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Definition of a Kalman filter and its application (concept)

I have a simple problem. I track the object and get its position in uneven time intervals. The speed and acceleration of an object are not constant.

data_=[time x,y,z]

To create a Kalman filter, I need to define

z=[x;y;z] % observation

% Estimation vector
xt=[xt;yt;zt;x't;y't;z't]  % ' first derivative



P=Covariance matrix of estimation vector 
R=Covariance matrix of measurement 
Q= covariance of noise

Question 1. What is the difference between the two R and P? If the measurement accuracy is 1 mm, then what will be P? Question 2. What is the use of using this Kalman filter in post-processing. This is necessary to get a foggy trajectory, if so, why do we need it.

Hope you have enough information from you.

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2 answers

Question 1

R is the covariance measurement matrix. This has nothing to do with your model and your ratings.

P - . , . P . update .

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Kalman - , , , ( ).

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, , , , , ; , , , .. - first , ( - ).

W () X ; t .

1: , :
. P (Xt | Wt) = ; ( R), W X ( ); , Wt, .. . . P (Wt | Wt-1), , (, , ); , ( , ), P, ( ); . Q? " " - , , . Q P, , , P Q .

2: - t, t, . ( ), " " , , .

, ( ). , t-1 t ( ), ( ). :

     prediction: current state guess  = transition_model * prev. state guess

P (Wt | Xt1..t-1) = [P (Wt | Wt-1) * P (Wt-1 | X1..t-1) dWt-1]

          measurement: best estimate = data_noise_model * current state guess

P (Wt | Xt1..t) = P (Xt | Wt) P (Wt | Xt1..t-1) /P (Xt1..t)

LHS ( t-1, - t, , ). , : . -, , / .

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