Chapter 453 Firepower covers precision strikes
Of the above three algorithms, the first two are based on point data and directly use the principle of parabola to reverse the gun position.
It’s just that the former is purely calculated based on the parabola formula. Even if factors such as air resistance are added, it is a relatively simple process. The advantage is that the calculation amount is small, but the disadvantage is that the error is not small.
The least squares fitting starts from 2 points to multiple points, and continuously uses the point data to perform the least squares method to fit the parabola. The more points, the better the fitting. Theoretically, the data is more accurate. This is actually a kind of filtering technology, but it is relatively primitive, the amount of calculation is not large, and the accuracy is average.
In fact, the flight process of the cannonball is a nonlinear process. In this process, nonlinear filtering technology needs to be used.
The Kalman filter is a classic filtering algorithm that uses the Bayesian filtering principle to iterate on the data and estimate the target trajectory. The accuracy of this thing will be better, but it is not as easy as the previous two, and it is not as good as the model quality. , the quantity and accuracy requirements of observation data are relatively high.
“Yes, we have tried all the algorithms we have now, and the accuracy is quite outrageous. At 5 points, the error can reach over a kilometer, and at 15 points it can be over 100 meters. And 15 points is basically approaching the limit of existing radar observation performance. During the flight of a typical artillery shell, combined with factors such as terrain, the typical amount of data that the radar can effectively output is only so much.”
This accuracy is basically unusable. As for the accuracy below 5 points, the potter did not say, but Gao Zhendong guessed that below 5 points, the accuracy is not usable at all. It is as bad as grandma’s house. This is determined by observation and algorithm principles. Yes, it's not something that can be changed by patting your head.
Gao Zhendong thought for a while, and these descriptions were somewhat qualitative, but not quantitative enough.
"Potter, if it's convenient, could you send me an encrypted email with the existing simulation data? Do you have an account through the email system of the National Defense Work Committee?"
The potter agreed without thinking: "Okay, I'll ask the comrades in our confidential room to send you a copy right away. I don't have the email system account of the National Defense Work Committee, but our unit's confidential room does."
"Okay, please send it to me. After I finish reading it, I will reply to you by email."
I won't call you anymore, it's really too much trouble for me to run a computer office. .
Gao Zhendong returned to the office. The potter was very fast. About ten minutes later, Gao Zhendong received an email. Not only did he have data, but he also had experimental design, mathematical models and other related materials.
Gao Zhendong looked at the data on the screen, thought for a long time, did some calculations on paper, and started writing an email.
About two hours later, a comrade in the confidential office of the Institute of Electromagnetics handed over a printout of an encrypted email to Potter. The printout had been desensitized and even the other party's mailbox could not be seen.
“Potters, see each other as if they had met each other.”
“After reading your simulation, I have two suggestions”
“One is to optimize the Kalman filtering algorithm as Extended Kalman filter algorithm. "
"The second is to combine single algorithms to form a weighted average prediction algorithm, trying to weaken the weaknesses of different algorithms under different data volumes, in order to obtain the best accuracy. "
"Based on your simulation and actual situation, the weighted average prediction algorithm I considered is designed as follows."
Potter and the backbone of the project team looked at Gao Zhendong's reply word by word, and their faces became happy.
“This comrade’s first suggestion is very insightful. Using Taylor series expansion to approximately convert nonlinear filtering into linear filtering, linear correlation theory can be used to solve nonlinear problems. , this is much easier than the original one, at least there are many more mathematical tools, and the calculation is not that troublesome."
"Yes, yes, although this seems to be a sub-optimal filtering algorithm, it is used here. It is very suitable, and it solves the calculation problem in our actual engineering applications. It turns out that direct Kalman filter calculation is not an ordinary trouble. "
"Let me tell you, this comrade is amazing. If you are forced to lose your ability, you are so stupid!" A comrade expressed such a simple emotion.
Computing non-linear problems requires a lot of mathematical skills, programming skills and computer performance.
Originally, I thought that this problem would be solved when the project is implemented in the future. Now it is just a simulation and I will ignore it. Unexpectedly, someone has solved it easily.
Only then did the potter realize what the artillery meant when they said "give them what they ask for".
If I hadn’t remembered what the artillery said and had an idea, not only did I give the other party the data they asked for, but also attached the algorithm and model, I guess they wouldn’t be able to know the model on my side. If there is a big problem with the algorithm, this solution will not be given.
Hey, it was worth it! Even if the accuracy problem is not solved, this first suggestion completely highlights his ability and value.
"Don't argue, don't argue. Let's look at the next algorithm design. That one is specifically designed to solve the positioning accuracy problem of our current algorithm."
"Old Tao, you are too greedy. Haha, you have solved a problem. It’s not enough.”
“This is the real owner, this is the real owner.”
It doesn’t seem complicated. Gao Zhendong fitted and extended Kalman filter based on least squares. For each weak and advantageous area, the prediction algorithm is segmented according to the number of points. Below a certain number of points, the least squares fitting is completely used. From a certain number of points to a certain number of points, a variable weight weighted average is used for both. Above a certain number of points, the extended Karl is completely used. Mann filtering is all written clearly. The most important thing is that Gao Zhendong also did two things. Based on the data, he determined the specific values of the above two dividing points, and also gave the specific values of the two algorithm weights according to the number of points between the two dividing points. Algorithm, this makes the comrades of the Institute of Electromagnetics very comfortable.
In this part, Gao Zhendong even extended the original particle ballistic model used in electromagnetics and gave an extended Kalman filter model.
In this model, in addition to conventional parameters such as ballistic coefficient, gravity acceleration, wind force, and radar error, he also introduced parameters such as virtual temperature, air density function, drag function, radar noise, and Gaussian white noise. And some parameters in the form of functions are very thoughtful.
It can be said that the model given by Gao Zhendong is a big step forward based on the original model. As for how he knows this, hey, he learned part of it from the tank fire control information of the Prairie Tractor Factory. , and some of it was what he recalled from other information.
This model actually has nothing to do with radar technology itself, but it looks like he understands it very well.
Looking at this model, the potter and his comrades were stunned.
"Potter, is this comrade some artillery ballistics expert? This model is much more advanced than ours, and ours can only be regarded as this."
The comrade said, He held out a little finger.
"What are you asking about!" The potter was not sure what Gao Zhendong did. Anyway, judging from the few words he heard about this comrade, it seemed that he did a little bit of everything.
“Don’t worry about what they do, just try to see if it works first!” The key is that my model was also given to me by the comrades who worked at the Beijing University of Technology. Everyone is an expert. If it doesn’t work, try it first. When trying, you can't just stare at it. It's fine to look at the complex one. There are good formulas and good models, which are as simple as possible.
Euler's formula: You are right!
A group of people hurriedly started doing simulations and calculations with Gao Zhendong's model. This took a lot of time, mainly because Gao Zhendong's model was much more complicated than the original one, and it was very troublesome to modify the program.
Fortunately, once the program is adjusted, the speed will be very fast.
Start the program and call the data file. The computer screen is basically still except for the jumping cursor.
Computers these days, in order to save resources, will not do fancy things like echo and process display unless necessary when working.
After a while, the final error analysis result appeared on the screen. As for the intermediate data, it was all stored in the memory and could not fit on the monitor.
When everyone stretched out their heads to take a look, the whole place was shocked.
“Wow!”
“Amazing!”
“Awesome!!” (broken sound)
Error analysis shows that from 5 Click to start, and the accuracy of this new model is far superior to that of my old model.
——Far ahead!
“The predicted vertical and horizontal errors at the five points are all about 200 meters. The firepower is covering it, the firepower is covering it!”
This accuracy can still be achieved with heavy artillery firepower coverage. Yes, but for the artillery of the battalion or company, it is out of power, both in terms of quantity and firepower.
“5 points is nothing. Look at 15 points, it’s less than 30 meters, 30 meters!”
If the accuracy of 200 meters is based on the current firepower configuration , if it can only be achieved by the military's long-range artillery support, then the accuracy of 30 meters can give the opponent a drink with the firepower of the battalion and even the company. If heavy artillery is still used, this accuracy can make the heavy artillery accurate. blow.
This thing can be done, it can be done!
Potter never expected that his algorithm problem would be completely solved with just one phone call.
Then, he turned around and gave his comrades a hand in return: "Are you happy? Are you happy? This is all the credit of my comrades who are experts from other places! Next, we still have a tough battle! How to do it? The radar that meets the requirements is coming!"
But his people didn't give him any face: "Potter, don't let me be happy now!"
The potter heard it! This made me laugh.
He left the happy crowd behind and made an ordinary phone call to Gao Zhendong.
"Thank you! The effect is remarkable!" I didn't say much, just this sentence.
"Well, it's good if it has curative effect." Gao Zhendong himself is also very happy. This model can be regarded as an original creation that he combined his own knowledge. It can be effective. He is happier than the potter.
(End of this chapter)