# Uncertainty in grid based fastslam

Given I am building a grid map, and poses are represented using particles, how can I calculate the uncertainty of a pose In a grid based fastslam 2.0?

$$q_{jk} = \frac{1}{N-1} \sum_{i=1}^{N} (x_{ij} - \bar{x}_j) (x_{ik} - \bar{x}_k)$$
where the covariance matrix is $$\mathbf{Q}$$ with entries $$q_{ji}$$. This is straightforward; however, different approaches exist. For estimating the uncertainty, you could then compute the trace or determinant of the covariance matrix, but other metrics exist as well.