information state space model is:

[0034] x k =Fx k-1 +w k-1

[0035] wherein F is a state transition matrix, x k , x k-1 is the motion state of the node at k, k-1 time, w k-1 is the state transition noise at k-1 time;

[0036] motion state wherein (x k , y k , z k ) is the position of the GNSS receiver antenna of the node in the ECEF coordinate system at k time, is the velocity at k time, is the acceleration at k time, b k is the receiver clock error at k time, is the clock drift at k time.

[0037] Further, the joint observation equation of the unified measurement model included in the cooperative positioning information state space model is:

[0038] y k =h(x k , v k );

[0039] wherein x k is the motion state of the node in the air-based navigation enhanced ad hoc network, v k is a measurement error matrix; the observation is the pseudorange observation value observed by the GNSS receiver in the node to n navigation satellites; is the ranging observation value observed by the GNSS receiver in the node to the relative ranging of m cooperatively perceived nodes;

[0040]

[0041] wherein, is the pseudorange error vector observed to n navigation satellites; is the relative ranging error vector of m cooperatively perceived nodes.

[0042] Further, the process of recursive calculation by using the improved particle filter includes:

[0043] Step S301, initialization of particle filtering is performed;

[0044] Step S302, importance sampling of particle filtering is performed to obtain a particle set from a starting time of recursion;

[0045] Step S303, time update and measurement update are performed on the particle set of the previous time to obtain a motion state estimation value of the current time;

[0046] Step S304, a mixing weight is calculated, the particle weight of the current time is updated, and normalization processing is performed to obtain a particle set of the mixing weight of the current time;

[0047] Step S305, it is judged whether a resampling condition is established; if yes, step S306 is entered to perform resampling; if no, the particle set of the mixing weight is taken as the particle set of the current time and step S307 is entered;

[0048] Step S306, a support vector method is used to estimate the posterior probability density, and resampling is performed therefrom to obtain a resampled particle set of the current time;

[0049] Step S307, state estimation is performed using the particle set of the current time, and a minimum mean square error estimation of the motion state of the node of the current time is output;

[0050] Steps S302-S307 are repeated until the recursion reaches an ending time.

[0051] Further, step S306 comprises:

[0052] 1) constructing a sample for density estimation according to the weighted particle; the sample is a triple including the motion state estimation of the particle, an empirical distribution function and an insensitive loss function;

[0053] 2) constructing a posterior probability density estimation problem based on the sample for constructing the posterior probability density estimation; the constructed posterior probability density estimation problem is a support vector solving problem in a Hilbert space;

[0054] 3) converting the posterior probability density estimation problem into a quadratic programming problem, and using a support vector method to solve the posterior probability density estimation; the quadratic programming problem is a minimum problem including a regular term and an empirical risk;

[0055] 4) performing random sampling based on the posterior probability density estimation to generate new particles, calculating the weight of each particle and performing normalization to generate a resampled particle set.

[0056] The present application can realize one of the following beneficial effects:

[0057] The node dynamic cooperative sensing method of the air-based navigation enhanced ad hoc network of the application adopts the stratosphere airship to form the air-based navigation enhanced ad hoc network which has strong survivability, long loitering time, fast response speed, wide coverage and high cost-effectiveness, adopts the upper and lower two-layer ad hoc network structure to provide better geometric configuration, improves the cooperative accuracy, and is convenient for expansion;

[0058] The evolution game-based cooperative mechanism is adopted to realize the accurate and complete dynamic sensing between the network nodes of the proposed air-based navigation enhanced ad hoc network;

[0059] The particle filtering algorithm based on support vector (SV) density estimation is adopted to perform information fusion of cooperative positioning, which can effectively and accurately estimate the posterior probability density and improve the filtering accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0060] The accompanying drawings are included to provide a further understanding of the application and are incorporated herein and constitute a part of the application.

[0061] Figure 1 The node dynamic cooperative sensing and positioning method flow chart of the air-based navigation enhanced ad hoc network in the embodiment of the application.

[0062] Figure 2 The top view schematic diagram of the air-based navigation enhanced ad hoc network structure in the embodiment of the application.

[0063] Figure 3 The side view schematic diagram of the air-based navigation enhanced ad hoc network structure in the embodiment of the application.

[0064] Figure 4 The cooperative group determination according to the cooperative region in the embodiment of the application.

