Multi-criterion joint optimization method for multi-aircraft hybrid distributed cooperative positioning system

Abstract

The invention relates to the technical field of multi-aircraft cooperative navigation, and provides a multi-criterion joint optimization method for a multi-aircraft hybrid distributed cooperative positioning system. Firstly, a spherical distribution constraint between master and slave nodes in a three-dimensional space is established through a positioning performance evaluation function between the master and slave nodes; secondly, establishing an optimization objective function based on a Fisher information matrix and a space geometric precision factor in combination with communication distance constraints; and finally, the system configuration is optimized by introducing a self-adaptive particle swarm optimization algorithm of a dynamic constraint projection mechanism, and the absolute and relative positioning precision of the cooperative positioning system is effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-aircraft collaborative navigation, and in particular to a multi-criteria joint optimization method for a multi-aircraft hybrid distributed collaborative positioning system. Background Art

[0002] With the widespread application of multi-aircraft systems in complex missions, single aircraft are limited by their blind spots and operating radius, making it difficult to meet the needs of global situational awareness. Collaborative positioning of heterogeneous nodes has become a key development direction. However, current research on collaborative positioning mainly focuses on underwater vehicles or small drones, and mainly focuses on the design of positioning algorithms. There is relatively little research on the configuration optimization of collaborative positioning systems. Existing research often focuses on master-slave architectures in two-dimensional static scenarios, resulting in the neglect of the coupling relationship between vertical positioning accuracy and planar accuracy. Although a few studies have considered three-dimensional space, their methods are still limited by the traversal search mechanism of fixed-position nodes, and cannot achieve the optimal configuration by actively adjusting node positions. Furthermore, all current studies have not incorporated communication distance constraints into the model, limiting their engineering practicality. Summary of the Invention

[0003] To address the above problems, the present invention provides a multi-criteria joint optimization method for a multi-aircraft hybrid distributed collaborative positioning system, comprising the following steps:

[0004] S1. Construct a collaborative positioning model for a multi-aircraft hybrid distributed architecture and define slave node state equations and nonlinear measurement equations.

[0005] S2. Based on the collaborative positioning model, construct a positioning performance evaluation function between the master and slave nodes based on the Fisher information matrix;

[0006] S3. Obtaining a spherical distribution constraint of master and slave nodes in three-dimensional space according to the positioning performance evaluation function;

[0007] S4. Constructing a joint configuration optimization objective function with the spherical distribution constraint and introducing a communication distance constraint;

[0008] S5. Adopting an adaptive particle swarm optimization algorithm combined with a constraint repair strategy to solve the joint configuration optimization objective function and output the optimal configuration.

[0009] 1. According to a multi-criteria joint optimization method for a multi-aircraft hybrid distributed collaborative positioning system provided by the present invention, the state equation of the slave node i in S1 is:

[0010]

[0011] in, is the state quantity of node i at time k+1, is a nonlinear state model, v ix,k ,v iy,k are the speeds of node i in the x and y directions at time k, w k is the state white noise at time k, and its covariance matrix is Q.

[0012] The measurement equation is:

[0013]

[0014] in, is the distance measurement from node i at time k, is a nonlinear measurement model, is the position vector of node i at time k, is the position vector of the master node j at time k, L ii',k and L ij,k are the mutual distances between slave nodes and master-slave nodes at time k, v k To measure white noise, its covariance matrix is R = σ 2 E, σ is the standard deviation of the measurement noise, and E is the unit matrix.

[0015] 2. According to the multi-criteria joint optimization method for a multi-aircraft hybrid distributed collaborative positioning system provided by the present invention, the Fisher information matrix I between the master and slave nodes in S2 Zi (α ij ,θ ij )for:

[0016]

[0017] Among them, i is the slave node number, j is the master node number, α ij and θ ij are the direction angle and altitude angle between the master and slave nodes respectively.

[0018] 3. According to the multi-criteria joint optimization method for a multi-aircraft hybrid distributed collaborative positioning system provided by the present invention, the positioning performance evaluation function S based on the Fisher information matrix in S2 * for:

[0019]

[0020] Where N is the number of slave nodes, μ i is the weight parameter, and det means finding the determinant value of the matrix.

[0021] 4. According to the multi-criteria joint optimization method for a multi-aircraft hybrid distributed collaborative positioning system provided by the present invention, the master-slave node spherical constraint in S3 is:

[0022]

[0023] in, is the position vector of the slave node i, is the position vector of the main node j, and r is the radius of the sphere with the center of the line connecting the two main nodes as the center of the sphere.

