Terrain contour matching method based on adaptive particle swarm optimization
The adaptive particle swarm optimization algorithm adjusts the inertia weight and acceleration factor, combined with the MSD algorithm and terrain feature similarity detection, solves the problem of insufficient terrain matching efficiency and accuracy, and achieves efficient and real-time terrain contour matching and positioning.
Patent Information
- Application Number
- CN202510313704.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-17
- Publication Date
- 2025-06-27
AI Technical Summary
The existing terrain matching assisted navigation methods lack analysis of terrain matching efficiency and matching search methods, and cannot effectively eliminate incorrect matching positioning results, resulting in low positioning accuracy and insufficient system real-time performance.
Adaptive particle swarm optimization algorithm is adopted to adaptively adjust the inertial weight and acceleration factor, combined with the MSD algorithm and terrain feature similarity detection to achieve terrain contour matching.
It improves the positioning accuracy and system real-time performance of terrain matching, reduces the unconvergence problem caused by the algorithm being trapped in local optimality, enhances the ability to adapt to measurement errors, and adapts to different terrain environments.
Smart Images
Figure CN120213016A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of navigation systems and relates to a terrain contour matching method based on adaptive particle swarm optimization. Background Art
[0002] The most commonly used autonomous navigation system for helicopters is the inertial navigation system. However, due to the characteristics of the system itself, the errors in the navigation process will accumulate over time. The terrain-aided navigation technology has the characteristics of high concealment, autonomy, and all-weather operation, and can effectively solve the problem of low positioning accuracy of helicopters without satellite signals.
[0003] The overall architecture of the terrain-aided navigation system is as Figure 1 shown. The combined use of an airborne barometric altimeter and a radar altimeter can provide the terrain height of the current position of the helicopter, and bind the terrain height information with the position information provided by the airborne inertial navigation. Then, terrain height matching is performed in the airborne terrain elevation database according to the adopted matching search algorithm, and the obtained helicopter position information is fed back to the integrated navigation filter to correct the position of the inertial navigation.
[0004] The E-System company in the United States developed the terrain matching navigation TERCOM system, which realizes the correction of position errors by comparing the height information measured in real time by the height sensor on the aircraft with the pre-stored airborne digital terrain height data; aiming at the problem that terrain matching is sensitive to heading errors, Liu Dan et al. from Harbin Engineering University added a rotation angle mechanism on the basis of the TERCOM algorithm, and through the process from rough matching to fine matching, effectively reduced the matching positioning error caused by inertial navigation heading errors and improved the matching accuracy; aiming at the matching problem under low-resolution terrain data, Cheng Xianghong et al. from Southeast University established a local terrain fine model using Gaussian process regression, solved the problem of inaccurate digital terrain models under low resolution, and improved the universality of the terrain matching algorithm under different digital terrains.
[0005] Currently, the research on terrain matching aided navigation methods lacks the analysis and research on terrain matching efficiency and matching search methods, lacks a judgment basis for the reliability and accuracy of matching positioning results, and cannot effectively eliminate incorrect matching positioning results. Summary of the Invention
[0006] The purpose of the present invention is to provide a terrain contour matching method based on adaptive particle swarm optimization.
[0007] The technical solution adopted by the present invention is: a terrain contour matching method based on adaptive particle swarm optimization, comprising the following steps:
[0008] Step 1: Generate a sequence of measured terrain heights based on the indicated position output by the airborne inertial navigation and the information from the airborne altitude sensor;
[0009] Step 2: Form a sequence of search areas according to the indicated position output by the airborne inertial navigation, randomly generate initial particles within the sequence of search areas, and generate a corresponding sequence of matching terrain heights based on the positions of the initial particles;
[0010] Step 3: According to the flow of the adaptive particle swarm optimization algorithm, calculate and iterate the optimization control parameters of the particle swarm, update the velocities and positions of the particles, and achieve matching positioning based on the optimal fitness values of the particles;
[0011] Step 4: Determine whether the maximum number of iterations is satisfied. If not, return to Step 3; if so, proceed to Step 5;
[0012] Step 5: Calculate the basis for judging the availability of the matching result, and judge the availability of the matching result based on its size relationship with the set threshold;
[0013] Step 6: The integrated navigation filter receives the matching result and outputs the corrected position information.
[0014] Furthermore, in Step 1, the generation of the sequence of measured terrain heights is achieved through the indicated position output by the airborne inertial navigation and the airborne altitude sensor. The sequence of measured terrain heights contains n units, and each unit consists of two types of information: position and terrain height. The position distance between adjacent units in the sequence satisfies being greater than the minimum grid size of the adopted airborne digital elevation model, and n is the set maximum sequence length.