[0065] Figure 5 The process schematic diagram of the evolution game-based cooperative mechanism for distributed cooperation in the embodiment of the application.

[0066] Figure 6 The recursive calculation flow chart of the improved particle filtering in the embodiment of the application. DETAILED DESCRIPTION

[0067] The preferred embodiments of the application will be specifically described below with reference to the accompanying drawings, wherein the drawings constitute a part of the application and are used to explain the principles of the embodiments of the application.

[0068] One embodiment of the application discloses a node dynamic cooperative sensing and positioning method of an air-based navigation enhanced ad hoc network, as shown in Figure 1 The method comprises the following steps:

[0069] Step S1, establishing a redundant distributed coordination relationship between nodes in a navigation-enhanced ad hoc network deployed in a near space, and performing dynamic coordination sensing between nodes based on an evolution game-based coordination mechanism;

[0070] Step S2, establishing a cooperative positioning information state space model according to node information obtained through dynamic coordination sensing;

[0071] Step S3, performing recursive filtering on the cooperative positioning information state space model to realize cooperative positioning between nodes.

[0072] The coordination refers to an information sharing relationship established between nodes. In the information sharing relationship, nodes interact sensing information including node state, ranging information and network structure through established communication links to realize cooperative sensing and cooperative positioning functions. Through coordination, the determinacy, timeliness and accuracy of information sharing are ensured, and through optimal neighbor nodes, uncontrolled diffusion of sensing information under certain network links and load resources is avoided, and the occupation of network resources is balanced.

[0073] Specifically, the step S1 includes the following sub-steps:

[0074] Step S101, establishing a redundant distributed coordination relationship between nodes in a space-based navigation-enhanced ad hoc network deployed in a near space;

[0075] Step S102, in the nodes establishing the redundant distributed coordination relationship, performing distributed coordination through an evolution game-based coordination mechanism, selecting optimal neighbor nodes for coordination, and interacting sensing information including node state, ranging information and network structure; to realize dynamic coordination sensing between nodes;

[0076] Specifically, as shown in Figure 2 The space-based navigation-enhanced ad hoc network in step S1 includes upper and lower layer networks; any three neighbor nodes in the lower layer network form an equilateral triangle; each node in the upper layer network is located directly above the centroid of the equilateral triangle formed by the lower layer neighbor nodes, and one upper layer node and the corresponding three lower layer nodes form a triangular pyramid; in the figure, “·” represents an upper layer node; represents a lower layer node.

[0077] Each node in the space-based navigation-enhanced ad hoc network is a space vehicle carrying the same navigation sensor and having independent navigation capability; nodes perform bidirectional ranging through established point-to-point connections, each node dynamically senses the state including the position of surrounding nodes and formation configuration, broadcasts its own state information, time calibration information and ranging information, and at the same time, uses these information to calibrate its own state to improve its own space-time reference.

[0078] In this embodiment, asFigure 3 As shown, the spacecraft is an airship. Each airship node orbits its designated position in a clockwise uniform circular motion with a radius of 1 km and a linear velocity of 5 m / s. The airship serving as the upper-level node flies at an altitude of 25 km ± 5 km, while the airship serving as the lower-level node flies at an altitude of 20 km ± 5 km. Using stratospheric airships to construct a navigation-enhanced self-organizing network offers strong survivability, long loiter time, fast response speed, wide coverage, and high cost-effectiveness. The two-layer self-organizing network structure provides a better geometric configuration, improves coordination accuracy, and facilitates expansion.

[0079] Previous research has shown that ranging information in navigation-enhanced ad hoc networks uses a full-broadcast mechanism, resulting in excessively high dimensionality and computational load in the collaborative distributed solution. In fact, excessively high requirements for the network's sensing range and timeliness will lead to the unrestrained diffusion of sensing information, thereby consuming too many network resources and potentially reducing the survivability of navigation-enhanced ad hoc networks.

[0080] Based on this, in step S101, during the establishment of redundant distributed cooperative relationships between nodes in the space-based navigation enhancement ad hoc network,

[0081] A circular collaborative region is drawn with any node as the center and the set maximum collaborative distance as the radius. The network nodes in the upper and lower layers of the network covered by the circular region are the nodes that establish redundant distributed collaborative relationships with the center node.

