Method for smoothing rising and falling rate of aircraft based on two-parameter Holt model

Abstract

The invention discloses a method for smoothing the rising and falling rate of an aircraft based on a two-parameter Holt model, and the method comprises the steps: collecting the track information of an automatic system within a certain time, and screening out a system fusion track containing the participation of an ADS-B (Automatic Dependent Surveillance-Broadcast) signal; the height of an ADS-B signal in the system fusion track is extracted, the ADS-B signal is sampled according to the updating period of the system fusion track, and a two-parameter full-time Holt model is established according to the ADS-B sampling height and the sampling period; establishing a weighted objective function of a normalized height mean square error and a normalized rising and falling rate mean square error, and determining model parameters in combination with a Monte Carlo method; establishing a two-parameter interval Holt model; and inputting the real-time track of the aircraft into the two-parameter interval Holt model, dynamically adjusting and optimizing model parameters, and outputting a real-time rising and falling rate. According to the method, a two-parameter Holt model is established according to the height and the rising and falling rate of a fused track, historical track information containing ADS-B signals is used for training model parameters, the model parameters are locally adjusted in a fixed interval, and the smooth rising and falling rate is output through a minimum objective function in the interval.

Description

Technical Field

[0001] The invention belongs to the field of air traffic management, and in particular relates to a method for smoothing an aircraft ascent and descent rate based on a double-parameter Holt model. Background Art

[0002] Aircraft ascent and descent rate is an important indicator in the air traffic automation system. Its accuracy and stability are directly related to the calculation results of conflict prediction and low altitude warning in the control system, which affects the judgment and control of controllers and is of great significance to the safety of air traffic management.

[0003] At present, the output rise and fall rate of the mainstream air traffic control automation system (taking NUMEN3000 as an example) is often obtained by weighted average of instantaneous rise and fall rates of several cycles, where the calculation of instantaneous rise and fall rate is the difference in the fused track altitude of adjacent cycles divided by the time difference of altitude update. The fused track is formed by the fusion of track information provided by multiple different types of signal sources such as multiple radars (divided into ordinary secondary radar and S-mode radar), ADS-B or multi-point, and the altitude of the fused track follows the most recent update strategy (that is, the reliable signal source closest to the fused track update cycle is preferentially selected). Different signal sources have different refresh cycles (generally 4s for radar, 1s for ADS-B or multi-point), and there are also differences in altitude accuracy (±50 feet for ordinary secondary radar, ±12.5 feet for S-mode, ADS-B and multi-point). When the altitude of the fused track switches between different signal sources, it is easy to have uneven altitude intervals and altitude update time intervals in adjacent cycles, causing the calculation results of the instantaneous rise and fall rate to fluctuate, and the system output rise and fall rate after weighted average is also unstable, resulting in false alarms in the alarm module of the automation system, which interferes with the judgment of control.

[0004] The two-parameter Holt model is a commonly used smoothing algorithm for analyzing trend time series. This method can smooth both the sequence value and the trend item and reduce the disordered fluctuation of the data. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the prior art, the purpose of the present invention is to provide a method for smoothing the aircraft ascent and descent rate based on a dual-parameter Holt model, so as to solve the problems of low precision and poor stability of the existing aircraft ascent and descent rate methods; the method of the present invention establishes a dual-parameter Holt model according to the altitude and ascent and descent rate of the fused track, trains the model parameters with the historical track information containing the ADS-B signal, locally adjusts the model parameters in a fixed interval, and outputs the smoothed ascent and descent rate with the minimum objective function within the interval.

[0006] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A method for smoothing aircraft ascent and descent rate based on a dual-parameter Holt model of the present invention comprises the following steps:

[0008] 1) Collect the track information of the automated system within a certain period of time and select the system fusion track involving ADS-B signals;

[0009] 2) Extract the height of the ADS-B signal in the system fusion track, sample the ADS-B signal according to the update period of the system fusion track, and establish a dual-parameter full-time Holt model based on the ADS-B sampling height and sampling period;

[0010] 3) Establish a weighted objective function of the normalized height mean square error and the normalized lift rate mean square error, and determine the model parameters in combination with the Monte Carlo method;

[0011] 4) Select model parameters according to aircraft type and take-off and landing status, and establish a two-parameter interval Holt model;

[0012] 5) Input the real-time trajectory of the aircraft into the dual-parameter interval Holt model, dynamically tune the model parameters, and output the real-time ascent and descent rate.

