Accuracy is not
one number.
A simple gait-speed example showing how PoseIQ thinks about measurement, uncertainty and evidence.
What are we actually measuring?
A person travels between two defined gates. We measure the known distance and the elapsed time, then calculate average speed.
Where can uncertainty enter?
Before talking about “accuracy”, identify the quantities that actually contribute uncertainty to the measurement.
Distance
The gates must be positioned using a physical measurement procedure.
Elapsed time
Timing depends on how the crossing events are defined, detected and timestamped.
What can sit inside temporal / event uncertainty?
In a vision-based measurement, a gate-crossing time is not only a clock problem. The observed event can be influenced by several components, and those components are not automatically independent.
Timestamp resolution, clock behaviour and synchronization relevant to the recording and measurement.
Video is temporally sampled. At 30 fps the nominal frame interval is about 33.3 ms; at 60 fps it is about 16.7 ms.
Spatial variation in the tracked landmark can shift the apparent instant at which a defined gate is crossed.
Threshold rules, temporal filtering or sub-frame interpolation can affect both random variation and systematic bias.
Now calculate the measurement.
Average speed is distance divided by elapsed time. The basic calculation is simple. The expandable section shows exactly how the stated standard uncertainties propagate into the reported speed.
Show the measurement maths
Model, assumptions, propagation, covariance and interpretation
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Define the measurand and measurement model
Let \(D\) denote the distance between Gate A and Gate B, and \(T\) denote the elapsed time between the two defined crossing events. The measurand is average speed:
For this illustrative example:
Define the uncertainty inputs
To make the propagation mathematically unambiguous, this example treats the following values as standard uncertainties (\(k=1\)):
| Input quantity | Estimate | Standard uncertainty | Relative standard uncertainty |
|---|---|---|---|
| Distance \(D\) | 5.000 m | \(u_D = 0.001\ \mathrm{m}\) | 0.020% |
| Elapsed time \(T\) | 3.33 s | \(u_T = 0.050\ \mathrm{s}\) | ≈ 1.5015% |
Calculate the sensitivity coefficients
For the measurement model \(v(D,T)=D/T\), the first-order sensitivity coefficients are:
These coefficients describe how strongly the reported speed responds to small changes in each input quantity.
Propagate independent standard uncertainties
If \(D\) and \(T\) are treated as independent input quantities, first-order propagation gives the combined standard uncertainty:
Substituting the sensitivity coefficients:
Equivalently, the relative combined standard uncertainty is:
Evaluate the uncertainty budget
Distance term:
Elapsed-time term:
Combined relative standard uncertainty:
Combined standard uncertainty in speed:
Elapsed-time uncertainty is not the same as per-gate uncertainty
The main example assumes that \(u_T=50\) ms belongs to the final A-to-B elapsed-time measurement. A different model is required if 50 ms belongs separately to each gate event.
The standard uncertainty of the already-computed interval \(T=t_B-t_A\) is 50 ms.
This produces the 1.5016% result above.
The standard uncertainty is 50 ms at Gate A and 50 ms at Gate B.
Their covariance must then be considered.
Since
the general variance expression is:
If the two timestamp errors are independent, the covariance term is zero:
Frame-rate quantisation is a component, not the whole answer
Video samples motion at discrete times. For example:
The frame interval is relevant to temporal resolution and quantisation, but it is not automatically equal to the measurement uncertainty. Event timing can also depend on timestamp quality, landmark localisation, event definition, interpolation and processing behaviour.
If the numbers are bounds rather than standard uncertainties
The propagation above assumes standard uncertainties. If ±50 ms instead means a symmetric hard limit and a rectangular distribution is appropriate, the standard uncertainty would be:
Likewise, if a quoted quantity were an expanded uncertainty \(U\) with coverage factor \(k\), it would first be converted to:
This is why the uncertainty convention must be stated before numbers are propagated or compared.
Combined standard uncertainty versus expanded uncertainty
The worked result above is a combined standard uncertainty:
If an expanded uncertainty is required, it is calculated as:
For example, choosing \(k=2\) would give:
What propagation does not establish
A mathematically correct uncertainty propagation does not by itself validate the measurement system. A defensible evidence profile may also need to establish:
| Trueness / bias | Systematic difference from an appropriate reference. |
| Precision | Variation across repeated measurements under defined conditions. |
| Distance setup | How the gate separation is established and verified. |
| Timestamp / timebase behaviour | Timing characteristics relevant to the recorded measurement. |
| Landmark localisation | How spatial tracking variation changes the detected crossing event. |
| Event-detection logic | Thresholds, temporal filtering, crossing definition and interpolation. |
| Operating conditions | Speed, viewpoint, visibility, occlusion, lighting and other relevant conditions. |
| Failure behaviour | When the system becomes unreliable, rejects the measurement or fails. |
The defensible statement for this worked example
Using \(D=5.000\) m and \(T=3.33\) s, and treating \(u_D=1\) mm and \(u_T=50\) ms as independent standard uncertainties:
Illustrative uncertainty contribution
Under the stated illustrative assumptions, temporal/event uncertainty dominates the uncertainty budget. Improving an already-small distance uncertainty would contribute little unless temporal/event performance were also improved.
Describe the result.
Under these illustrative assumptions, first-order uncertainty propagation gives approximately:
Turn the measurement into an Evidence Card.
Instead of attaching one accuracy number to an entire platform, document the evidence for the measurement that matters.
Average gait speed
Who validates the measurement?
PoseIQ provides the technology, measurement tools and assurance framework. This worked example demonstrates a process for defining, quantifying and evaluating a measurement. It is not a claim that PoseIQ has validated every possible use, configuration or environment.
Validation is application-specific.
Actual measurement performance can depend on the measurand, task, protocol, camera configuration, equipment, population, environment, operating conditions and intended use. A validation result obtained under one set of conditions should not automatically be assumed to apply to another.
Users and research partners can therefore evaluate the measurements that matter to them using appropriate reference methods and test conditions for their application. PoseIQ provides the technical platform and measurement framework that can support that process.
That is the framework.
PoseIQ Assurance moves the question from a vague platform-level accuracy claim to an inspectable measurement and its evidence.
Don't validate a vague accuracy number. Validate the measurement.
Gait speed is one simple example. The same reasoning can be applied to joint angles, range of motion, gait events, jump measures, asymmetry and other movement measurements.