[0015] Furthermore, in Step 2, the generation of the sequence of search areas and the sequence of matching terrain heights is achieved through the indicated position information output by the airborne inertial navigation and the airborne digital elevation model.
[0016] The sequence of search areas is formed by extracting a corresponding terrain area from the airborne digital elevation model with the position information in the sequence of measured terrain heights generated in Step 1 as the center.
[0017] The initialization operation of the particle swarm is carried out under the search area. Under the search area, N positions are randomly selected as the initial positions of each particle, where N is the set number of particles in the particle swarm. The corresponding sequence of matching terrain heights for the particles is generated by arranging the map height information corresponding to the same relative positions in the sequence of search areas.
[0018] Furthermore, in Step 3, the flow of the adaptive particle swarm optimization algorithm and the update process of its control parameters are as follows:
[0019] In the adaptive particle swarm optimization algorithm, the solution space is two-dimensional, using V i =(vi1 , v i2 ), X i =(x i1 , x i2 ) represent the velocity and position information of particle i respectively. The next position is updated according to the velocity and the iteration number t. The update formula for each particle is shown in equations (1) and (2):
[0020]
[0021] x id (t + 1)=x id (t)+v id (t + 1) (2)
[0022] For each particle, equations (1) and (2) are used to update the velocity v id and the position x id respectively. d represents the dimension, d = 1, 2; In equation (1), p id (t) is the historical best position of particle i itself at the t-th iteration, p gd (t) is the historical best position of all particles in the particle swarm at the t-th iteration, w id (t) is the inertia weight of particle i at the t-th iteration, which plays a role in balancing the global and local optimization abilities of the particle. c1(t) and c2(t) are the acceleration factors at the t-th iteration, representing the ability of the particle to advance towards its own extreme value and the global extreme value. T is the maximum number of iterations, t is the current number of iterations, and e is the influence factor;
[0023] To make the adaptive particle swarm optimization algorithm more stable and have a better convergence effect, the inertia weight is adaptively changed, and the change rule is shown in equation (3) below:
[0024]
[0025] In equation (3), w min and w max are the pre-set minimum and maximum inertia weight coefficients; f(x id (t)) is the fitness value of the i-th particle at the t-th iteration; and represent the minimum fitness and maximum fitness of all particles at the t-th iteration respectively; represents the average fitness of all particles at the t-th iteration, which is expressed by equation (4):
[0026]
[0027] To avoid particles falling into local extrema, the acceleration factor is updated according to the adaptive inertia weight, and its update formula is shown in Equations (5) and (6):
[0028]
[0029] In Equations (5) and (6), c start and c end are the preset initial value and final value respectively.
[0030] Furthermore, in Step 3, the optimal fitness of the particle is required to achieve matching and positioning. The calculation method of the particle fitness is as follows:
[0031] Taking the MSD (Mean Square Difference) algorithm as the calculation method of the particle fitness, its specific expression is as follows:
[0032]
[0033] In Equation (7), n is the maximum sequence length; h r,i and h m,i are the measured terrain height and the height indicated by the airborne digital elevation model at the i-th sampling point respectively;
[0034] According to Equation (8), calculate the absolute error of each sampling point in the matching terrain height sequence;
[0035]
[0036] In the above formula, and are the average heights of the measured terrain height sequence and the matching terrain height sequence respectively, and ε i is the absolute error calculated at the i-th sampling point;
[0037] Set the threshold θ, accumulate the absolute errors of each sampling point and compare them with the threshold θ, and calculate the maximum accumulation times R when the accumulated error is less than the threshold, as shown in Equation (9);
[0038]
[0039] Combine the calculated accumulation times R with the J MSD calculated by the mean square error algorithm, and the specific combination method is shown in Equation (10):
[0040]
[0041] When the accumulation times R is the largest and J MSD is the smallest, H can be maximized, and the matching terrain height sequence at this time is the optimal matching sequence.
[0042] Further, in step 5, whether the matching result is available is judged according to the similarity between the measured terrain elevation sequence data and the terrain features presented by the matched terrain elevation sequence data. For the description of terrain features, the following terrain features are used as the judgment basis:
[0043] (1) Terrain undulation degree
[0044]
[0045] In the above formula, Δ h represents the terrain undulation degree, that is, the difference between the maximum elevation and the minimum elevation of the terrain elevation sequence (including the measured terrain elevation sequence and the matched terrain elevation sequence).
[0046] (2) Terrain elevation standard deviation
[0047]
[0048] In the above formula, σ h represents the terrain elevation standard deviation of the terrain elevation sequence (including the measured terrain elevation sequence and the matched terrain elevation sequence), represents the average elevation value of the terrain elevation sequence (including the measured terrain elevation sequence and the matched terrain elevation sequence).
