Chapter 453: Firepower Coverage to Precision Strike

Among the three algorithms above, the first two are based on point data and directly use the principle of parabola to reverse the gun position.

However, 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 amount of calculation is small, but the disadvantage is that the error is not small.

The least squares fitting starts from 2 points and continues to multiple points, using the point data to continuously fit a parabola using the least squares method. The more points there are, the more accurate the fitted data will be in theory. This is actually also a 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 a projectile is a nonlinear process, in which nonlinear filtering technology is needed.

The Kalman filter is a classic filtering algorithm that uses the principle of Bayesian filtering to iterate data and estimate the target trajectory. This method has better accuracy, but it is not as good as the previous two methods. It also has higher requirements for model quality, quantity of observation data and accuracy.

"Yes, we have tried all the algorithms we have now, and the accuracy is quite outrageous. When there are 5 points, the error can reach more than a thousand meters, and 15 points is also more than a hundred meters. And 15 points is basically approaching the limit of existing radar observation performance. In the typical flight of artillery shells, combined with factors such as terrain, the typical amount of data that the radar can effectively output is only this much."

This accuracy is basically unusable. As for the accuracy below 5 points, the potter did not say, but Gao Zhendong could guess that the accuracy below 5 points is totally unusable. It is extremely poor. This is determined by the principles of observation and algorithm, and it is not something that can be changed by just thinking about it.

Gao Zhendong thought about it and felt that these descriptions were somewhat qualitative, but not quantitative enough.

"Mr. Tao, if it's convenient, could you send me the existing simulation data in an encrypted email? You have an account in the Defense Work Committee's email system, right?"

Without thinking, Mr. Tao agreed: "Okay, I'll ask our confidential office to send you a copy right away. I don't have the email system account of the National Defense Committee, but our confidential office does."

"Okay, please send it. I'll email you back after I've read it."

I won’t call anymore. It’s too much trouble to go to the confidential office all the time.

Gao Zhendong returned to the office. Potter was very fast and about ten minutes later, Gao Zhendong received an email containing not only data but also 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 from the Institute of Electromagnetism's confidential office handed over a printed copy of an encrypted email to Mr. Tao. The printed copy had been anonymized, and even the other party's mailbox could not be seen.

"Potter, seeing words is like meeting someone."

"After reading your simulation, I have two suggestions"

“The first is to optimize the Kalman filter algorithm to an extended Kalman filter algorithm.”

“The second is to combine the single algorithms to form a weighted average prediction algorithm, and try 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."

Mr. Tao and the backbone members of the project team read Gao Zhendong's reply word by word, and their faces gradually became happier.

"This comrade's first suggestion is very insightful. By using Taylor series expansion to approximately transform nonlinear filtering into linear filtering, we can use linear correlation theory to solve nonlinear problems. This is much easier than before. At least there are more mathematical tools and the calculations are not that troublesome."

"Yes, yes, yes. Although this seems to be a suboptimal filtering algorithm, it is very suitable for use here. It also solves the calculation problem in our actual engineering application. It turns out that direct Kalman filtering is very troublesome."

"Let me tell you, this comrade is extremely capable and awesome!" A comrade expressed such a simple emotion.

Computers can solve nonlinear problems, which requires a lot of mathematical skills, programming skills and computer performance.

I had originally thought of leaving this problem to be solved when the project was implemented in the future. Now that it was just a simulation, I ignored it. I didn't expect that someone would solve it so easily.

Only then did the potter understand what the artillery meant by "give me whatever you want".

If I hadn't remembered what the artillery said and hadn't had an idea, not only would I have given them the data they wanted, but I would have also attached the algorithm and model. I guess they wouldn't have known that there were big problems with their model and algorithm, and they wouldn't have given this solution.

Hey, it's worth it! Even if the accuracy problem is not solved, this first suggestion fully highlights the ability and value of others.

"Stop arguing, stop arguing, and look at the next algorithm design. That one is specifically designed to solve the positioning accuracy problem of our current algorithm."

"Lao Tao, you are too greedy. Haha, solving one problem is not enough."

"This is the real one, this is the real one."

It doesn't seem complicated to say. Gao Zhendong divided the prediction algorithm into segments according to the number of points based on the weaknesses and strengths of the least squares fitting and the extended Kalman filter. It clearly stated how many points below the least squares fitting method is used, how many points to how many points the two methods use a weighted average of variable weights, and how many points above the extended Kalman filter is used. Most importantly, Gao Zhendong did two things. He determined the specific values ​​of the two dividing points based on the data, and also gave the specific algorithm for the weights of the two algorithms to change according to the number of points between the two dividing points, which made the comrades in the Institute of Electromagnetism very comfortable.

In this part, Gao Zhendong even expanded the original particle ballistic model used in electromagnetism and gave an extended Kalman filter model.

In this model, in addition to conventional parameters such as ballistic coefficient, gravitational acceleration, wind force, radar error, etc., he also introduced parameters such as virtual temperature, air density function, drag function, radar noise, Gaussian white noise, and some parameters that appear in the form of functions, which is 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 knew all this, hehe, part of it was learned from the tank fire control materials of the Grassland Tractor Factory, and part of it was recalled from other materials.

This model actually has basically nothing to do with radar technology itself, but it looks like he knows a lot about it.

Looking at the model, the potter and his comrades were stunned.

"Mr. Tao, is this comrade an expert in artillery ballistics? His model is much more advanced than ours. Ours is just this level."

As the comrade spoke, he extended his little finger.

"What are you asking?" Mr. Tao was not sure what Gao Zhendong did. From the few words he heard about this comrade, it seemed that he was involved in everything.

"Don't worry about what they do, just try to see if it works first!" The key is that my model was given to me by a comrade from Beijing University of Technology. They are all experts. No, no, I have to try it first. I can't just use the staring method and think that whichever one looks more complicated is better. Some good formulas and models are extremely simple.

Euler's formula: You are right!
A group of people began to busily perform simulations and calculations on Gao Zhendong's model, which took a lot of time. The main reason was that Gao Zhendong's model was much more complicated than the original one, and it was quite troublesome to modify the program.

Fortunately, once the program is adjusted, the speed will be much faster.

Start the program, call the data file, and the computer screen is basically still except for the jumping cursor.

In order to save resources, computers these days will not use fancy things like echo and process display when working unless it is necessary.

After a while, a final error analysis result appeared on the screen. As for the intermediate data, they were all stored in the memory and could not fit on the display.

When everyone looked up, the whole place was shocked.

"Wow!"

"It's amazing!"

"Awesome!!" (broken voice)

Error analysis shows that starting from point 5, the accuracy of the new model is far superior to that of the old model.

——Far ahead!
"The predicted vertical and horizontal errors of the five points are all around 5 meters. We can cover them with firepower! We can cover them with firepower!"

This level of accuracy can be achieved by using heavy artillery firepower, but it is beyond the capability of battalion or company artillery because of the lack of quantity and firepower.

"Five points are nothing. Look at the 5 points. It's less than 15 meters. 30 meters!"

If the accuracy of 200 meters, with the current firepower configuration, can only be achieved by the long-range support artillery of the military, then the accuracy of 30 meters can give the enemy a hard time even with the firepower of a battalion or a company. If heavy artillery is still used, this accuracy can enable the heavy artillery to achieve precise strikes.

This thing can be done, it can definitely be done!
The potter never expected that he could completely solve his algorithm problem with just one phone call.

Then, he turned around and gave his comrades a hand back: "Are you happy? Are you happy? This is all thanks to the experts from other places! Next, we still have a tough battle! How to make a radar that meets the requirements!"

But his people didn't give him face at all: "Potter, don't spoil my fun, let me be happy about this matter first!"

When the potter heard this, he laughed himself.

He left everyone happy and made a normal phone call to Gao Zhendong.

"Thank you! The effect is remarkable!" He didn't say much, just this one sentence.

"Well, as long as it works." Gao Zhendong himself was also very happy. This model could be considered his original creation based on his own knowledge. It worked, and he was happier than the potter.

(End of this chapter)