Kalman Filters are super efficient to calculate - they're what kept the Apollo program on track (60s compute!). Another post gives the asymptotic complexity - but as a rule of thumb if you can do any practical computation at all you can run a Kalman Filter.
Basically they're both implementations of a recursive Bayesian filter, but the Kalman filter requires very strong assumptions about the distribution (all Gaussian) and the particle filter requires none.
The Kalman filter is optimal for the Gaussian case (and is very efficient to calculate), whilst the particle filter can use more accurate distributions but is far less efficient to calculate.
You kinda use them in different places - a Kalman filter is useless for pedestrian dead reckoning (step made + estimate of direction), whilst a particle filter would be similarly dumb on submarines.
Basically they're both implementations of a recursive Bayesian filter, but the Kalman filter requires very strong assumptions about the distribution (all Gaussian) and the particle filter requires none.
The Kalman filter is optimal for the Gaussian case (and is very efficient to calculate), whilst the particle filter can use more accurate distributions but is far less efficient to calculate.
You kinda use them in different places - a Kalman filter is useless for pedestrian dead reckoning (step made + estimate of direction), whilst a particle filter would be similarly dumb on submarines.