52 4. DesignTherefore, all three jumps are equal probable. If additional sensory accelerationinformation become available in a future upgrade of the system, these jumps can bedifferently weighted.The first take on the sequential nature of the problem, is made implicitly by choosingthe(5, 5, 3)-transition-model. This can be interpreted as setting p( s| s)= 0 for all sthat are not included in the(5, 5, 3) neighbourhood, effectively forcing the resultingpath hypothesis to resemble a chain of locations that skips at most one state. Themodelled jump width of(0, 1, 2) is the classical approach to allow a time alignmentof the received emissions to the hidden states. In other terms, the model can adaptto different speeds of movement. Standing at a position, is by that reason modelledas a series of 0-transitions, whereas faster movement leads to series of transitionswith a higher probability of skipping states by using a jump width of 2.By utilizing the(5, 5, 3)-model, a maximum movement speed is also introduced. Twoconsecutive signal vectors are only mapped to states that are at most 1. 2 m awayassuming a states represents a cube with edge size 0. 6 m. So in the case of gapsin the received data stream, accompanied by movements exceeding such distancethresholds, the model will not be able to compensate. Therefore, the sequence ofmeasurements is interpolated to ensure, that there are enough time frames t tocover a distance that is needed by an assumed maximum walking speed of 3 ms- 1(see figure 4.4). Instead of such seemingly artificial restrictions it would alternativelybe possible to increase the maximum jump width by employing a(7, 7, 7)- or evenlarger model. But since this leads to a cubic increase in the number of allowedand therefore processable transitions for each state, this is computational expensive.Thus, the chosen(5, 5, 3)-model seems to be a good compromise between adaptivityand computational efforts.The limitation of the maximum jump width to 1 in the vertical direction reduces thenumber of allowed transitions from 125 to 75 and is justified with the observation,that natural walking movements are primarily in the horizontal 2D-plane. Theremaining adaptivity in the vertical dimension has proven to suffice for handlingtracks containing significant parts of stairway zones6.The next source of information that is exploited to adjust p( s| s) for the remainingtransitions defined by the(5, 5, 3)-model is the 3D-Scene. If the 3D-cube, representedby either s or s, intersects with a face of a 3D-object that has a material flagged asblocking, then p( s| s)= 0. For transitions with a jump width of two, it is additionallychecked if there exists an unblocked path of at most two steps between the sourceand the destination state of the jump. If this is not the case, then p( s| s)= 0. Thisremoves the possibility to jump over blocked cubes. See example 5 in figure 4.5.If one of the both states is more than 2 m above cubes with blocking material,then p( s| s)= 0. This removes the possibility to fly. And the last condition forp( s| s)= 0 is given by states, that are located above cubes containing materialflagged as impassable. This removes the possibility to walk over furniture like tablesbut only if the 3D-model exhibits detail at this level.After applying these constraints, the probability mass for the transitions will thenbe evenly distributed over all p( s| s)= 0. This results in an already reasonable6Although the author guesses that using the elevator that is present in the UMIC scene, willprobably break this approach.