[0082] More specifically, such as Figure 4 As shown, in this embodiment, the maximum cooperative distance is the distance between a node in the lower-level network and its nearest neighbor. Therefore, in the circular cooperative region, each lower-level network node acting as the center node X establishes a redundant cooperative relationship with its six adjacent lower-level network nodes and six upper-level network nodes, forming a cooperative group. Similarly, each upper-level network node acting as the center node establishes a redundant cooperative relationship with its three adjacent lower-level network nodes and nine upper-level network nodes, forming a cooperative group. Clearly, the positioning accuracy of the center node X improves with the increase in the number of its cooperating neighbor nodes and the improvement in its geometric distribution.

[0083] Within the ranging range, there is a certain degree of redundancy in the ranging information of neighboring nodes. In order to save load resources, it is necessary to select the optimal neighboring node for collaboration.

[0084] Based on this, in step S102, in the node establishing the redundant distribution coordination relationship, the Public Goods Game (PGG) theory is used for node perception in coordination, the network node is regarded as an intelligent individual participating in the game, the connection between the node and other nodes in the coordination group is regarded as the interaction relationship between the game individuals, and the dynamic coordination of the nodes in the coordination group reflects the dynamics of the evolutionary game. In the coordination group, each network node selects whether to participate in coordination through the game. Through game evolution, the positioning accuracy of each node is improved.

[0085] Specifically, as shown in FIG. 1, a coordination group with a node X as the center in a lower network based on a basic networking unit of a navigation-enhanced ad hoc network is shown. The coordination problem of each node at time k is regarded as a PGG problem. Neighbor nodes Y around X are regarded as game individuals and need to adopt a strategy to participate in the game, that is, whether to participate in the coordination of X. On the one hand, the increase of the income of the public pool brings the improvement of the positioning accuracy of X. On the other hand, for the node X, in addition to participating in the PGG with itself as the center, the node X also participates in the PGG with the neighbor nodes as the center. When considering the PGG group with Y as the center, the geometric distribution improvement and the positioning accuracy improvement of X and Y cooperation also improve the positioning accuracy of Y, that is, the income of Y is increased. Figure 4

[0086] More specifically, in step S102, a triple G (A, S, Q) is used to define the game interaction behavior model of the group,

[0087] wherein,

[0088] A is an adjacency matrix, used to represent the interaction relationship between the individuals participating in the game;

[0089] The elements in the adjacency matrix A are:

[0090]

[0091] wherein, N is the total number of nodes in the networking; M is the number of nodes in the coordination group, M = 12.

[0092] S is a strategy space matrix, used to represent the strategy relationship between the individuals;

[0093] The elements in the strategy space matrix S are:

[0094]

[0095] ​Q is a synergy benefit function, used to represent the synergy benefit of the current synergy group; the synergy benefit includes the total benefit obtained by the center node of the synergy group and the benefit obtained by the neighbor nodes; wherein the total benefit obtained by the center node includes the unilateral total benefit obtained by the center node in the current synergy group and the benefit obtained by the neighbor nodes when playing the game for the center nodes of other synergy groups.

[0096] Specifically, the synergy benefit function is represented as Q(M x ,M y ); wherein M x is the total benefit of the center node x i , including the unilateral total benefit and the benefit obtained by the neighbor nodes when playing the game for the center node; M y is the benefit obtained by each neighbor node y j .

[0097] Then, for each edge x i -y j in the synergy group, the center node x i obtains the unilateral benefit:

[0098]

[0099] wherein, is the number of neighbors of the center node x i , also referred to as is the degree of the synergy group in which the node x i participates, i.e., each node in the group participates in PGG synergy groups;

[0100]

[0101] C is the communication cost paid by each player if participating in the synergy, contributing distance information and time information; r ij is the heterogeneous investment gain, the improvement degree of the positioning accuracy of the center node after the synergy of different neighbor nodes is different, i.e., the benefit generated by the cooperative node in the navigation-enhanced ad hoc network is related to the relative position, and the investment of the participating node has great heterogeneity.

