Hello. Your question relates to whether a filter (i.e. a state estimator) can be used as a parameter estimator. Whether the filter is Kalman based or Monte Carlo (particle filter) based, it does not matter. You need to set the problem up so that you have a constant state equation, i.e. x(k+1) = x(k) or perhaps x(k+1) = f(x(k)), essentially without any process noise term. The Kalman filter will compute a recursive weighted least squares estimate of x (the parameter vector) based on the noisy measurements y(1), ..., y(k), where y(k)=Hx(k)+w(k), w(k) ~ N(0,R).  It will be the recursive equivalent of minimising a sum of squares cost function of the form sum (1..k) (y(j)-Hx(j))^T R^(-1) (y(j)-Hx(j)) + (x(j)-x(0))^TQ^(-1)(x(j)-x(0)), where Q is the process noise covariance (zero in your case).

If the system functions are nonlinear, you need an approximate estimator, like EKF, UKF, etc. The particle filter should handle the nonlinearity without problems, but the question is do you really need a recursive estimator? If not, use a batch estimator like iteratively reweighted least squares (I call it ILS), which is OK for any nonlinearity of the form y=h(x)+w. This is a really nice, simple technique that you can code up very easily in Matlab, having calculated the derivative of your measurement function. Have a look at the references in the paper below for ILS.

Article Analysis of a Nonlinear Least Squares Procedure Used in Glob...

Beyond the Kalman Filter

Branko Ristic, Sanjeev Arulampalam, Neil Gordon

Also see "A Tutorial on Particle Filtering and Smoothing: Fifteen years later" by Doucet and Johansen, for a generic SMC algorithm.