Update parameter estimation notebook

[lymichelle21]

• Add table of contents
• Fix formatting for consistency

[github-actions]

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[kjjarvis]

These changes look great. I like the consistency a lot! Just a couple minor edits (all based on the previous work that was done, not the new stuff). And one question regarding the metadata in the notebook. Great work!

[teubert]

A few cosmetic suggestions (including some for lines you didn't touch). But overall it looks great! Good work!

[teubert]

Suggested change

	"Parameter estimation is used to tune the parameters of a general model so that its behavior matches that of a specific system. Parameter Estimation can be considered more of an art than a science. For example, the parameters of a battery model can be tuned to configure the model to more accurately describe the behavior of a specific battery.\n",
	"Parameter estimation is used to tune the parameters of a general model so that its behavior matches that of a specific system. For example, the parameters of a battery model can be tuned to configure the model to more accurately describe the behavior of a specific battery.\n",

That sentence felt a little awkward here

[teubert]

Suggested change

"Generally, parameter estimation is done by tuning the parameters of the model so that the simulation (see __[01 Simulation](01_Simulation.ipynb)__) best matches the behavior observed in some available data. This is done using a mixture of data, knowledge (e.g., from system specs), and intuition. For large, complex models, it can be VERY difficult and computationally expensive. Fortunately, in this case we have a relatively simple model.\n",

"Generally, parameter estimation is done by tuning the parameters of the model so that the simulation (see __[01 Simulation](01_Simulation.ipynb)__) best matches the behavior observed in some available data. This is done using a mixture of data, knowledge (e.g., from system specs), and intuition. For large, complex models, it can be VERY difficult and computationally expensive.\n",

We introduce the model later

[teubert]

Suggested change

	"In ProgPy, this is done using the `progpy.PrognosticsModel.estimate_params()` method. This method takes input and output data from one or more runs, and uses `scipy.optimize.minimize` function to estimate the parameters of the model. For more information, refer to the documentation [here](https://nasa.github.io/progpy/prog_models_guide.html#parameter-estimation).\n",
	"In ProgPy, parameter estimation is done using the `progpy.PrognosticsModel.estimate_params()` method. This method takes input and output data from one or more runs, and uses `scipy.optimize.minimize` function to estimate the parameters of the model. For more information, refer to the documentation [here](https://nasa.github.io/progpy/prog_models_guide.html#parameter-estimation).\n",

[teubert]

Do we want to link to calc_error documentation here?

[teubert]

Suggested change

	"Now we will show an example demonstrating model parameter estimation. In this example, we estimate the model parameters from data. In general, the data will usually be collected from the physical system or from a different model (model surrogacy). In this case, we will use example data."
	"In this example, we estimate the model parameters from data. In general, the data will usually be collected from the physical system or from a different model (model surrogacy). In this case, we will use example data."

I don't think the first sentence adds anything not in the second sentence.

[teubert]

Suggested change

	"Finally, let's call `estimate_params()` with all the collected data."
	"Finally, we will call `estimate_params()` with all the collected data."

I used let's too many times in a row here

[teubert]

Suggested change

	"The previous examples all used a simple model, the ThrownObject. For large, complex models, it can be VERY difficult and computationall expensive.\n",
	"The previous examples all used a simple model, the ThrownObject. For large, complex models, it can be VERY difficult and computationally expensive.\n",

[teubert]

Suggested change

	"Now let's do it for the step runs. Note that this is actually multiple runs that we need to combine. `relativeTime` resets for each \"run\". So if we're going to use multiple runs together, we need to stitch these times together."
	"Now we will do it for the step runs. Note that this is actually multiple runs that we need to combine. `relativeTime` resets for each \"run\". So if we're going to use multiple runs together, we need to stitch these times together."

Again, I use let's too much. let's fix it!

[teubert]

Line 663, below, has too many let's.

[teubert]

Suggested change

"There are 7 parameters to set (assuming initial SOC is always 1). We can start with setting a few parameters we know. We know that $v_L$ is about 4.2 (from the battery), we expect that the battery internal resistance is the same as that in the electrochemistry model, and we know that the capacity of this battery is significantly smaller."

"There are 7 parameters to set (assuming initial SOC is always 1). We can start with setting a few parameters we know. We know that $v_L$ is about 4.2 (from the battery specs). We also expect that the battery internal resistance is the same as that in the electrochemistry model (which also uses an 18650). Finally, we know that the capacity of this battery is significantly smaller than the default values for the larger pouch battery."