[0049] (3) Terrain elevation entropy
[0050]
[0051] In the above formula, S h is the terrain elevation entropy, which is used to describe the irregularity of high information in the terrain elevation sequence (including the measured terrain elevation sequence and the matched terrain elevation sequence), and can be considered as the degree of terrain undulation change. P i is the proportion of each elevation value in the terrain elevation sequence (including the measured terrain elevation sequence and the matched terrain elevation sequence) to the total elevation value;
[0052] Normalize each feature according to formula (14):
[0053]
[0054] In the above formula, ξ refers to various terrain feature descriptions mentioned in formulas (11), (12), and (13), ξ′ is the terrain feature description after scale unification processing, ξ m and ξ r are the terrain feature descriptions of the matched terrain elevation sequence and the measured terrain elevation sequence respectively;
[0055] Based on the above descriptions and normalization of various terrain features, the specific expression of the terrain matching availability judgment criterion is shown as the following formula:
[0056] γ = k1Δ′ h + k2σ h ′ + k3S h ′ (15)
[0057] In formula (15), k1, k2, and k3 are the weights of the above descriptions of various terrain features, and the weights satisfy k1 + k2 + k3 = 1. Δ h ′, σ h ′, and S h ′ are the results after normalization of various terrain features. The relationship between the terrain matching availability judgment criterion and the set threshold is as follows:
[0058]
[0059] In the above formula (16), P T is the position obtained by this terrain matching, P INS is the inertial navigation position input for this terrain matching, and P is the position information finally output to the integrated navigation filter. When the terrain matching availability judgment criterion is less than or equal to the set threshold of 0.1, the terrain matching result of this time is retained and the result is input into the integrated navigation filter to output the corrected position information; if the availability judgment criterion is greater than the set threshold of 0.1, the inertial navigation result is input into the integrated navigation filter to output the corrected position information, and the integrated navigation filter uses a Kalman filter.
[0060] The beneficial effects of the present invention are as follows: (1) The terrain contour matching method based on adaptive particle swarm optimization proposed by the present invention uses the particle swarm optimization algorithm as the matching search strategy. On the basis of the traditional particle swarm optimization algorithm, the inertial weight and acceleration factor are adaptively changed according to the particle fitness, effectively taking into account the global and local optimization capabilities of the algorithm, and being able to search for the optimal position with fewer iterations and greatly reducing the problem of non-convergence caused by the algorithm falling into local optima; (2) By introducing the correlation calculation based on sequential similarity detection on the basis of the commonly used MSD correlation criterion, the present invention effectively improves the adaptability to measurement errors; (3) Designing an availability judgment criterion for the matching result, by making full use of inertial navigation information and terrain contour feature information, it can effectively cope with the influence of flat terrain on the matching performance and further improve the matching positioning accuracy; (4) Simulation experiments show that compared with traditional terrain matching methods, the terrain contour matching method based on adaptive particle swarm optimization proposed by the present invention can greatly reduce the time-consuming of a single match, improve the real-time performance of the system, and in different terrain environments, this method shows better matching positioning accuracy.
[0061] In addition to the purposes, features, and advantages described above, the present invention has other purposes, features, and advantages. The present invention will be described in further detail below with reference to the drawings. Description of the Drawings
[0062] Figure 1 It is a structural diagram of a terrain-aided navigation system.
[0063] Figure 2 It is a composition diagram of the measured altitude sequence.
[0064] Figure 3 It is a composition diagram of the search area sequence and the matched terrain altitude sequence.
[0065] Figure 4 It is a diagram of the steep terrain profile change.
[0066] Figure 5 It is a diagram of the flat terrain profile change.
[0067] Figure 6 It is a simulation diagram of a steep track.
[0068] Figure 7 It is a diagram of the attitude angle change of a steep track.
[0069] Figure 8 It is a simulation diagram of a flat track.
[0070] Figure 9 It is a diagram of the attitude angle change of a flat track.
[0071] Figure 10 It is a diagram of the matching positioning error (5m) of two algorithms under steep terrain.
[0072] Figure 11 It is a diagram of the matching positioning error (10m) of two algorithms under steep terrain.
[0073] Figure 12 It is a diagram of the matching positioning error (5m) of two algorithms under flat terrain.
[0074] Figure 13 It is a diagram of the matching positioning error (10m) of two algorithms under flat terrain. Detailed Embodiment
[0075] The present invention will be described in detail below in conjunction with the drawings and the detailed embodiment.