[0102] The benefit obtained by the neighbor node y j when playing the game for the center node of other synergy groups is:

[0103]

[0104] wherein, is the degree of the synergy group in which the node y j serves as the center node;

[0105] Then, the total benefit of the node x i is:

[0106]

[0107] Each neighbor node y j Obtain the income:

[0108]

[0109] After each round of game of evolutionary game, each node randomly selects a neighbor to learn and update the strategy, and the learning probability is:

[0110]

[0111] Wherein is the positioning error estimation variance of the neighbor node y j , as a noise factor for selecting a learning strategy object; in addition, the total income of the individual represents its fitness in the group, and the greater the fitness, the more adaptable to the game environment. Therefore, the higher the income, the smaller the noise factor, and the higher the probability of being selected. Then x i The cooperative strategy of single epoch cooperation:

[0112] Specifically, the cooperative strategy of learning probability update:

[0113]

[0114] Where P cutoff is the cut-off probability.

[0115] In addition, for the group shown in Figure 4 , the neighbor nodes of X are divided into A-type nodes of the upper layer network and B-type nodes of the lower layer network. Obviously, cooperation with A-type nodes can only improve the horizontal positioning accuracy of X, and cooperation with B-type nodes can improve the horizontal and vertical positioning accuracy of X at the same time.

[0116] Further, the improvement of the geometric distribution when the same type of different nodes cooperates with X is also different, that is, the income generated by increasing the cooperative nodes in the navigation-enhanced ad hoc network is related to the relative position, and there is great heterogeneity.

[0117] Specifically, the heterogeneous investment gain:

[0118]

[0119] Where θ ij is the elevation angle of node y j relative to node x i , and β is the heterogeneous investment adjustment factor.

[0120] More specifically, the distributed cooperation process based on the cooperative mechanism of evolutionary game, as shown in Figure 5 , includes the following steps:

[0121] 1) At the start of perception time k, initialize the network node state information and the game model G(A) k S k Q k );

[0122] 2) k = k + 1, the central node x of the cooperative group i choose neighbor node y j The central node and selected neighboring nodes perform bidirectional ranging;

[0123] 3) Central node x i In a game, if the neighbor node y after the game... j strategy Then the central node x i To neighbor node y j Send an inquiry signal;

[0124] 4) Each neighbor node y that receives the query signal j If a game is played and the result is that the central node x... i Strategy Then towards the central node x i Send neighbor node y j Status information As a response signal; if the central node x after the game... i Strategy Then it will not respond;

[0125] In the middle, x k Including neighbor node y at time k j The position, velocity, acceleration, receiver clock bias, and clock drift information of the GNSS receiver antenna in the ECEF coordinate system; P k Estimating the covariance of neighboring node states; P k This includes neighbor node y j Positioning error estimation variance use The computing node itself calculates the learning probability

[0126] 5) Central node x i Received neighbor node y j After receiving the response signal, coordination is performed, and a message containing the information of the central node x is sent. i Status information The secondary response signal;

[0127] In the middle, x k Including the central node x at time k iposition, velocity, acceleration, receiver clock bias and clock drift information of GNSS receiver antenna in ECEF coordinate system of the node x k covariance estimation of the central node state;

[0128] 6) neighbor node y j cooperates with the central node x i using the secondary response signal;

[0129] 7) calculate the node income Q k+1 in the game model, update the strategy space S k+1 ;

[0130] Return to step 2), repeat steps 2) to 7) until the end of the perception time. The end of the perception time is set according to the specific actual situation.

[0131] Specifically, in the distributed cooperative process, the navigation receivers of the two nodes can use the existing method for bidirectional ranging method, such as TDOA method, which is not limited herein and does not affect the protection scope of the present application.

[0132] Specifically, in step S2, the established cooperative positioning information state space model includes a node motion model and a unified measurement model.

[0133] The state equation of the node motion model included in the cooperative positioning information state space model is:

[0134] x k = Fx k-1 + w k-1

[0135] Wherein, F is a state transition matrix, x k , x k-1 is the motion state of the node at time k and k-1, w k-1 is the state transition noise at time k-1.

[0136] Motion state Wherein, (x k , y k , z k ) is the position of the GNSS receiver antenna of the node in the ECEF coordinate system at time k, is the velocity at time k, is the acceleration at time k, b k is the receiver clock bias at time k, is the clock drift at time k.

