Particle Filters for Rover Fault Diagnosis

states (see Figure 2). In addition to the physical state set D, the variable resolution model consists of a set of M abstract states { } ) ( ) 1 ( M a a A = that represent sets of states and/or other abstract states: = ) i ( i ) k ( j a d a A (somewhat simplified) algorithm for abstracting and refining states in the VRPF is shown in Figure 3. Figure 3: Variable resolution particle filter algorithm. [Equation 8] The initial set of particles { } N 1 i ] i 0 ] i 0 0 x , a B = = are drawn from the prior distribution. R0 is set to the set of unique states (physical or abstract) represented in B0. The particle set, Bt is then recursively drawn from Bt-1 as follows: 1. Project all the particles to physical states to use the physical transition and measurement models. If a particle, 1 t ) j ( ] i [ 1 t B d a − − ∈ = , is in an abstract state, one of its descendant physical states } d { ) j ( , is selected proportional to the prior probability of the physical states as follows: