Popular high school students to achieve a detailed tutorial can understand explanation Kalman filter Kalman Filter theory and Python - From Theory to Practice

Original link: https: //blog.csdn.net/varyshare/article/details/95065650

Note: If you see a little bit here from my previous article, when you put Benpian reading, I'm sure you already understand the Kalman filter is very profound

Contact sensor data students must inevitably see the name of a "Kalman filter." This is the story behind? Look at the back remains to be seen. Often do not understand the algorithm is a problem because many of the concepts on which you do not understand, directly see the details of the course can not read. The most critical thing is that you have to first understand dim Kalman filter in the end, what its original intention? Next, I just want to talk to crack some cognitive impairment Kalman filter on the concept of the thing

Cognitive shackles on crack concepts: Kalman filter to do

Kalman filter to do is: For example, the known position of the aircraft on time, know the location of the aircraft radar measurements of this moment received. With the first two of data to estimate the location of the aircraft at this time . Streamlined, that is to know the last time state, we know the measurement data, the integration of these two data to find the current status.

You must ask now know that the measurement data of the current moment so I think the current state of the measurement data is not like it ? In other words: "You must feel radar measured aircraft position is the current position of the aircraft is not the only thing Why do we use the Kalman filter to estimate the current position of the aircraft??."
A: The current position of the aircraft's radar signal received by the measurement of the time really is not necessarily true of the current position of the aircraft . First radar signal measurement has an error. Secondly, I think you now receive radar signals that are transmitted signal before last and then returned. This process is not to time? Maybe this time the aircraft flying to over 200 times the speed of sound, maybe direct crash, these are likely **. That even receive measurement data but still uncertain position in which the aircraft **. So I have to need to estimate the current position of the aircraft's position before a moment of time in conjunction with the measurement data into account to estimate the current aircraft position . This is the role of the Kalman filter.

Then you must ask according to a previous estimate of time aircraft position how you can estimate the current position of the aircraft this moment of ?
A: ** Kalman think that all state changes (position change) are linear. ** What is called linear? The position is 0.3 time speed is 0.2. So I guess the next time position is 0.5. This is called linear.

Then you will ask that not all of the changes in state linear how to do? You like wind speed it is not linear.
A: Congratulations, you've invented new algorithms. In fact people have been named for this algorithm is called extended Kalman filter . Now we have to learn is the Kalman filter. You only need to remember the Kalman filter is to think that all changes are linear.

So now I know how to spend the estimated position of the aircraft in time aircraft position at the current time, but also had to know the current time by means of measurement data received comprehensive consideration to estimate the current position of the aircraft. So how considering it? This involves a proportion. In the end how much these two data accounted for? This is the core essence of the Kalman filter. Kalman filter algorithm to dynamically adjust the ratio. (A kind of tone of moderation, not only the measurement data channel, not only the time position of the current channel estimated position of the time.)

Ideas filtering algorithm development?

If you do not understand the idea of ​​filtering so learned a Kalman filter through tomorrow there is a Kalman filter you want to learn today. If you learn these ideas filtering algorithm, we put them together and then remember it is much simpler. In essence is the use of multiple data filtering algorithm to estimate the true state of fusion. The following two examples cited from deep to shallow.

How to combine the "speed of the aircraft and radar measurements of the aircraft's position" to estimate the position of the aircraft at the time t2?

But how to estimate the speed of the aircraft ah? Because the aircraft are not necessarily uniform to go. We have based on
now I want to estimate the speed of the aircraft.
There are two ways to estimate the speed:

How to combine the "aircraft speed, acceleration, aircraft radar measurements of position" to estimate the position of the aircraft?

How Kalman filter for filtering?

As can be seen from the above paragraph, the Kalman filter the most critical is the need to obtain two kinds of variance. One is purely dependent on the variance of this method of estimation. Second, the variance of the measuring instrument. Just know these two values then you can know the proportion of the estimated value and the measured value in the final results. The method of calculation of the variance in different application scenarios need to be different to the actual situation.
Note: The estimated position of the current time is not the only method to estimate this kind of method based on velocity and acceleration according to the states. There are many others. For example, I can estimate the airplane flight distance (the law of conservation of energy, the driving force × distance = work) according to the driving force aircraft engines at this time and this time the burning of gasoline.

Program realization

From theory to practical - how to understand that the Chang-e into space Kalman filter algorithm Kalman filter?