Prediction of the function values
$begingroup$
There is a function: $f(t,x,y,z)$, where $t$- time, $x,y,z$- some arguments.
The values of $f$ for $tin [a,b]$ are known (100 samples). What is the most accurate way of predicting the value of $f$ for $t=b+1$, if the values of $x,y,z$ for $tin [a,b+1]$ are known?
ADDITIONAL INFO
I'm propagating the satellite position using an analytical method. During the propagation, the errors accumulate. I endeavor to predict the future position errors. $f$ represents the error value and arguments $x,y,z$ are the affecting parameters, such as distance to the Moon, Sun, solar flux, atmospheric density, etc.
statistics
asked Jan 13 at 19:24
LeelooLeeloo
1011
$endgroup$
add a comment |
$begingroup$
There is a function: $f(t,x,y,z)$, where $t$- time, $x,y,z$- some arguments.
The values of $f$ for $tin [a,b]$ are known (100 samples). What is the most accurate way of predicting the value of $f$ for $t=b+1$, if the values of $x,y,z$ for $tin [a,b+1]$ are known?
ADDITIONAL INFO
I'm propagating the satellite position using an analytical method. During the propagation, the errors accumulate. I endeavor to predict the future position errors. $f$ represents the error value and arguments $x,y,z$ are the affecting parameters, such as distance to the Moon, Sun, solar flux, atmospheric density, etc.
statistics
asked Jan 13 at 19:24
LeelooLeeloo
1011
$endgroup$
add a comment |
$begingroup$
There is a function: $f(t,x,y,z)$, where $t$- time, $x,y,z$- some arguments.
The values of $f$ for $tin [a,b]$ are known (100 samples). What is the most accurate way of predicting the value of $f$ for $t=b+1$, if the values of $x,y,z$ for $tin [a,b+1]$ are known?
ADDITIONAL INFO
I'm propagating the satellite position using an analytical method. During the propagation, the errors accumulate. I endeavor to predict the future position errors. $f$ represents the error value and arguments $x,y,z$ are the affecting parameters, such as distance to the Moon, Sun, solar flux, atmospheric density, etc.
statistics
asked Jan 13 at 19:24
LeelooLeeloo
1011
$endgroup$
There is a function: $f(t,x,y,z)$, where $t$- time, $x,y,z$- some arguments.
The values of $f$ for $tin [a,b]$ are known (100 samples). What is the most accurate way of predicting the value of $f$ for $t=b+1$, if the values of $x,y,z$ for $tin [a,b+1]$ are known?
ADDITIONAL INFO
I'm propagating the satellite position using an analytical method. During the propagation, the errors accumulate. I endeavor to predict the future position errors. $f$ represents the error value and arguments $x,y,z$ are the affecting parameters, such as distance to the Moon, Sun, solar flux, atmospheric density, etc.
statistics
statistics
asked Jan 13 at 19:24
LeelooLeeloo
1011
asked Jan 13 at 19:24
LeelooLeeloo
1011
edited Jan 14 at 16:55
Leeloo
asked Jan 13 at 19:24
LeelooLeeloo
1011
asked Jan 13 at 19:24
LeelooLeeloo
1011
asked Jan 13 at 19:24
LeelooLeeloo
1011
1011
add a comment |
add a comment |
1 Answer
1
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oldest
votes
$begingroup$
Without any a priori information about $f$, the problem seems ill-posed. Because you have data values only along a curve and you know little of $f$ . Extrapolation will be hazardous.
If you have a mathematical model with unknown parameters, you can estimate the parameters from the known values.
Otherwise, you can just relate $f$ to the curvilinear abscissa along the trajectory and perform univariate interpolation.
answered Jan 13 at 19:49
Yves DaoustYves Daoust
126k672225
$endgroup$
$begingroup$
I suppose it may be predicted by means of statistical methods.
$endgroup$
– Leeloo
Jan 13 at 21:03
$begingroup$
@Leeloo: if your data is noisy, even less !
$endgroup$
– Yves Daoust
Jan 14 at 7:32
$begingroup$
What about the Gaussian distribution, maximum likelyhood method etc.?
$endgroup$
– Leeloo
Jan 14 at 16:55
$begingroup$
@Leeloo: if you are after magic, try deep learning.
$endgroup$
– Yves Daoust
Jan 14 at 19:46
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Without any a priori information about $f$, the problem seems ill-posed. Because you have data values only along a curve and you know little of $f$ . Extrapolation will be hazardous.
If you have a mathematical model with unknown parameters, you can estimate the parameters from the known values.
Otherwise, you can just relate $f$ to the curvilinear abscissa along the trajectory and perform univariate interpolation.
answered Jan 13 at 19:49
Yves DaoustYves Daoust
126k672225
$endgroup$
$begingroup$
I suppose it may be predicted by means of statistical methods.
