CAD.5:4.2 - Form realizable observation and timing alternatives

For each offered channel (j), specify its observed quantity (C_jx), error model, sampling rule, delivery rule and resource demand. For a nonsaturating bounded-error channel, a packet contains

(j,\tau,y),\qquad y=C_jx_\tau+v,\qquad v\in V_j,

where (\tau) is the sample time and (k-\tau) is its age when used. The channel’s constraint on the sampled state is the set

M(j,\tau,y)=\{x_\tau:y-C_jx_\tau\in V_j\}.

A quantized symbol instead denotes its whole quantizer cell, including the noise bound. A saturated extreme cell may be unbounded; do not replace it with a small symmetric error interval. For adaptive thresholds, retain or communicate the thresholds used for that particular sample.

Construct a finite set of feasible channel-and-schedule alternatives. Include the resource coupling that can change their timing: two sensors sharing a bus, for example, need not retain their isolated delivery bounds. State which loss and delay combinations are allowed. A fixed periodic schedule or an explicitly bounded family of allowed modes supplies timing conditions for the error calculation. The number of cases and the cost of set propagation still have to fit the design and execution effort. Arbitrary online sensing policies require a separate policy construction.

A rapid narrow channel, a slow complete channel and their combination are useful candidates when the problem suggests them. They are not compulsory categories. Future-disturbance preview is different from a delayed observation of the current plant; give it its own prediction model rather than treating its timestamp as negative measurement delay.

Do not assume a universal law exchanging accuracy for speed. Obtain that relation from the proposed device, encoding, bandwidth, energy or other physical constraint. If a fast complete channel fits the same total budget, it may remove the reason for a heterogeneous arrangement.