[0024] 5. According to the multi-criteria joint optimization method for a multi-aircraft hybrid distributed collaborative positioning system provided by the present invention, the joint configuration optimization objective function J in S4 is:

[0025]

[0026] Among them, min means taking the minimum value, λ is the weighting coefficient, For S * Linear normalization processing, PDOP norm It is the linear normalization processing of the position precision dilution.

[0027] 6. According to the multi-criteria joint optimization method for a multi-aircraft hybrid distributed collaborative positioning system provided by the present invention, the communication distance constraint condition in S4 is:

[0028]

[0029] in, is the position vector of the remaining nodes different from node i, d max is the maximum communication distance.

[0030] 7. According to a multi-criteria joint optimization method for a multi-aircraft hybrid distributed collaborative positioning system provided by the present invention, the adaptive particle swarm optimization algorithm with a constraint repair strategy in S5 includes: initializing the position and velocity of the particle swarm; calculating the individual optimal value and the group optimal value based on the fitness function, and the fitness function F(X) is:

[0031] F(X)=J+ηP

[0032] Among them, η is the penalty coefficient, P is the penalty term, and its expression is:

[0033]

[0034] Among them, max means taking the maximum value.

[0035] Dynamically adjust the particle position and speed, the update formula is:

[0036]

[0037] Where V(t+1) and V(t) are the particle velocities at time t+1 and time t, respectively; X(t+1) and X(t) are the particle positions at time t+1 and time t, respectively; ω(t) is the inertia factor at time t; c1(t) and c2(t) are the adaptive learning factors at time t; r1 and r2 are uniformly distributed random numbers in the interval [0,1] generated independently at each iteration; P best is the individual optimal value, G best is the optimal value for the group.

[0038] Perform position mapping repair on particles that do not meet the constraints: Force projection to two master nodes and For a sphere with a diameter of for:

[0039]

[0040] When the distance between particles is greater than the maximum communication distance, or Direction scaled to d max , and obtain the one that satisfies the communication constraints for:

[0041] BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 Flowchart of an embodiment of the present invention

[0043] Figure 2 Positioning scene graph for embodiments of the present invention

[0044] Figure 3 Flowchart of the adaptive particle swarm optimization algorithm according to the embodiment of the present invention DETAILED DESCRIPTION

[0045] The present application will be further described in detail below in conjunction with the accompanying drawings and embodiments. The specific embodiments described herein are only used to explain the relevant invention and are not intended to limit the invention. In the absence of conflict, the embodiments and features in the embodiments of this application may be combined with each other.

[0046] like Figure 1 As shown, the present invention provides a multi-criteria joint optimization method for a multi-aircraft hybrid distributed collaborative positioning system, comprising the following steps:

[0047] (1) According to Figure 2 For the positioning scenario, define the slave node state equation and nonlinear measurement equation:

[0048]

[0049]

[0050] in, and are the positions of node i in the x and y directions at time k+1, and are the x- and y-direction positions of node i at time k, △t is the time interval, and L ii' and L ij Respectively expressed as:

[0051]

[0052] (2) Based on the above positioning model, the positioning performance evaluation function between the master and slave nodes is constructed as follows:

[0053]

[0054] Among them, I Zi is the Fisher information matrix between the master and slave nodes in the spherical coordinate system, expressed as:

[0055]

[0056] (3) According to the positioning performance evaluation function, the spherical constraint between the master and slave nodes is obtained as follows:

[0057]

[0058] (4) Constructing the joint configuration optimization objective function:

[0059]

[0060] Among them, PDOP is the position precision dilution, and the specific expression is:

[0061]

[0062] in, is the observation matrix in the navigation coordinate system, and its specific expression is:

[0063]

[0064] The communication constraints introduced are:

[0065]

[0066] (5) Design an adaptive particle swarm optimization algorithm with a constraint repair strategy. First, establish the fitness function F(X) with a penalty term as follows:

[0067] F(X)=J+ηP

[0068] Among them, the penalty coefficient η is set to η=10 3 , the specific expression of the penalty term P is:

[0069]

[0070] Then the constraint feedback mechanism is introduced. The specific implementation method is: when the particle violates the spherical constraint, the particle position Force projection to two master nodes and For a sphere with a diameter of When the distance between particles is greater than the maximum communication distance, it is necessary to or Direction scaled to d max After constraint correction Expressed as:

[0071]

[0072] (6) The proposed joint configuration optimization objective function is solved using the proposed adaptive particle swarm optimization algorithm. The specific implementation method is as follows: Figure 3 As shown: Randomly initialize M particle positions X0 and velocities V0 in the feasible domain, and set the main node position coordinates Calculate individual optimal value and the group optimal value G best .