[0137] More specifically, the state transition matrix is:

[0138]

[0139] wherein,

[0140] B is the state transition matrix of the receiver clock: τ is the sampling period of the system;

[0141] State transition noise w k In the above equation, the first derivative of acceleration and clock drift both satisfy zero-mean Gaussian noise, i.e. σ 2 is the noise variance;

[0142] State transition noise variance:

[0143]

[0144]

[0145] The joint observation equation of the unified measurement model included in the cooperative positioning information state space model is:

[0146] y k = h(x k ,v k );

[0147] wherein, x k is the motion state of the node in the base navigation enhanced ad hoc network, v k is the measurement error matrix; the observation is the pseudo-range observation value observed by the GNSS receiver in the node to n navigation satellites; is the ranging observation value of the relative ranging of m cooperatively sensed nodes by the GNSS receiver in the node;

[0148]

[0149] wherein, is the pseudo-range error vector observed to n navigation satellites; is the relative ranging error vector of m nodes.

[0150] Specifically, on the basis of GNSS positioning, the nodes are sensed through the cooperative mechanism, the bidirectional ranging information and ranging error between the nodes are introduced, the satellite pseudo-range equation and the node ranging equation are distributedly solved, information fusion is realized, and optimal estimation of the node state is realized.

[0151] Due to the nonlinearity of the observation equation and the non-Gaussianity of the ranging error, particle filtering is used for information fusion and state estimation. In previous studies, the EKF and UKF are used to estimate the mean and variance of the particles to approximate the importance density function, introduce observation information, improve the proposal distribution for particle sampling and mixed weight updating, which can improve the particle degeneracy problem that may occur in the standard particle filter to some extent.

[0152] However, the extended particle filter (EPF) in the particle filter has the problem of introducing truncation error, and the EPF and UPF (Unscented Particle Filter algorithm) improve the proposal distribution to approximate the posterior distribution by Gaussian assumption, which is not completely suitable for solving the problem. In addition, for the case where the observation noise is narrow and the likelihood distribution is far from the prior distribution, if the prior distribution is used as the proposal distribution, the particles will deviate from the high-likelihood region, and the particles and their weights cannot accurately express the likelihood distribution, which may lead to the loss of likelihood information; although EPF and UPF can solve this problem under narrow observation noise, narrow likelihood leads to the concentration of sampling particles in a narrow region, and for the non-Gaussian case, when the EKF and UKF fitting proposal distribution are not accurate enough, additional errors may be introduced, which leads to a high possibility of particle deviation from the likelihood region, low particle quality, and particle impoverishment problem for general resampling methods: due to the duplication of large-weight particles and the reduction of small-weight particles, the particle diversity is reduced, leading to large deviation in state estimation.

[0153] In order to solve the above problems and make the weighted particles more effectively describe the posterior distribution, the present patent uses support vector to estimate the posterior probability density, from which new particles with more diversity are obtained by resampling, effectively improving the performance of particle filtering. Through support vector density estimation, new particles are randomly sampled in the high-probability region, and the corresponding weights are calculated according to the fitting function. The posterior distribution of the state is described by these weighted particles, effectively overcoming the particle degeneracy phenomenon and improving the state estimation accuracy.

[0154] In the estimation of posterior probability density, support vector regression (SVR) maps the low-dimensional nonlinear function to a high-dimensional feature space through nonlinear mapping, and performs linear regression in the feature space. In the cooperative positioning process, the state space is 11-dimensional, in order to avoid the curse of dimensionality, a suitable kernel function needs to be selected, and in the process of constructing the kernel function, the particle sample probability distribution information is combined, and SVR is used for solving, then the resampled posterior probability density can be represented by the newly constructed kernel function.

[0155] Specifically, as shown in Figure 6 The recursive calculation process of the improved particle filter includes:

[0156] Step S301, initialize the particle filter;

[0157] In the initialization, the initialization of the recursion time (k=0) is performed, and the initialization value x0 of the node state and the state noise covariance matrix Q0 are set.

[0158] In step S302, the importance sampling of the particle filter is performed from the starting time of the recursion to obtain a particle set;

[0159] The importance probability density function is:

[0160]

[0161]

[0162] wherein is the likelihood function probability density approximation estimate, which can be obtained according to the observation equation.

[0163] The particle set at the k-1 time obtained by the importance sampling is:

[0164]

[0165] is the motion state of the i th particle at the k-1 time, is the particle weight at the k-1 time, and N is the number of particles in the particle set.

[0166] In step S303, the particle set at the previous time is subjected to time update and measurement update to obtain the motion state estimation value at the current time.