[0013] Furthermore, the step 1) specifically includes:

[0014] The collected system fusion tracks are grouped according to aircraft type and ascent and descent status. The aircraft types are divided into three categories: heavy aircraft, medium aircraft and light aircraft. The ascent and descent status are divided into two categories: ascent and descent. A total of six groups are established. When grouping, only the ADS-B altitude and corresponding time of the corresponding period of the ascent and descent status are recorded, which is represented as an altitude time series. The recorded period is a continuous movement process in the same direction (ascent or descent), and the altitude changes evenly during this period. The ascent and descent rate within this period is set to fluctuate slightly, and the period that does not meet the requirements is discarded and not recorded.

[0015] Furthermore, the step 2) specifically includes:

[0016] The ADS-B altitude time series recorded in step 1) is sampled according to the update period of the system fusion track, and the initial two-parameter full-time Holt model is established for the sampled altitude time series. The formula is as follows:

[0017]

[0018] Among them, H t+1 is the height smoothing value at time t+1; h t+1 is the trend smoothing value at time t+1; X t+1 is the input parameter at time t+1, i.e. the ADS-B altitude after sampling; α and β are smoothing parameters, ranging from 0 to 1; where the full period is the duration of a continuous movement in the same direction recorded in step 1), and its value is N*T, where N is the number of sampling points; the subscript t ranges from 0 to (N-1); different groups correspond to different smoothing parameter values, which characterize the grouping characteristics;

[0019] Replace the term h in equation (1) with the instantaneous rise and fall rate g*sampling period T, and we get the following equation:

[0020]

[0021] Among them, g t+1 is the smoothed value of the rise and fall rate at time t+1, g t is the smoothed value of the rise and fall rate at time t; compensate for one cycle to reduce the impact of measurement accuracy on the instantaneous rise and fall rate after smoothing (for the case of a small rise and fall rate, such as when the height difference of ADS-Bs in adjacent sampling cycles is less than the quantization scale of 25ft, it may cause the measured heights of adjacent ADS-Bs to be equal or enlarged, resulting in smoothed g t The sequence will also have corresponding fluctuations). After period compensation, the final dual-parameter full-time Holt model is obtained, which is expressed as follows:

[0022]

[0023] Furthermore, the step 3) specifically includes:

[0024] Randomly select a system fusion track in the group established in step 1) to perform parameter tuning on the full-time dual-parameter Holt model established in step 2) to determine the smoothing parameter; the smoothing parameter and the moving average M in the sliding average algorithm conform to the relationship as follows:

[0025] α,β=2 / (M+1) (4)

[0026] Among them, the smaller M is, the larger α and β are, indicating that the recent data has a greater impact; the preliminary selection range is determined as follows:

[0027] 0.65≤α≤0.95 , 0.30≤β≤0.65 (5)

[0028] The two principles of parameter tuning are: small deviation between smoothed altitude and ADS-B sampling altitude and stable smoothed ascent and descent rate, corresponding to small variance, as follows:

[0029]

[0030] Among them, min∑ t (H t -X t ) 2 Represents H calculated under different smoothing parameter groups t -X t The minimum value of the sum of squares of the sequence, min∑ t (g t -E(g t )) 2Represents g calculated under different smoothing parameter groups t -E(g t ) sequence, E(g t ) is g t The mean of the sequence, H t -X t Sequence and g t -E(g t ) The sum of squares of the sequences do not reach the minimum value at the same time. After weighting equation (6) and removing the scale for normalization, the weighted objective function f is established. opt for:

[0031]