[0076] A terrain contour matching method based on adaptive particle swarm optimization includes the following steps:
[0077] Step 1: Generate a measured terrain altitude sequence according to the indicated position output by the airborne inertial navigation and the information of the airborne altitude sensor;
[0078] Step 2: According to the indicated position output by the airborne inertial navigation, form a search area sequence, randomly generate initial particles within the search area sequence, and generate a corresponding matching terrain height sequence based on the initial particle positions;
[0079] Step 3: According to the process of the adaptive particle swarm optimization algorithm, calculate and iterate the optimization control parameters of the particle swarm, update the velocities and positions of the particles, and achieve matching positioning based on the optimal fitness values of the particles;
[0080] Step 4: Determine whether the maximum number of iterations is satisfied. If not, return to Step 3; if so, proceed to Step 5;
[0081] Step 5: Calculate the basis for judging the availability of the matching result, and judge the availability of the matching result based on its size relationship with the set threshold;
[0082] Step 6: The integrated navigation filter receives the matching result and outputs the corrected position information.
[0083] Further, in the above Step 1, the generation of the measured terrain height sequence is achieved through the indicated position output by the airborne inertial navigation and the airborne altitude sensor, and its sequence composition is as Figure 2 shown. The measured terrain height sequence contains n units, and each unit consists of two types of information: position and terrain height. The position distance between adjacent units in the sequence satisfies being greater than the minimum grid size of the adopted airborne digital elevation model, and n is the set maximum sequence length.
[0084] Further, in the above Step 2, the generation of the search area sequence and the matching terrain height sequence is achieved through the indicated position information output by the airborne inertial navigation and the airborne digital elevation model. The composition of the search area sequence and the generation of the matching terrain height sequence are as follows Figure 3 shown,
[0085] The search area sequence is formed by extracting a corresponding terrain area from the airborne digital elevation model with the position information in the measured terrain height sequence generated in Step 1 as the center, Figure 3 where the red dots are the position information of each unit in the measured terrain height sequence, and the red area is the formed search area,
[0086] Figure 3 where the initialization operation of the particle swarm is carried out under the search area. Under the search area, N positions are randomly selected as the initial positions of each particle, and N is the set number of particles in the particle swarm, Figure 3 where the black solid circle is one of the initialized particles, and the corresponding matching terrain height sequence of this particle is generated by arranging the map height information corresponding to the same relative position ( Figure 3 the black hollow circle in) in the search area sequence.
[0087] Furthermore, in step 3, the process of the adaptive particle swarm optimization algorithm and the update process of its control parameters are as follows:
[0088] In the adaptive particle swarm optimization algorithm, the solution space is two-dimensional. Let V i =(v i1 , v i2 ) and X i =(x i1 , x i2 ) represent the velocity and position information of particle i respectively. The next position is updated according to the velocity and the iteration number t. The update formula for each particle is shown in equations (1) and (2):
[0089]
[0090] x id (t + 1)=x id (t)+v id (t + 1) (2)
[0091] For each particle, equations (1) and (2) are used to update the velocity v id and the position x id respectively. d represents the dimension, d = 1, 2. In equation (1), p id (t) is the historical best position of particle i itself at the t-th iteration, p gd (t) is the historical best position of all particles in the particle swarm at the t-th iteration, w id (t) is the inertia weight of particle i at the t-th iteration, which plays a role in balancing the global optimization and local optimization capabilities of the particle. c1(t) and c2(t) are the acceleration factors at the t-th iteration, representing the ability of the particle to advance towards its own extreme value and the global extreme value. T is the maximum number of iterations, t is the current number of iterations, and e is the influence factor;
[0092] To make the adaptive particle swarm optimization algorithm more stable and have a better convergence effect, the inertia weight is adaptively changed, and the change rule is shown in equation (3) as follows:
[0093]
[0094] In equation (3), w min and w max are the pre-set minimum and maximum inertia weight coefficients; f(x id (t)) is the fitness value of the i-th particle at the t-th iteration; and represent the minimum fitness and the maximum fitness of all particles at the t-th iteration respectively; Denote the average fitness of all particles at the $t$-th iteration, which is expressed by Equation (4):
[0095]
[0096] To prevent particles from falling into local optima, the acceleration factors are updated according to an adaptive inertia weight, and the update formulas are shown in Equations (5) and (6):
[0097]
[0098] In Equations (5) and (6), $c_1$ start and $c_2$ end are the preset initial value and final value, respectively.