[0167] The particle after the time update and the measurement update is:

[0168]

[0169] is the motion state estimation value of the i th particle at the k time.

[0170] In step S304, the mixing weight is calculated, the particle weight at the current time is updated, and normalization processing is performed to obtain the particle set of the mixing weight at the current time.

[0171] The updated particle weight at the k time is:

[0172]

[0173] is the likelihood probability density function, is the prior probability density function.

[0174] After the normalization processing, the particle weight estimation value at the k time is:

[0175]

[0176] Thus, the particle set with mixed weights is obtained as:

[0177]

[0178] is the normalized particle weight estimate.

[0179] Step S305, it is judged whether the resampling condition is established; if yes, it goes to step S306 for resampling; if no, the particle set with mixed weights is taken as the particle set at the current time and goes to step S307;

[0180] Specifically, the resampling condition is to judge whether the effective particle number N eff is less than the particle number threshold N th .

[0181] Step S306, if the resampling condition is met, the support vector method is used to estimate the posterior probability density p(x k |y 1:k ), and resampling is performed therefrom to obtain the resampled particle set at the current time;

[0182] Specifically, step S306 includes:

[0183] 1) constructing a sample for density estimation according to the weighted particles; the sample is a triple including the motion state estimate of the particle, the empirical distribution function and the insensitive loss function;

[0184] According to the obtained weighted sample , the empirical distribution function is constructed to obtain the sample triple:

[0185]

[0186] The empirical distribution function is an empirical function of the distribution function obtained according to the motion state estimate of the particle;

[0187] The empirical distribution function

[0188] The insensitive loss function is the estimation accuracy of the empirical distribution function to the distribution function value;

[0189] The insensitive loss function of the i-th support vector is denoted as:

[0190]

[0191] Wherein, c is a penalty coefficient, σ i is the noise variance corresponding to the i-th support vector;​

[0192] Since the distribution function is unknown, the following estimation is used to approximate The insensitive loss function ε is obtained i

[0193]

[0194] Where δ is a small parameter.

[0195] 2) Construct a posterior probability density estimation problem based on the sample constructed by the posterior probability density estimation, and the constructed posterior probability density estimation problem is a support vector solving problem in a Hilbert space;

[0196] The to-be-estimated probability density function can be represented as the following function in a Hilbert space:

[0197]

[0198] Where w=(w1,…,w n ,…) is a feature vector coefficient, and Φ(x)=(φ1(x),…,φ n (x),…) is a feature vector after sample mapping. The probability distribution function can be represented as:

[0199]

[0200] Where the operator A represents a mapping relationship, Ψ(x)=(ψ1(x),…,ψ n (x),…), and ψ r (x)=Aφ r (x).

[0201] The solution of the probability density is equivalent to the solution of the feature vector coefficient w in the Hilbert space, which is solved by the support vector method.

[0202] The probability density function and the distribution function solved by the support vector method are represented as:

[0203] Distribution function

[0204] Probability density function

[0205] is the jth support vector;

[0206] The support vector coefficient set β=(β1,…,β j ,…,β l ), the support vector coefficient β j ≥0, j=1,2,…,l; l is the number of support vectors;

[0207] where the cross kernel function is a Laplace kernel;

[0208] Specifically, γ is a kernel width;

[0209] kernel function is an integral function.

[0210] 3) converting the posterior probability density estimation problem into a quadratic programming problem, and solving the posterior probability density estimation by using a support vector method; the quadratic programming problem is to minimize an empirical risk problem containing a regularization term and an ε insensitive loss function;

[0211] where the regularization term is:

[0212]

[0213] The square insensitive function R emp (β) is:

[0214]

[0215] The estimation solution of the posterior probability density function is solved by minimizing the following empirical risk:

[0216] R(β,f) = R emp (β) + γ l W(f)

[0217] where γ l is a regularization coefficient.

[0218] The posterior probability density estimation is converted into solving the following quadratic programming problem:

[0219]

[0220]

[0221]

[0222]

[0223] ξ i ≥0, β i ≥0, i = 1, 2, …, N;

[0224] where, is the motion state estimation value of the i-th and j-th particle at the k-th moment; F l (·) is an empirical distribution function, c is a penalty coefficient, and ξ i , ​ε represents the first and second slack variables. i Let β be the insensitive loss function value corresponding to the i-th particle sample. i These are the coefficients of the eigenvector.

