Skip to content
Merged
Show file tree
Hide file tree
Changes from all commits
Commits
File filter

Filter by extension

Filter by extension

Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
2 changes: 1 addition & 1 deletion local_optimization/BXNL/Readme.md
Original file line number Diff line number Diff line change
Expand Up @@ -22,7 +22,7 @@ Figure 1 shows an illustrative simple problem of data fitting ([Jupyter Notebook
</table>

**Figure 1.** Example of a NLLS orbital data fitting.
Given a set of 7 orbital data points the task is to estimate an optimal orbit path that minimizes the error between the path and the fixed data points. For this example assume that expert knowledge provides insight on the reliability of each measument and that for this satellite configuration operational orbit height should around 250 +/-3 units. Center plot shows a simple fit where each measurement (data point) contributes the same amount and provides an optimal orbit height of 238.76 units. The fit is quite poor in the sense that it does not satisfy expert advice. Evidently data point 0 (yellow cross closest to earch surface) unreliablity should be taken into account while doing the fitting. Weights for the residuals should be proportional to the inverse of their variability. For this example suppose we are provided with the accuracy for each of the data measurements, this can be factored using weighted nonlinear least-squares. The rightmost plot shows the weighted optimal solution with orbit height of 254.90 units wich is withing the suggested tolerance. Image credit: [Image of Earth](http://pics.eumetsat.int/viewer/index.html) was taken from [EUMETSAT, Copyright 2020](http://pics.eumetsat.int/viewer/index.html#help).
Given a set of 7 orbital data points the task is to estimate an optimal orbit path that minimizes the error between the path and the fixed data points. For this example assume that expert knowledge provides insight on the reliability of each measument and that for this satellite configuration operational orbit height should around 250 +/-3 units. Center plot shows a simple fit where each measurement (data point) contributes the same amount and provides an optimal orbit height of 238.76 units. The fit is quite poor in the sense that it does not satisfy expert advice. Evidently data point 0 (yellow cross closest to earch surface) unreliablity should be taken into account while doing the fitting. Weights for the residuals should be proportional to the inverse of their variability. For this example suppose we are provided with the accuracy for each of the data measurements, this can be factored using weighted nonlinear least-squares. The rightmost plot shows the weighted optimal solution with orbit height of 254.90 units wich is withing the suggested tolerance. Image credit: [Image of Earth](https://pics.eumetsat.int/viewer/index.html) was taken from [EUMETSAT, Copyright 2020](https://pics.eumetsat.int/viewer/index.html#help).


# More Info
Expand Down
4 changes: 2 additions & 2 deletions local_optimization/BXNL/notebooks/simple_BXNL.ipynb
Original file line number Diff line number Diff line change
Expand Up @@ -43,7 +43,7 @@
"etched nuclear track data to a convoluted distribution. A target\n",
"sheet is scanned and track diameters (red wedges in\n",
"the following Figure 1) are recorded into a histogram and a mixed Normal and log-Normal model is to be fitted to the experimental histogram (see Figure 2).\n",
"![PADC](tracks.png)\n"
"![PADC](../images/tracks.png)\n"
]
},
{
Expand Down Expand Up @@ -560,4 +560,4 @@
},
"nbformat": 4,
"nbformat_minor": 2
}
}