How to Determine Probability of Overlap or Create a Smaller CI?

13 Views Asked by At

I have two independent confidence intervals (CIs) each with a $95\%$ confidence level, representing observations of the same object in a target tracking area. These CIs overlap because they pertain to the same object. I'd like to calculate the probability of the overlap area between these CIs or determine how to construct a smaller CI based on these two overlapping intervals. I have access to the pdf of the two observations. Can someone guide me on how to perform these calculations or provide insights on reducing the size of the CI given the overlapping information?