[0032] Among them, max∑ t (H t -X t ) 2 Represents H calculated under different smoothing parameter groups t -X t The maximum value of the sum of squares of the sequence, max∑ t (g t -E(g t )) 2 Represents g calculated under different smoothing parameter groups t -E(g t ) is the maximum value of the sum of squares of the sequence, λ is the proportional coefficient, and λ>1 means that the ascending and descending rate is more important than the height in the optimization objective;

[0033] Obtain the weighted objective function f by traversing the parameter group opt The minimum value of corresponds to the optimal smoothing parameter of the track for the entire period. Monte Carlo test is carried out in the same group, and the average value of the test track parameters after tuning is used to characterize the model parameters of the group characteristics. The specific steps are as follows:

[0034] Step a: Under the constraint condition of equation (5), the smoothing parameter group is solved by ergodic method so that the weighted objective function f opt To minimize; first use a large step length to roughly traverse and weight the objective function f under different α and β opt Take the value and find the α corresponding to the minimum value 1 , β 1 ; Then traverse in a small step, at α 1 , β 1 The weighted objective function f is calculated again in the local range of opt , set the minimum value corresponding to the smoothing parameter as α o , β o , represents the optimal smoothing parameter of the track over the entire period;

[0035] Step b: Repeat step a in the same group and conduct Monte Carlo test. Determine the number of tests in proportion to the capacity of the number of tracks in each group and use the average value of the optimal smoothing parameter obtained from the test tracks under the group as the smoothing parameter of the group.

[0036] Furthermore, the step 4) specifically includes:

[0037] Obtain the real-time track, determine the aircraft model and take-off and landing status, and then select the grouping model parameters calculated in step 3) to establish a two-parameter interval Holt model, which is expressed as follows:

[0038]

[0039] Among them, Na represents the current cycle and Nb represents the interval length.

[0040] Furthermore, the step 5) specifically includes:

[0041] The grouping model parameters called in step 4) are used as the initial value α of the smoothing parameter of the two-parameter interval Holt model. o , β o , input the altitude sequence of the real-time track, determine the smoothing coefficient that matches the real-time track through dynamic local tuning, and adjust α 0 -0.01, α 0 , α 0 +0.01 respectively with β 0 -0.01, β 0 , β 0 +0.01, and the weighted objective function f is obtained by local traversal. opt The smallest corresponding smoothing parameter group is used as the initial value of the smoothing parameter of the two-parameter interval Holt model for the next cycle of the track, and the local tuning process of the current cycle is repeated until the track altitude trend changes from rising to flat, and the smoothed rising and falling rate of the current cycle is output at the same time.

[0042] Beneficial effects of the present invention:

[0043] The present invention can use the collected historical track information to establish a dual-parameter full-time Holt model, use the high-precision ADS-B altitude sequence to train the model, obtain model parameters suitable for the aircraft type and the ascent and descent state, and apply the dual-parameter interval Holt model of the real-time track to obtain a real-time smooth ascent and descent rate; compared with the multi-period simple weighted algorithm, the algorithm has higher accuracy and is more stable, and improves the stability of various alarm calculations involved in the ascent and descent rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 The figure is a flow chart of the method of the present invention.

[0045] Figure 2This is a schematic diagram of the change of the objective function with the smoothing coefficient group when simulating a uniform rising target.

[0046] Figure 3 Schematic diagram of the error distribution of the simulated target smoothing rate.

[0047] Figure 4 This is a schematic diagram comparing the actual target smoothing rate and the multi-period weighted result. DETAILED DESCRIPTION

[0048] In order to facilitate the understanding of those skilled in the art, the present invention is further described below in conjunction with embodiments and drawings. The contents mentioned in the implementation modes are not intended to limit the present invention.

[0049] Reference Figure 1 As shown, a method for smoothing aircraft ascent and descent rate based on a dual-parameter Holt model of the present invention comprises the following steps:

[0050] 1) Collect the track information of the automated system within a certain period of time and select the system fusion track involving ADS-B signals; specifically include:

[0051] The collected system fusion tracks are grouped according to aircraft type and ascent and descent status. The aircraft types are divided into three categories: heavy aircraft, medium aircraft and light aircraft. The ascent and descent status are divided into two categories: ascent and descent. A total of six groups are established. When grouping, only the ADS-B altitude and corresponding time of the corresponding period of the ascent and descent status are recorded, which is represented as an altitude time series. The recorded period is a continuous movement process in the same direction (ascent or descent), and the altitude changes evenly during this period. The ascent and descent rate within this period is set to fluctuate slightly, and the period that does not meet the requirements is discarded and not recorded.

[0052] 2) Extract the height of the ADS-B signal in the system fusion track, sample the ADS-B signal according to the update period of the system fusion track, and establish a dual-parameter full-time Holt model based on the ADS-B sampling height and sampling period; specifically include:

[0053] The ADS-B altitude time series recorded in step 1) is sampled according to the update period of the system fusion track, and the initial two-parameter full-time Holt model is established for the sampled altitude time series. The formula is as follows:

[0054]

[0055] Among them, H t+1 is the height smoothing value at time t+1; h t+1 is the trend smoothing value at time t+1; X t+1is the input parameter at time t+1, i.e. the ADS-B altitude after sampling; α and β are smoothing parameters, ranging from 0 to 1; where the full period is the duration of a continuous movement in the same direction recorded in step 1), and its value is N*T, where N is the number of sampling points; the subscript t ranges from 0 to (N-1); different groups correspond to different smoothing parameter values, which characterize the grouping characteristics;

[0056] Replace the term h in equation (1) with the instantaneous rise and fall rate g*sampling period T, and we get the following equation:

[0057]

[0058] Among them, g t+1 is the smoothed value of the rise and fall rate at time t+1, g t is the smoothed value of the rise and fall rate at time t; compensate for one cycle to reduce the impact of measurement accuracy on the instantaneous rise and fall rate after smoothing (for the case of a small rise and fall rate, such as when the height difference of ADS-Bs in adjacent sampling cycles is less than the quantization scale of 25ft, it may cause the measured heights of adjacent ADS-Bs to be equal or enlarged, resulting in smoothed g t The sequence will also have corresponding fluctuations). After period compensation, the final dual-parameter full-time Holt model is obtained, which is expressed as follows:

[0059]

[0060] 3) Establish a weighted objective function of the normalized height mean square error and the normalized lift rate mean square error, and determine the model parameters in combination with the Monte Carlo method; specifically,

[0061] Randomly select a system fusion track in the group established in step 1) to perform parameter tuning on the full-time dual-parameter Holt model established in step 2) to determine the smoothing parameter; the smoothing parameter and the moving average M in the sliding average algorithm conform to the relationship as follows:

[0062] α,β=2 / (M+1) (4)

[0063] Among them, the smaller M is, the larger α and β are, indicating that the recent data has a greater impact; the preliminary selection range is determined as follows:

[0064] 0.65≤α≤0.95,0.30≤β≤0.65 (5)

[0065] The two principles of parameter tuning are: small deviation between smoothed altitude and ADS-B sampling altitude and stable smoothed ascent and descent rate, corresponding to small variance, as follows:

[0066]

[0067] Among them, min∑ t (Ht -X t ) 2 Represents H calculated under different smoothing parameter groups t -X t The minimum value of the sum of squares of the sequence, min∑ t (g t -E(g t )) 2 represents the g calculated under different smoothing parameter groups t -E(g t ) sequence, E(g t ) is g t The mean of the sequence, H t -X t Sequence and g t -E(g t ) The sum of squares of the sequences do not reach the minimum value at the same time. After weighting equation (6) and removing the scale for normalization, the weighted objective function f is established. opt for:

[0068]

[0069] Among them, max∑ t (H t -X t ) 2 Represents H calculated under different smoothing parameter groups t -X t The maximum value of the sum of squares of the sequence, max∑ t (g t -E(g t )) 2 represents the g calculated under different smoothing parameter groups t -E(g t ) is the maximum value of the sum of squares of the sequence, λ is the proportional coefficient, and λ>1 means that the ascending and descending rate is more important than the height in the optimization objective;

[0070] By traversing the parameter group to obtain the minimum value, the optimal smoothing parameter of the corresponding track for the entire period is tested by Monte Carlo method in the same group, and the average value of the test track parameters after tuning is used to characterize the model parameters of the group characteristics; the specific steps are as follows:

[0071] Step a: Under the constraint condition of equation (5), the smoothing parameter group is solved by ergodic method so that the weighted objective function f opt To minimize; first use a large step length to roughly traverse and weight the objective function f under different α and β opt Take the value and find the α corresponding to the minimum value 1 , β 1 ; Then traverse in a small step, at α 1 , β1 The weighted objective function f is calculated again in the local range of opt , set the minimum value corresponding to the smoothing parameter as α o , β o , represents the optimal smoothing parameter of the track over the entire period;

[0072] Step b: Repeat step a in the same group and conduct Monte Carlo test. Determine the number of tests in proportion to the capacity of the number of tracks in each group and use the average value of the optimal smoothing parameter obtained from the test tracks under the group as the smoothing parameter of the group.

[0073] 4) Select model parameters according to aircraft type and ascending and descending status, and establish a two-parameter interval Holt model; specifically including:

[0074] Obtain the real-time track, determine the aircraft model and take-off and landing status, and then select the grouping model parameters calculated in step 3) to establish a two-parameter interval Holt model, which is expressed as follows:

[0075]

[0076] Among them, Na represents the current cycle and Nb represents the interval length.

[0077] 5) Input the real-time trajectory of the aircraft into the dual-parameter interval Holt model, dynamically tune the model parameters, and output the real-time ascent and descent rate; specifically, including:

[0078] The grouping model parameters called in step 4) are used as the initial value α of the smoothing parameter of the two-parameter interval Holt model. o , β o , input the altitude sequence of the real-time track, determine the smoothing coefficient that matches the real-time track through dynamic local tuning, and adjust α 0 -0.01, α 0 , α 0 +0.01 respectively with β 0 -0.01, β 0 , β 0 +0.01, and the weighted objective function f is obtained by local traversal. opt The smallest corresponding smoothing parameter group is used as the initial value of the smoothing parameter of the two-parameter interval Holt model of the next track cycle, and the local tuning process of the current cycle is repeated until the track altitude trend changes from rising to flat, and the smoothed rising and falling rate of the current cycle is output at the same time.

[0079] For example, let's simulate an ideal uniformly ascending target, where the altitude rises from 0ft to 24000ft at 20ft / s for 20 minutes (300 track update cycles). Since the accuracy of ADS-B detection altitude is 12.5ft, corresponding to the minimum measurement scale of 25ft and an update cycle of 1s, it needs to be quantified and sampled; the changes of the target's true altitude and ADS-B quantified altitude over time are shown in Table 1 below:

[0080] Table 1

[0081] T / s 1 2 3 4 5 6 7 8 9 … H / ft 20 40 60 80 100 120 140 160 180 … ADS 25 50 50 75 100 125 150 150 175 …

[0082] After sampling ADS at T=4, the height sequence becomes 25, 100, 175…;

[0083] The Holt smoothing model is established for the sampled ADS-B altitude sequence, and the objective function is calculated under different smoothing coefficients. Figure 2 The objective function changes with α under different smoothing coefficients β. The optimal smoothing coefficients of the track are α = 0.76 and β = 0.40. The relative error distribution of the smoothed ascent and descent rate under these parameters is as follows: Figure 3 As shown, for comparison, the relative error of the instantaneous rise and fall rate without smoothing is shown as the dotted line, and the relative error of the rise and fall rate after smoothing is reduced from 10% to 3%.