[0099] Furthermore, in Step 3, the optimal fitness of the particles is required to achieve matching and positioning. The calculation method of the particle fitness is as follows:
[0100] Taking the MSD (Mean Square Difference) algorithm as the calculation method of the particle fitness, its specific expression is as follows:
[0101]
[0102] In Equation (7), $n$ is the maximum sequence length; $h_i$ r,i and $h_i^{'}$ m,i are the measured terrain height and the height indicated by the airborne digital elevation model at the $i$-th sampling point, respectively;
[0103] According to Equation (8), calculate the absolute error of each sampling point in the matching terrain height sequence;
[0104]
[0105] In the above formula, and are the average heights of the measured terrain height sequence and the matching terrain height sequence, respectively, and $\epsilon_i$ i is the absolute error calculated at the $i$-th sampling point;
[0106] Set a threshold $\theta$, accumulate the absolute errors of each sampling point and compare them with the threshold $\theta$, and calculate the maximum accumulation times $R$ when the accumulated error is less than the threshold, as shown in Equation (9);
[0107]
[0108] Combine the calculated accumulation times $R$ with $J$ MSD calculated by the mean square deviation algorithm, and the specific combination method is shown in Equation (10):
[0109]
[0110] When the number of accumulations R is maximum and J MSD is minimum, H can be maximized, and the matching terrain height sequence at this time is the optimal matching sequence.
[0111] Furthermore, in step 5, whether the matching result is available is judged according to the similarity between the measured terrain height sequence data and the terrain features presented by the obtained matching terrain height sequence data. For the description of terrain features, the following terrain features are used as the judgment basis:
[0112] (4) Terrain undulation degree
[0113]
[0114] In the above formula, Δ h represents the terrain undulation degree, that is, the difference between the maximum elevation and the minimum elevation of the terrain height sequence (including the measured terrain height sequence and the matching terrain height sequence).
[0115] (5) Standard deviation of terrain elevation
[0116]
[0117] In the above formula, σ h represents the standard deviation of the terrain elevation of the terrain height sequence (including the measured terrain height sequence and the matching terrain height sequence), and represents the average elevation value of the terrain height sequence (including the measured terrain height sequence and the matching terrain height sequence).
[0118] (6) Entropy of terrain elevation
[0119]
[0120] In the above formula, S h is the entropy of terrain elevation, which is used to describe the irregularity of high information in the terrain height sequence (including the measured terrain height sequence and the matching terrain height sequence), and can be considered as the degree of terrain undulation change. P i is the proportion of each elevation value in the terrain height sequence (including the measured terrain height sequence and the matching terrain height sequence) to the total elevation value;
[0121] Normalize each feature according to formula (14):
[0122]
[0123] In the above formula, ξ refers to various terrain feature descriptions mentioned in formulas (11), (12), and (13), ξ′ is the terrain feature description after scale unification processing, ξ m and ξ rThey are the terrain feature descriptions that match the terrain altitude sequence and the terrain feature descriptions of the measured terrain altitude sequence respectively;
[0124] Based on the above terrain feature descriptions and normalization, the specific expression of the terrain matching availability judgment criterion is shown as the following formula:
[0125] γ = k1Δ′ h + k2σ′ h + k3S′ h (15)
[0126] In formula (15), k1, k2, and k3 are the weights of the above terrain feature descriptions, and the weights satisfy k1 + k2 + k3 = 1. Δ′ h , σ′ h and S′ h are the results after normalization of each terrain feature. When the terrain features of the measured terrain altitude sequence and the matching terrain altitude sequence are more similar, γ is closer to 0. The relationship between the terrain matching availability judgment criterion and the set threshold is as follows:
[0127]
[0128] In the above formula (16), P T is the position obtained by this terrain matching, P INS is the inertial navigation position input for this terrain matching, and P is the position information finally output to the integrated navigation filter. When the terrain matching availability judgment criterion is less than or equal to the set threshold of 0.1, the terrain matching result of this time is retained and the result is input into the integrated navigation filter to output the corrected position information; if the availability judgment criterion is greater than the set threshold of 0.1, the inertial navigation result is input into the integrated navigation filter to output the corrected position information, and the integrated navigation filter uses a Kalman filter.
[0129] To verify the effectiveness of the algorithm proposed in the present invention, terrain contour matching based on adaptive particle swarm optimization is simulated and verified. The simulation verification is based on the ASTER GDEM V3 digital elevation model, and the map resolution of this model is 30m, and the elevation standard deviation is 12.1m. Two different terrain change flight tracks are selected in the northwest region of China, representing the flight track in the steep area and the flight track in the flat area respectively. The terrain undulation changes of the selected flight tracks are as Figure 4 and Figure 5 shown, and the specific terrain feature parameters are shown in Table 1.
[0130] Table 1 Terrain Feature Parameters
[0131]
[0132] The selected terrain feature parameters can simply describe the terrain features, information richness, and terrain changes. Classified according to terrain roughness, steep tracks have a higher roughness than flat tracks, and the terrain undulations are more intense. These two types of tracks can represent different terrain features to verify the matching performance of the algorithm under different terrain features.
