Read the equation
The first distance compares the current representation zₜ with its current reference rₜ. The second compares zₜ with the representation recorded at the declaration time. These answer different questions: current mismatch versus movement from a fixed historical state. The final manuscript uses the latter as a secondary descriptive quantity, avoiding a declaration-defined origin for its primary onset detector.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| delta_t | Current-reference discrepancy |
| delta_t_0 | Displacement from the declaration-time representation |
| d | Specified distance |
| t_D | Detected declaration time |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
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Original context
Read the surrounding source passage
Let zt=H(St) denote an internally maintained estimate or report. Let rt=ρ(St) denote a reference for the same target, obtained by a prespecified measurement procedure that does not infer correctness from zt. In this notation, independently collected reference measurements are part of the observation record. Both maps must return objects in a common comparison space. An estimated hand position and a measured hand position can be compared in shared coordinates; a physical robot and a sentence about it cannot be compared merely because both are called the self. For a specified nonnegative discrepancy function d, I distinguish discrepancy from the current reference and displacement from the first declared representation: δt=d(zt,rt), δt0=d(zt,ztD). (2.2) The declaration time tD is defined below. The second quantity is available only when that declaration and its representation have been observed. It freezes the declared representation as a reference, whereas the first quantity can compare an estimate with a changing target. An estimate can move away from its first declaration while correctly tracking the present. An unchanged estimate can become inaccurate when its target changes. [Context excerpt; full source linked.]
Exact original notation
{\delta }_{t}=d({z}_{t},{r}_{t}), {\delta }_{t}^{0}=d({z}_{t},{z}_{{t}_{D}}).Related builds
Sources & provenance
{\delta }_{t}=d({z}_{t},{r}_{t}), {\delta }_{t}^{0}=d({z}_{t},{z}_{{t}_{D}}).
{\delta }_{t}=d({z}_{t},{r}_{t}), {\delta }_{t}^{0}=d({z}_{t},{z}_{{t}_{D}}).
{\delta }_{t}=d({z}_{t},{r}_{t}), {\delta }_{t}^{0}=d({z}_{t},{z}_{{t}_{D}}).
{\delta }_{t}=d({z}_{t},{r}_{t}), {\delta }_{t}^{0}=d({z}_{t},{z}_{{t}_{D}}).