[0084] For real targets, the error judgment of their smoothed ascent and descent rate can be compared with the pressure altitude ascent and descent rate of the ground-to-air short data link transmitted by the airborne S-mode transponder. This airborne downlink data belongs to the selected content in the radar protocol (it is sent only after receiving the radar inquiry). For most tracks, this data item cannot be obtained continuously. Therefore, it is necessary to screen out the tracks that continuously contain this data for analysis. Consider a certain target track, extract the ADS-B altitude of the fused track and the real-time pressure altitude ascent and descent rate data transmitted by the airborne, and similar analysis can obtain the optimal smoothing coefficient value for the track. Under the optimal smoothing coefficient, the smoothed ascent and descent rate is different from the actual ascent and descent rate transmitted by the airborne as follows: Figure 4 As shown in the figure, the solid line + circle is the airborne downlink, the solid line + upper triangle is the Holt smoothing, and for comparison, the instantaneous rise and fall rate of multi-cycle weighting is shown in the dotted line + lower triangle. From the comparison, it can be seen that the trend of the Holt smoothing rise and fall rate is basically consistent with the rise and fall rate of the airborne downlink, while the instantaneous rise and fall rate of the multi-cycle weighting fluctuates greatly and is prone to peaks, such as the circle.

[0085] The present invention has many specific application paths. The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements can be made without departing from the principle of the present invention. These improvements should also be regarded as the protection scope of the present invention.

Claims

1. A method for smoothing aircraft ascent and descent rate based on a dual-parameter Holt model, characterized in that: Here are the steps: 1) Collect the track information of the automated system within a certain period of time and select the system fusion track involving ADS-B signals; 2) Extract the height of the ADS-B signal in the system fusion track, sample the ADS-B signal according to the update period of the system fusion track, and establish a dual-parameter full-time Holt model based on the ADS-B sampling height and sampling period; 3) Establish a weighted objective function of the normalized height mean square error and the normalized lift rate mean square error, and determine the model parameters in combination with the Monte Carlo method; 4) Select model parameters according to aircraft type and take-off and landing status, and establish a two-parameter interval Holt model; 5) Input the real-time trajectory of the aircraft into the dual-parameter interval Holt model, dynamically tune the model parameters, and output the real-time ascent and descent rate.

2. The method for smoothing aircraft ascent and descent rate based on the dual-parameter Holt model according to claim 1, characterized in that: The step 1) specifically includes: The collected system fusion tracks are grouped according to aircraft type and ascent and descent status. The aircraft types are divided into three categories: heavy aircraft, medium aircraft and light aircraft. The ascent and descent status are divided into two categories: ascent and descent. A total of six groups are established. When grouping, only the ADS-B altitude and corresponding time of the corresponding period of the ascent and descent status are recorded, which is represented as an altitude time series. The recorded period is a continuous movement process in the same direction, and the altitude changes evenly during this period. The ascent and descent rate within this period is set to fluctuate slightly, and the period that does not meet the requirements is discarded and not recorded.

3. The method for smoothing aircraft ascent and descent rate based on the dual-parameter Holt model according to claim 1, characterized in that: The step 2) specifically includes: The ADS-B altitude time series recorded in step 1) is sampled according to the update period of the system fusion track, and the initial two-parameter full-time Holt model is established for the sampled altitude time series. The formula is as follows: Among them, H t+1 is the height smoothing value at time t+1; h t+1 is the trend smoothing value at time t+1; X t+1 is the input parameter at time t+1, i.e. the ADS-B altitude after sampling; α and β are smoothing parameters, ranging from 0 to 1; where the full period is the duration of a continuous movement in the same direction recorded in step 1), and its value is N*T, where N is the number of sampling points; the subscript t ranges from 0 to (N-1); different groups correspond to different smoothing parameter values, which characterize the grouping characteristics; Replace the term h in equation (1) with the instantaneous rise and fall rate g*sampling period T, and we get the following equation: Among them, g t+1 is the smoothed value of the rise and fall rate at time t+1, g t is the smoothed value of the rise and fall rate at time t; one cycle is compensated to reduce the influence of measurement accuracy on the instantaneous rise and fall rate after smoothing. After the cycle compensation processing, the final dual-parameter full-time Holt model is obtained, which is expressed as follows:

4. The method for smoothing aircraft ascent and descent rate based on a dual-parameter Holt model according to claim 3, characterized in that: The step 3) specifically includes: Randomly select a system fusion track in the group established in step 1) to perform parameter tuning on the full-time dual-parameter Holt model established in step 2) to determine the smoothing parameter; the smoothing parameter and the moving average M in the sliding average algorithm conform to the relationship as follows: α,β＝2 / (M+1)(4) Among them, the smaller M is, the larger α and β are, indicating that the recent data has a greater impact; the preliminary selection range is determined as follows: 0.65≤α≤0.95,0.30≤β≤0.65(5) The two principles of parameter tuning are: small deviation between smoothed altitude and ADS-B sampling altitude and stable smoothed ascent and descent rate, corresponding to small variance, as follows: Among them, min∑ t (H t -X t ) 2 Represents H calculated under different smoothing parameter groups t -X t The minimum value of the sum of squares of the sequence, min∑ t (g t -E(g t )) 2 represents the g calculated under different smoothing parameter groups t -E(g t ) sequence, E(g t ) is g t The mean of the sequence, H t -X t Sequence and g t -E(g t ) The sum of squares of the sequences do not reach the minimum value at the same time. After weighting equation (6) and removing the scale for normalization, the weighted objective function f is established. opt for: Among them, max∑ t (H t -X t ) 2 Represents H calculated under different smoothing parameter groups t -X t The maximum value of the sum of squares of the sequence, max∑ t (g t -E(g t )) 2 represents the g calculated under different smoothing parameter groups t -E(g t ) is the maximum value of the sum of squares of the sequence, λ is the proportional coefficient, and λ>1 means that the ascending and descending rate is more important than the height in the optimization objective; Obtain the weighted objective function f by traversing the parameter group opt The minimum value of corresponds to the optimal smoothing parameter of the track for the entire period. Monte Carlo test is carried out in the same group, and the average value after the test track parameters are tuned represents the model parameters of the group characteristics. The specific steps are as follows: Step a: Under the constraint condition of equation (5), the smoothing parameter group is solved by ergodic method so that the weighted objective function f opt To minimize; first use a large step length to roughly traverse and weight the objective function f under different α and β opt Take the value and find the α1 and β1 corresponding to the minimum value; then traverse with a small step length and calculate the weighted objective function f again in the local range of α1 and β1 opt , set the minimum value corresponding to the smoothing parameter as α o , β o , represents the optimal smoothing parameter of the track over the entire period; Step b: Repeat step a in the same group and conduct Monte Carlo test. Determine the number of tests in proportion to the capacity of the number of tracks in each group and use the average value of the optimal smoothing parameter obtained from the test tracks under the group as the smoothing parameter of the group.

5. The method for smoothing aircraft ascent and descent rate based on the dual-parameter Holt model according to claim 4, characterized in that: The step 4) specifically includes: Obtain the real-time track, determine the aircraft model and take-off and landing status, and then select the grouping model parameters calculated in step 3) to establish a two-parameter interval Holt model, which is expressed as follows: Among them, Na represents the current cycle and Nb represents the interval length.

6. The method for smoothing aircraft ascent and descent rate based on a dual-parameter Holt model according to claim 1, characterized in that: The step 5) specifically includes: The grouping model parameters called in step 4) are used as the initial value α of the smoothing parameter of the two-parameter interval Holt model. o , β o , input the altitude sequence of the real-time track, determine the smoothing coefficient matching the real-time track through dynamic local tuning, and locally traverse the 9 groups of smoothing coefficients consisting of α0-0.01, α0, α0+0.01 and β0-0.01, β0, β0+0.01 to obtain the weighted objective function f opt The smallest corresponding smoothing parameter group is used as the initial value of the smoothing parameter of the two-parameter interval Holt model of the next track cycle, and the local tuning process of the current cycle is repeated until the track altitude trend changes from rising to flat, and the smoothed rising and falling rate of the current cycle is output at the same time.

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