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Kalman filter are an optimal solution to the linear problem (PF are not). If you do not have a linear problem, of course there may be better alternatives. PF and KF solves different problems.

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When applied to a linear system with Gaussian noise, the particle filter will (approximately) recover the solution of the Kalman filter. So yes, they solve different problems, but the particle filter is more of a generalization of the Kalman filter.

What does 'linear' mean in this case exactly? Does it mean, that if the measurements are in space (i.e. location), then Kalman filter can only be applied when location is changing linearly, i.e. speed is constant?

Linear problems are ones in the form of sum(a_i * f_i(x)). So all Newton ballistics are linear because acceleration is a*x^2. Sometimes people who deal in probably refer to systems where the noise is Brownian as linear as well. So, both descriptions of linearity apply to a regular Kalman filter.

There are Extended Kalman Filter and Unscented Kalman Filters that are designated to relax both of these constraints, but they aren’t perfect.

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