[0133] Experiment 1: Verification of the Optimization Performance of the Adaptive Particle Swarm Algorithm
[0134] To verify the optimization performance of the adaptive particle swarm optimization algorithm, the performance of the basic PSO algorithm and the algorithm of the present invention are compared. The experiment sets the number of particle swarms to 100. In the improved PSO algorithm, based on the value-taking experience of the parameters of the basic PSO algorithm, the inertial weight w min and w max are set to 0.3 and 1.3 respectively, and the acceleration factors c start and c end are set to 2 and 1 respectively. Equation (10) is used as the fitness calculation function of the particles for optimization. During the optimization process, the track in the steep area is used as the simulation track, and the search range is set as a square area of 2000m in each of the four directions of east, south, west, and north centered on the inertial navigation indicated position. The optimization accuracy is determined by the positioning error being less than twice the digital terrain resolution, and the non-convergence rate of the optimization is determined by the positioning error being greater than 10 times the digital terrain resolution. The positioning error is represented by the root mean square error (RMSE) of the optimized position after removing the non-convergent values. Based on the optimization positioning error, optimization accuracy, non-convergence rate of the optimization, and single matching time, the performance of the two algorithms is judged. Table 2 shows the comparison summary of the positioning error, optimization accuracy, non-convergence rate of the optimization, and single matching time of the two algorithms under different iteration times.
[0135] Table 2 Summary of Optimization Experiment Results
[0136]
[0137] Through the above experimental results, at different numbers of iterations, the optimization and positioning performance of the adaptive PSO algorithm is significantly better than that of the basic PSO algorithm. Compared with the basic PSO algorithm, since the inertia weight of the adaptive PSO algorithm adaptively changes according to the particle fitness, taking into account both the global and local optimization capabilities of the algorithm, it can search for the optimal position in fewer iterations. At the same time, according to the change of the inertia weight, the acceleration factor also changes adaptively, appropriately adjusting the cognitive ability of the particles and the social information sharing ability. The problem of non-convergence of the optimization caused by the algorithm falling into the local optimum is greatly reduced. At different numbers of iterations, the optimization accuracy of the adaptive PSO algorithm is higher than that of the basic PSO algorithm. Compared with the basic PSO algorithm that needs to increase the number of iterations to reduce the occurrence of non-convergence problems, the adaptive PSO algorithm can avoid the occurrence of non-convergence problems in fewer iterations, and the positioning error after removing the non-convergent part is still better than that of the basic PSO algorithm. According to the above analysis, the basic PSO algorithm requires more iterations to converge the algorithm to obtain a good optimization effect, while the adaptive PSO algorithm can achieve a better optimization effect in fewer iterations, thereby reducing the impact of the relatively long time-consuming for single matching by setting fewer iterations and improving the optimization efficiency of the algorithm.
[0138] Experiment 2: Verification of terrain matching effect
[0139] To verify the performance of the terrain matching algorithm based on the adaptive particle swarm, the algorithm of the present invention is compared with the traditional TERCOM algorithm under different measurement noises and terrain features, mainly from two aspects: matching positioning error and matching time consumption. In the simulation verification, the flight altitude of the helicopter is set to 2000m, the search range is the same as that set in Experiment 1, the terrain matching time interval is the time taken for the helicopter to cross the terrain elevation database grid size, the terrain matching distance error is obtained by taking the square root of the matching longitude and latitude error, and the positioning error is represented by the root mean square error of the combined navigation output position error after matching positioning. Random noises with standard deviations of 5m and 10m are added to the altitude measurement as measurement errors. The specific simulation parameter settings are shown in Table 3. Figure 6 、 Figure 8 respectively show the true values, pure inertial navigation tracks, and matching combined navigation tracks of two different terrain feature tracks on the map. Figure 7 、 Figure 9 respectively show the change curves of the attitude angles during the simulation process under the corresponding terrain tracks.
[0140] Table 3 Simulation parameters
[0141]
[0142] According to Figure 4And according to the information in Table 1, the steep track has a more undulating terrain profile, which well meets the requirements of terrain matching for terrain features. Figure 10 、 Figure 11 They are respectively the positioning performances of the algorithm of the present invention and the traditional TERCOM algorithm under different measurement noises on this track. Table 4 is the summary of the matching result information.
