Can you seed a Kalman filter with a particle filter?

Is there a way of initializing a Kalman filter using a population of particles that belong to the same "cluster"? How can you determine a good estimate for the mean value (compute weighted average ?) and the covariance matrix ? Each particle is represented as $[ x , y , θ , weight]$.

I can conceive of a few methods for doing so if you really must. The most naive would be to calculate the mean and covariance of each $[x, y, \theta]$ vector. This neglects the weights and as such will be impacted by outliers (in this case particles of low weights).
It may be better to calculate the mean and covariance of each $[x, y, \theta]$ vector using the normalized weight values as the probability of the vector. This may be what you were driving at in your question.