Improving Location History Accuracy
More accuracy is technically achievable, but at a cost. Keeping GPS turned on and recording positions more often draws power, making the battery run down more quickly. That wouldn't be appropriate for something that always run in the background like Google Location History, but there are other location tracking apps (such as running apps) that let you choose your own trade-off between accuracy and battery life.

You might even be better off making your own Android client, so you have full control, and can set up everything just right for your situation. Since this is a site for end-user questions, not programmers, we can't help you any further with that side of things.