[0225] Solve the quadratic programming problem to obtain the state x at time k. k The posterior probability density p(x) k |y 1：k (estimation) for:

[0226]

[0227] 4) Based on the estimated posterior probability density New particles are generated by random sampling, the weight of each particle is calculated and normalized, and a resampled particle set is generated.

[0228]

[0229]

[0230]

[0231] in, To generate new particles at time k by random sampling based on posterior probability density estimation; The normalized new particle weights at time k; These are the particle weights updated at time k after resampling.

[0232] Step S307: Use the particle set at the current time to perform state estimation and output the minimum mean square error estimate of the motion state of the node at the current time.

[0233] The particle set after resampling in step S306 Perform state estimation at the current time and output the motion state x of the node at time k. k The minimum mean square error estimate is:

[0234]

[0235] Repeat steps S302-S307 until the end time is reached; the end time is set according to the specific actual situation.

[0236] In summary, the node dynamic cooperative sensing method of the airborne navigation enhancement ad hoc network of the present invention adopts a stratospheric airship to form a navigation enhancement ad hoc network with strong survivability, long loiter time, fast response speed, wide coverage and high cost-effectiveness. The two-layer ad hoc network structure can provide better geometric configuration, improve cooperative accuracy and facilitate expansion.

[0237] The distributed cooperation based on the evolutionary game cooperation mechanism can realize accurate and complete dynamic perception between network nodes of the proposed air-based navigation enhancement ad hoc network.

[0238] The information fusion of the cooperative positioning by using the particle filter algorithm based on the support vector (SV) density estimation can effectively and accurately estimate the posterior probability density and improve the filtering precision.

[0239] The above merely describes the preferred embodiments of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of changes or replacements within the technical range disclosed by the present application, which should be covered within the protection scope of the present application.

Claims

1. A method for dynamic cooperative sensing and positioning of nodes in a space-based navigation augmentation ad hoc network, characterized in that, The method comprises the following steps: S1, establishing a redundant distributed coordination relationship between nodes in a navigation-enhanced ad hoc network arranged in a near space, and performing dynamic coordination sensing between nodes based on an evolutionary game coordination mechanism; S2, establishing a cooperative positioning information state space model according to node information obtained through dynamic coordination sensing; S3, performing recursive filtering on the cooperative positioning information state space model to realize cooperative positioning between sensing nodes. The air-based navigation-enhanced ad hoc network comprises an upper layer network and a lower layer network; any three neighboring nodes in the lower layer network form an equilateral triangle; each node in the upper layer network is located directly above the centroid of the equilateral triangle formed by the neighboring nodes in the lower layer network, and one upper layer node and the corresponding three lower layer nodes form a triangular pyramid; Each node in the air-based navigation-enhanced ad hoc network is a space vehicle carrying the same navigation sensor and having independent navigation capability; Nodes are connected through point-to-point connection to perform bidirectional ranging, and each node dynamically senses the state including the position of the surrounding nodes and the formation configuration; A circular coordination region is drawn with any node as the center and a set maximum coordination distance as the radius, and the network nodes in the upper and lower layer networks covered by the circular region are nodes that establish a redundant distributed coordination relationship with the center node.

2. The method according to claim 1, wherein the recursive filtering is improved particle filtering; in the recursive calculation process of the improved particle filtering, a support vector regression is used to estimate the posterior probability density, and new particles are obtained through resampling.

3. The method according to claim 2, wherein in the nodes of the navigation-enhanced ad hoc network that establish a redundant distributed coordination relationship, a coordination mechanism based on evolutionary game is used for distributed coordination, a public goods game theory is used for node sensing in coordination, the optimal neighboring nodes are selected for coordination, and the sensing information including the node state, ranging information and network structure is exchanged to realize dynamic coordination sensing between nodes.