[0143] Table 4 Terrain matching results in the steep area
[0144]
[0145] It can be seen from the information in Table 4 that for the steep terrain, both the algorithm of the present invention and the traditional TERCOM algorithm have achieved good positioning effects. However, the algorithm of the present invention uses adaptive particle swarm optimization as the search strategy, and the single - match positioning time consumption is only 35.4% of that of the traditional TERCOM algorithm, having better real - time performance; under different measurement noises, the positioning errors of the algorithm of the present invention are respectively 68.9% and 65.9% of the positioning errors of the TERCOM algorithm. Especially under larger measurement errors, the positioning accuracy of the algorithm of the present invention is improved more because sequential similarity detection is added on the basis of the traditional similarity calculation, which can better cope with the adverse effects of the increase in measurement errors on the calculation of terrain profile similarity, making the algorithm have better robustness.
[0146] According to Figure 5 and the information in Table 1, compared with the steep track, the flat track has a smaller terrain undulation degree and relatively fewer terrain features, which has a greater impact on the terrain matching accuracy. Figure 12 、 Figure 13 They respectively show the matching and positioning performances of the algorithm of the present invention and the TERCOM algorithm for the flat terrain under different measurement noises. Table 5 is the summary of the matching result information.
[0147] Table 5 Terrain matching results in the flat area
[0148]
[0149] From the above information, in flat terrain, the matching effect of the algorithm of the present invention is significantly better than that of the traditional TERCOM algorithm. Under different measurement noises, the positioning errors of the algorithm of the present invention are only 41.4% and 23.8% of those of the traditional TERCOM algorithm. Due to the fact that the traditional TERCOM algorithm is sensitive to terrain undulations and vulnerable to measurement errors, larger measurement errors and fewer terrain undulation features lead to a significant increase in its matching and positioning errors, making it unable to meet the positioning accuracy requirements for helicopter flight navigation. Since the algorithm of the present invention designs a matching availability judgment criterion, it no longer solely relies on terrain elevation information, but fully utilizes inertial navigation information and various different terrain profile features to evaluate the availability of the matching result, effectively eliminating error information and greatly improving the integrated navigation accuracy. This design effectively addresses the adverse effects on terrain matching caused by the lack of significant terrain features in flat areas, thus ensuring the positioning performance of the terrain matching system.
[0150] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.
Claims
1. A terrain contour matching method based on adaptive particle swarm optimization, characterized in that: The following steps are involved: Step 1: Generate a measured terrain elevation sequence based on the indicated position output by the airborne inertial navigation system and the information from the airborne altitude sensor; Step 2: According to the indicated position output by the airborne inertial navigation, a search area sequence is formed, initial particles are randomly generated in the search area sequence, and a corresponding matching terrain elevation sequence is generated according to the initial particle position; Step 3: According to the adaptive particle swarm optimization algorithm process, the optimal control parameters of the particle swarm are calculated and iterated, the speed and position of the particles are updated, and matching positioning is achieved according to the optimal fitness value of the particles; Step 4: Determine whether the maximum number of iterations is met. If not, return to step 3; if yes, proceed to step 5; Step 5: Calculate the basis for judging the availability of the matching result, and use the relationship between the basis and the set threshold to judge the availability of the matching result; Step 6: The integrated navigation filter receives the matching results and outputs the corrected position information.
2. The terrain contour matching method based on adaptive particle swarm optimization according to claim 1 is characterized in that: In the step 1, the generation of the measured terrain elevation sequence is realized by the indicated position output by the airborne inertial navigation and the airborne altitude sensor. The measured terrain elevation sequence includes n units, each unit is composed of two types of information: position and terrain height. The position distance between adjacent units in the sequence satisfies that it is greater than the minimum grid size of the adopted airborne digital elevation model, and n is the set maximum sequence length.
3. The terrain contour matching method based on adaptive particle swarm optimization according to claim 2 is characterized in that: In step 2, the generation of the search area sequence and the matching terrain elevation sequence is realized through the indicated position information output by the airborne inertial navigation and the airborne digital elevation model. The search area sequence is formed by extracting a corresponding terrain area from the airborne digital elevation model based on the position information in the measured terrain elevation sequence generated in step 1. The initialization operation of the particle swarm is performed in the search area. In the search area, N positions are randomly selected as the initial positions of each particle, where N is the number of particles set in the particle swarm. The matching terrain elevation sequence corresponding to the particle is generated by selecting the map height information corresponding to the same relative position in the search area sequence and arranging them.