[0073] During each iteration, update the particle velocity and position:

[0074]

[0075] Update individual optimal and group optimal values: Calculate the fitness function value F(X′) of the particle X′ that has completed constraint repair. If Then update the individual optimal position If F(X′) <F(G best ), then update the optimal position of the group G best ←X′.

[0076] Test termination condition: If the number of iterations t is greater than the maximum number of iterations T max , the algorithm terminates; otherwise, iterates again with t←t+1. The optimal configuration is obtained after the iteration is terminated.

[0077] The above description is only a preferred embodiment of this embodiment and does not limit this embodiment in any way. Any simple modification, change and equivalent change made to the above embodiment based on the essence of the invention technology shall still fall within the protection scope of the technical solution of this embodiment.

Claims

1. A multi-criteria joint optimization method for a multi-aircraft hybrid distributed collaborative positioning system, characterized in that Here are the steps: S1. Construct a collaborative positioning model for a multi-aircraft hybrid distributed architecture and define slave node state equations and nonlinear measurement equations. S2. Based on the collaborative positioning model, construct a positioning performance evaluation function between the master and slave nodes based on the Fisher information matrix; S3. Obtaining a spherical distribution constraint of master and slave nodes in three-dimensional space according to the positioning performance evaluation function; S4. Constructing a joint configuration optimization objective function with the spherical distribution constraint and introducing a communication distance constraint; S5. Adopting an adaptive particle swarm optimization algorithm combined with a constraint repair strategy to solve the joint configuration optimization objective function and output the optimal configuration.

2. A multi-criteria joint optimization method for a multi-aircraft hybrid distributed collaborative positioning system according to claim 1, characterized in that: The Fisher information matrix I between the master and slave nodes in S2 Zi (α ij ,θ ij )for: Where i is the slave node number, j is the master node number, σ is the standard deviation of the measurement noise, α ij and θ ij are the direction angle and altitude angle between the master and slave nodes respectively.

3. A multi-criteria joint optimization method for a multi-aircraft hybrid distributed collaborative positioning system according to claim 1, characterized in that: The positioning performance evaluation function S based on the Fisher information matrix described in S2 * for: Where N is the number of slave nodes, μ i is the weight parameter, and det means finding the determinant value of the matrix.

4. A multi-criteria joint optimization method for a multi-aircraft hybrid distributed collaborative positioning system according to claim 1, characterized in that: The spherical constraints of the master and slave nodes in S3 are: in, is the position vector of the slave node i, is the position vector of the main node j, and r is the radius of the sphere with the center of the line connecting the two main nodes as the center of the sphere.

5. A multi-criteria joint optimization method for a multi-aircraft hybrid distributed collaborative positioning system according to claim 1, characterized in that: The joint configuration optimization objective function J described in S4 is: Among them, min means taking the minimum value, λ is the weighting coefficient, For S * Linear normalization processing, PDOP norm It is the linear normalization processing of spatial geometric precision dilution.

6. A multi-criteria joint optimization method for a multi-aircraft hybrid distributed collaborative positioning system according to claim 1, characterized in that: The adaptive particle swarm optimization algorithm with a constraint repair strategy described in S5 includes: initializing the position and velocity of the particle swarm; calculating the individual optimal value and the group optimal value based on the fitness function; dynamically adjusting the particle position and velocity by updating the formula; using the projection operator to perform position mapping repair on particles that do not meet the constraints; and outputting the global optimal configuration after cyclic iteration until the termination condition is met.

7. An adaptive particle swarm optimization algorithm with a constraint repair strategy as claimed in claim 6, characterized in that: The fitness function F(X) used to calculate the individual optimality over the group optimality is: F(X)=J+ηP Among them, η is the penalty coefficient, P is the penalty term, and its expression is: Among them, max means taking the maximum value, is the position vector of the remaining slave nodes other than slave node i, d max is the maximum communication distance.

8. An adaptive particle swarm optimization algorithm with a constraint repair strategy as claimed in claim 6, characterized in that: The projection operator for performing position mapping repair on particles that do not meet the constraints is: Force projection to two master nodes and The sphere with diameter is obtained from the node position vector that satisfies the spherical constraint. for: When the distance between particles is greater than the maximum communication distance, or Direction scaled to d max , and obtain the one that satisfies the communication constraints for:

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