A121 Figure of Merits

A121 Figure of Merits#

The Sparse IQ Figure of Merits applies to A121 sensors. The definitions below apply only to the A121 sensor.

Radial resolution#

Radial resolution is described by the full width at half maximum (FWHM) envelope power.

Let \(x(f, s, d)\) be a (complex) point at a radial distance \(d\) where the number of distances is \(N_d\), in a sweep \(s\) where the number of sweeps per frame is \(N_s\), in a frame \(f\) where the number of frames collected is \(N_f\).

Then, let the (average) envelope power

(14)#\[y(d) = |\text{mean}_{f,s}(x)|^2\]

The FWHM of \(y\) is what describes the radial resolution.

Distance#

Preliminaries#

Let \(d_{est}(f, d)\) be the estimated distance to a target located at distance \(d\), formed by processing frame \(f\) in accordance with the steps outline in the Distance Detector documentation. \(f\) is a single frame in a set of frames of size \(N_f\).

Next, let \(e(f, d)=d_{est}(f, d) - d\) be the estimation error of a single frame/measurement.

Lastly, form the mean error by averaging over the frames, \(\overline{e}(d)=\text{mean}_{f}(e(f,d))\).

\(\overline{e}(d)\) describes the average error for a single sensor. The metrics calculated in the following sections are based on data from a set of sensors. To indicate what sensor the mean error is associated with, the argument \(s\) is added, \(\overline{e}(d,s)\).

Accuracy#

The distance estimation accuracy is characterized through the following two sets of metrics:

  • Mean error(\(\mu\)) and standard deviation(\(\sigma\)).

  • Mean absolute error(\(\text{MAE}\)).

Mean and standard deviation#

The mean error for a set of sensors is given by \(\mu=\text{mean}_{d,s}(\overline{e}(d,s))\).

The standard deviation for a set of sensors is given by \(\sigma=\text{std}_{d,s}(\overline{e}(d,s))\).

Mean absolute error#

The mean absolute error for a set of sensor is given by \(\text{MAE}=mean_{d,s}(|\overline{e}(d,s)|)\).

Linearity#

Linearity refers to the variation in the distance estimate error as a function of the distance to the target.

The distance linearity is characterized through the mean of the standard deviation of the estimation error over a number of distances, \(\sigma=\text{mean}_{s}(\text{std}_{d}(\overline{e}(d,s)))\).

The distance linearity is evaluated over two sets of distances:

  • Micro: A number of distances within a few wavelengths.

  • Macro: A number of distances over many wavelengths.

Temperature sensing#

The accuracy of the built-in temperature sensor is described by the relative deviation:

(15)#\[k = \left| \frac{\hat{x} - x}{x} \right|\]

where \(x\) is the actual temperature change and \(\hat{x}\) is the measured temperature change.

The evaluated temperature span is typically the range from -40°C to 105°C.

Note

The built-in temperature sensor is not designed for absolute measurements and should therefore not be used for that. For this reason, the absolute accuracy is not described as a FoM.