4. The terrain contour matching method based on adaptive particle swarm optimization according to claim 3 is characterized in that: In step 3, the adaptive particle swarm optimization algorithm flow and its control parameter update process are as follows: In the adaptive particle swarm optimization algorithm, the solution space is 2-dimensional, using V i =(v i1 ,v i2 ), X i =(x i1 ,x i2 ) represent the speed and position information of particle i respectively. The next position is updated according to the speed and the number of iterations t. The update formula of each particle is shown in equations (1) and (2): x id (t+1)=x id (t)+v id (t+1) (2) For each particle, the velocity v of the particle is calculated using equations (1) and (2) respectively. id and position x id Update, d represents the dimension, d = 1, 2; in formula (1), p id (t) is the best historical position of particle i itself in the tth iteration, p gd (t) is the best historical position of all particles in the particle swarm at the tth iteration, w id (t) is the inertia weight of particle i at the t-th iteration, which plays a role in balancing the global optimization and local optimization capabilities of the particle. c1(t) and c2(t) are the acceleration factors at the t-th iteration, representing the ability of the particle to advance to its own extreme value and the global extreme value. T is the maximum number of iterations, t is the current number of iterations, and e is the influence factor. The inertia weight is adaptively changed, and the change rule is shown in the following formula (3): In formula (3), w min and w max are the preset minimum and maximum inertia weight coefficients; f(x id (t)) is the fitness of the i-th particle at the t-th iteration; and They represent the minimum fitness and maximum fitness of all particles at the tth iteration respectively; represents the average fitness of all particles at the tth iteration, which is expressed by formula (4): The acceleration factor is updated according to the adaptive inertia weight, and its update formula is shown in equations (5) and (6): In formulas (5) and (6), c start and c end They are the preset initial value and final value respectively.
5. The terrain contour matching method based on adaptive particle swarm optimization according to claim 4 is characterized in that: In step 3, the optimal fitness of the particles is required to achieve matching positioning. The particle fitness is calculated as follows: The MSD (Mean Square Difference) algorithm is used as the particle fitness calculation method, and its specific expression is as follows: In formula (7), n is the maximum sequence length; h r,i and h m,i are the measured terrain height and the indicated height of the airborne digital elevation model at the i-th sampling point, respectively; According to formula (8), the absolute error of each sampling point in the matching terrain elevation sequence is calculated; In the above formula, and are the average heights of the measured terrain elevation sequence and the matched terrain elevation sequence, ε i is the absolute error calculated for the i-th sampling point; Set the threshold θ, accumulate the absolute errors of each sampling point and compare them with the threshold θ, and calculate the maximum accumulation times R when the accumulated error is less than the threshold, as shown in formula (9); The calculated cumulative number R and the J calculated by the mean square error algorithm are MSD The specific combination method is shown in formula (10): When the cumulative number R is the largest and J MSD When it is minimum, H can be maximized, and the matching terrain height sequence at this time is the optimal matching sequence.
6. The terrain contour matching method based on adaptive particle swarm optimization according to claim 5, characterized in that: In step 5, whether the matching result is available is judged based on the similarity between the terrain features presented by the measured terrain elevation sequence data and the matched terrain elevation sequence data obtained by matching. For the description of the terrain features, the following terrain features are used as the basis for judgment: (1) Terrain relief In the above formula, Δ h It represents the terrain relief, that is, the difference between the maximum elevation and the minimum elevation of the terrain elevation series. (2) Standard deviation of terrain elevation In the above formula, σ h represents the standard deviation of the terrain elevation of the terrain elevation series, Indicates the average elevation value of the terrain elevation series. (3) Terrain elevation entropy In the above formula, S h is the terrain elevation entropy, which is used to describe the irregular shapes with high information in the terrain elevation series. i It is the proportion of each elevation value in the terrain elevation series to the total elevation value; Each feature is normalized according to formula (14): In the above formula, ξ refers to the various terrain feature descriptions mentioned in formulas (11), (12), and (13), ξ′ is the terrain feature description after scale uniformization, and ξ m and r They are the terrain feature description of the matched terrain elevation sequence and the terrain feature description of the measured terrain elevation sequence; Based on the description and normalization of the above terrain features, the specific expression of the basis for judging the availability of terrain matching is as follows: γ=k1Δ′ h +k2σ′ h +k3S′ h (15) In formula (15), k1, k2 and k3 are the weights of the above-mentioned terrain feature descriptions, and each weight satisfies k1+k2+k3=1, Δ h ′、σ h ′ and S h ′ is the result after normalization of terrain features. The relationship between the matching result availability judgment basis and the set threshold is as follows: In the above formula (16), P T is the position obtained by this terrain matching, P INS is the inertial navigation position input for this terrain matching, P is the position information finally output to the integrated navigation filter, when the availability judgment basis of this terrain matching is less than or equal to the set threshold value 0.1, the terrain matching result of this time is retained and the result is input into the integrated navigation filter to output the corrected position information; If the availability judgment basis is greater than a set threshold value of 0.1, the inertial navigation result is input into the integrated navigation filter to output the corrected position information, and the integrated navigation filter adopts a Kalman filter.