4. The method according to claim 3, wherein when performing dynamic coordination sensing between nodes, a triple G(A, S, Q) is used to define a game interaction behavior model of a coordination group. A is an adjacency matrix, which is used to represent the interaction relationship between individuals participating in the game. The elements in the adjacency matrix A are as follows: N is the total number of nodes in the network. S is a strategy space matrix, which is used to represent the strategy relationship between individuals. The elements in the strategy space matrix S are as follows: Q is a coordination benefit function, which is used to represent the coordination benefit of the coordination group; the coordination benefit includes the total benefit obtained by the center node of the coordination group and the benefit obtained by the neighboring nodes; the total benefit obtained by the center node includes the unilateral total benefit obtained by the center node in the coordination group and the benefit obtained by the neighboring nodes when they are the center nodes of other coordination groups. ​ ​ ​ ​ 5. The method of claim 4, wherein the distributed collaborative sensing process based on the evolutionary game-based coordination mechanism comprises the following steps: Returning to step 2), repeating steps 2) to 7) until the end of the sensing time. 1) At the perception start time k, initialize network node state information, game model G(A k , S k , Q k ); 2) k = k + 1, the center node x of the coordination group i selecting a neighbor node y j , the center node and the selected neighbor node perform bidirectional ranging; 3) the central node x i plays the game, if the strategy j of the neighbor node y after the game is i sent to the neighbor node y j an inquiry signal; 4) each neighbor node y that receives the query signal j plays the game, and if the game results in a strategy for the center node x i that is then the neighbor node y i sends the state information to the center node x j as a response signal; if the game results in a strategy for the node that is then the node does not respond; 5) central node x i Upon receipt of the reply signal from the neighbor node y j , the cooperation is performed and a secondary reply signal containing the status information of the central node x i is sent. 6) Neighbor node y j Utilizing the secondary response signal of the central node x i for coordination; 7) calculating the node payoff Q in a game model k+1 , updating the strategy space S k+1 ; 6. The method of claim 1 to 5, wherein the state equation of the motion model of the nodes included in the state space model of the collaborative positioning information is:

7. The method of claim 6, wherein the joint observation equation of the unified measurement model included in the state space model of the collaborative positioning information is:

8. The method of claim 7, wherein the process of recursively calculating using the improved particle filter comprises: x k = Fx k-1 + w k-1 where F is a state transition matrix, x k , x k-1 is the motion state of the node at time k, k-1, w k-1 is the state transition noise at time k-1. Motion state where (x k ,y k ,z k ) is the position of the GNSS receiver antenna of the node in the ECEF coordinate system at time k, is the velocity at time k, is the acceleration at time k, b k is the receiver clock bias at time k, is the clock drift at time k. Step S301, initializing the particle filter; Step S302, performing importance sampling of the particle filter to obtain a particle set from the start time of recursion; y k = h(x k , v k ); wherein x k is the motion state of the node in the base navigation enhanced ad hoc network, v k is the measurement error matrix; the observation is the pseudorange observation value observed by the GNSS receiver in the node to n navigation satellites; is the ranging observation value of the relative ranging of the m nodes in the cooperative perception by the GNSS receiver in the node; wherein, is a pseudo-range error vector for n navigation satellites observed; is a relative ranging error vector for m co-sensing nodes. Step S303, performing time update and measurement update on the particle set at the previous time to obtain the motion state estimation value at the current time; Step S304, calculating the mixing weight, updating the particle weight at the current time, and performing normalization processing to obtain the particle set of the mixing weight at the current time; Step S305, determining whether the resampling condition is met; if yes, proceeding to step S306 for resampling; if no, taking the particle set of the mixing weight as the particle set at the current time and proceeding to step S307; Step S306, estimating the posterior probability density using the support vector method and resampling therefrom to obtain the resampled particle set at the current time; Step S307, performing state estimation using the particle set at the current time and outputting the minimum mean square error estimation of the motion state of the node at the current time; Repeating steps S302 to S307 until the end of the recursion. Step S306 comprises: 1) constructing a sample for density estimation according to the weighted particles; the sample is a triple including the motion state estimation of the particle, the empirical distribution function, and the insensitive loss function; 2) constructing a posterior probability density estimation problem based on the sample for constructing the posterior probability density estimation, the constructed posterior probability density estimation problem being a support vector solving problem in a Hilbert space; 3) converting the posterior probability density estimation problem into a quadratic programming problem and solving the posterior probability density estimation using the support vector method; the quadratic programming problem is a minimization problem including a regularization term and an empirical risk; 9. The method of claim 8, wherein, 4) performing random sampling based on the posterior probability density estimation to generate new particles, calculating the weight of each particle and performing normalization to generate a resampled particle set. ​ ​ ​ ​

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