$endgroup$
– Leeloo
Jan 13 at 21:03
$begingroup$
@Leeloo: if your data is noisy, even less !
$endgroup$
– Yves Daoust
Jan 14 at 7:32
$begingroup$
What about the Gaussian distribution, maximum likelyhood method etc.?
$endgroup$
– Leeloo
Jan 14 at 16:55
$begingroup$
@Leeloo: if you are after magic, try deep learning.
$endgroup$
– Yves Daoust
Jan 14 at 19:46
add a comment |
$begingroup$
Without any a priori information about $f$, the problem seems ill-posed. Because you have data values only along a curve and you know little of $f$ . Extrapolation will be hazardous.
If you have a mathematical model with unknown parameters, you can estimate the parameters from the known values.
Otherwise, you can just relate $f$ to the curvilinear abscissa along the trajectory and perform univariate interpolation.
answered Jan 13 at 19:49
Yves DaoustYves Daoust
126k672225
$endgroup$
$begingroup$
I suppose it may be predicted by means of statistical methods.
$endgroup$
– Leeloo
Jan 13 at 21:03
$begingroup$
@Leeloo: if your data is noisy, even less !
$endgroup$
– Yves Daoust
Jan 14 at 7:32
$begingroup$
What about the Gaussian distribution, maximum likelyhood method etc.?
$endgroup$
– Leeloo
Jan 14 at 16:55
$begingroup$
@Leeloo: if you are after magic, try deep learning.
$endgroup$
– Yves Daoust
Jan 14 at 19:46
add a comment |
$begingroup$
Without any a priori information about $f$, the problem seems ill-posed. Because you have data values only along a curve and you know little of $f$ . Extrapolation will be hazardous.
If you have a mathematical model with unknown parameters, you can estimate the parameters from the known values.
Otherwise, you can just relate $f$ to the curvilinear abscissa along the trajectory and perform univariate interpolation.
answered Jan 13 at 19:49
Yves DaoustYves Daoust
126k672225
$endgroup$
Without any a priori information about $f$, the problem seems ill-posed. Because you have data values only along a curve and you know little of $f$ . Extrapolation will be hazardous.
If you have a mathematical model with unknown parameters, you can estimate the parameters from the known values.
Otherwise, you can just relate $f$ to the curvilinear abscissa along the trajectory and perform univariate interpolation.
answered Jan 13 at 19:49
Yves DaoustYves Daoust
126k672225
answered Jan 13 at 19:49
Yves DaoustYves Daoust
126k672225
answered Jan 13 at 19:49
Yves DaoustYves Daoust
126k672225
answered Jan 13 at 19:49
Yves DaoustYves Daoust
126k672225
126k672225
$begingroup$
I suppose it may be predicted by means of statistical methods.
$endgroup$
– Leeloo
Jan 13 at 21:03
$begingroup$
@Leeloo: if your data is noisy, even less !
$endgroup$
– Yves Daoust
Jan 14 at 7:32
$begingroup$
What about the Gaussian distribution, maximum likelyhood method etc.?
$endgroup$
– Leeloo
Jan 14 at 16:55
$begingroup$
@Leeloo: if you are after magic, try deep learning.
$endgroup$
– Yves Daoust
Jan 14 at 19:46
add a comment |
$begingroup$
I suppose it may be predicted by means of statistical methods.
$endgroup$
– Leeloo
Jan 13 at 21:03
$begingroup$
@Leeloo: if your data is noisy, even less !
$endgroup$
– Yves Daoust
Jan 14 at 7:32
$begingroup$
What about the Gaussian distribution, maximum likelyhood method etc.?
$endgroup$
– Leeloo
Jan 14 at 16:55
$begingroup$
@Leeloo: if you are after magic, try deep learning.
$endgroup$
– Yves Daoust
Jan 14 at 19:46
$begingroup$
I suppose it may be predicted by means of statistical methods.
$endgroup$
– Leeloo
Jan 13 at 21:03
$begingroup$
I suppose it may be predicted by means of statistical methods.
$endgroup$
– Leeloo
Jan 13 at 21:03
$begingroup$
@Leeloo: if your data is noisy, even less !
$endgroup$
– Yves Daoust
Jan 14 at 7:32
$begingroup$
@Leeloo: if your data is noisy, even less !
$endgroup$
– Yves Daoust
Jan 14 at 7:32
$begingroup$
What about the Gaussian distribution, maximum likelyhood method etc.?
$endgroup$
– Leeloo
Jan 14 at 16:55
$begingroup$
What about the Gaussian distribution, maximum likelyhood method etc.?
$endgroup$
– Leeloo
Jan 14 at 16:55
$begingroup$
@Leeloo: if you are after magic, try deep learning.
$endgroup$
– Yves Daoust
Jan 14 at 19:46
$begingroup$
@Leeloo: if you are after magic, try deep learning.
$endgroup$
– Yves Daoust
Jan 14 at 19:46
add a comment |
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