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7 Compiled Mode Estimation Algorithms

Chapter 6 presented the ideas and innovations for performing mode estimation using a compiled model. The online mode estimation algorithms have been described to convey the key ideas behind each algorithm. This chapter details the algorithms for all portions of Online Mode Estimation, and gives specifics for implementation. The methods described in this chapter have been used to generate results for the validation experiments described in Chapter 6.

The chapter begins with the detail of the Compiled Conflict Recognition algorithms in section 0, followed by the Dynamic Mode Estimate Generation algorithms in section 7.2. The chapter ends with a description of the top level Online Mode Estimation algorithm, which enables the Compiled Conflict Recognition and the Dynamic Mode Estimate Generation algorithms to work together to produce mode estimates.

Diagnosis Generator. This section only presents the Constituent Diagnosis Generator for brevity. The algorithm for the Dissent and Transition Triggers are presented in Appendix D.

7.1.1 Constituent Diagnosis Generator

The Constituent Diagnosis Generator uses the Enabled Dissents and Enabled Transitions to determine the set of Constituent Diagnoses and Reachable Current Modes. In addition, it passes on the Enabled Transitions. There are two distinct tasks within the Constituent Diagnosis Generator that produce the desired outputs. The first is to use the enabled transitions to determine the set of reachable current modes as described in Chapter 6. The second task is to map the enabled dissents to the set of constituent diagnoses, also described in Chapter 6. The inputs and outputs of the Constituent Diagnosis Generator are shown below.

Constituent Diagnosis Generator

Enabled Dissents

Enabled Transitions

Constituent Diagnoses Reachable Current Modes

Enabled Transitions Figure 7-1 - Inputs and Outputs of Conflict Generator

A reachable current mode in the set of reachable current modes, ΠmCurrent, stores:

1. Transition probabilities for a given Reachable current mode 2. List of previous mode estimates for a given Reachable current

mode

3. xim = vij identifying this reachable current mode

A particular component mode may be the target of more than one transition, depicted in Figure 7-2.

(x_2m = v₂₃)^t

(x_2m = v₂₄)^t (x_2m = v₂₁)^t

(x_2m = v₂₂)^t+1

p_T p_T

p_T

Figure 7-2 - A Reachable Current Assignment with Multiple Previous Sources

If a component mode is reachable from multiple previous mode estimates, then the probability of the component mode changes with respect to the previous mode estimate at time ‘t’. The component mode assignment, (x2m

= v22), stores the previous mode estimates that mention (x2m = v21), (x2m = v23) and (x2m = v24), as well as the individual transition probabilities, pT for each transition, giving the transition probability distribution. Storing this information is enabled by the previous list of component modes determined by the Compress-Mode-Estimates algorithm, given in Appendix D. All that is required is to go through the list of enabled transitions, and access the stored component modes in the source and the transition probabilities.

This computation results from the need to track the previous belief state, not just a single previous mode estimate. A reachable component mode stores the transition probability distribution and the previous mode estimates that are the sources of these transitions. This is used to simplify the calculations of the Dynamic Mode Estimate Generation algorithm.

The second step of the Constituent Diagnosis Generator algorithm transforms the Enabled Dissents into Constituent Diagnoses. This transformation uses the set of all component mode assignments, Πm in the approximate belief state and the dissents to determine the set of constituent diagnoses for the conflict in each Enabled Dissent. The conflicts restrict the

component modes by specifying infeasible combinations. The algorithm then looks for all assignments of a particular component variable not in the conflict, and places these in the set of constituent diagnoses of the conflict.

The set of constituent diagnoses corresponds one to one with the set of enabled dissents. The resultant Constituent Diagnosis Generator algorithm that captures these computations is given below.

function Constituent-Diagnosis-Generator(DSEN, TEN, Π^m)

returns Reachable current modes, ΠmCurrent, Constituent diagnoses, CD, and enabled transitions, T_EN

for each Ti in TEN

for (x_im = v_ij) in destination mode of T_i

transition probability ← P(Ti) for (xim = vij)

mode estimate ← mode estimate from source (x_im = v_ij) of T_i unless (xim = vij) ∉ΠmCurrent

ΠmCurrent ← (x_im = v_ij) ∪ΠmCurrent

end

for each di in DSEN

for each (x_im = v_ij) in d_i

cd ← cd ∨ (xim = vim) ∀ vim≠ vij∈ D(xim) end

CD ← cd ∪ CD end

return ΠmCurrent, CD, and TEN

Figure 7-3 – Constituent Diagnosis Generator Algorithm

The algorithms given here for the Compiled Conflict Recognition map the compiled model, the current observations and commands to the Constituent Diagnoses, the Reachable Current Modes, and the Enabled Transitions.

This information, along with the constituent diagnoses and enabled transitions, guide the search that produces the current mode estimates.