Most current proximity sensing methods fail the stringent requirements of modern smartphones. A position-sensing device (PSD) requires a laser placed some distance away from the sensor, intensity-based solutions are sensitive to changes in reflectivity, and ultrasound-based sensors cannot measure small distances because of resonance. With modern transistors getting smaller and smaller, single-photon detectors have become feasible. Using a single-photon detector called a SPAD and a laser, the travel time of light can be measured. This technique, called time-of-flight, existed for several decades where radar and ultrasound are concerned but only recently includes single-photon detectors. Several products exist that use single-photon time of flight to measure proximity. However, they are limited in terms of maximum distance, resolution and ambient light tolerance. The question arises what the best possible performance of such a system is. For radar and ultrasound, this has been calculated long ago already, but for time of flight, no such analysis exists. This analysis is the main contribution of this thesis. A formula is calculated that takes all parameters of the system into account and produces an expected standard error. This formula is verified using a simulator. The effect of an increasing opening angle of laser and SPAD is analyzed, as well as different waveforms of the laser, using multiple SPADs in smart ways, and increasing the time of a single measurement. It is shown that when less than a thousand SPADs are used, no smart way of combining hits on different SPADs exists. The waveform emitted by a laser is typically a mix of a sine, a square wave and some effects resembling RC-behavior. The nearer to a square wave this is, the smaller the resulting standard error is. The most power-hungry aspect of such a proximity sensing solution is often the time discretization device. To obtain a high resolution in the order of millimeters, the time resolution should be in the order of picoseconds. Such an extremely high resolution, below the switching time of a single transistor, can typically only be obtained by trading trade area, power and read-out time for resolution. This thesis analyzes a solution using a low-resolution time-to-digital converter (TDC) and multiple sub-intervals for a shorter time to increase resolution.

For both security and analytics, much research has gone into person tracking already. As a result, many
different state of the art technologies exist. However, in darkness or without a direct line of sight, much
less technologies are capable of this. The choices become especially limited when the setup needs to
be portable.
A method for person localisation and tracking is implemented. This method consists of a localisation
part, which works with any range-based detection method. Least square estimation is used to determine
the location from the radar detections. With two or more people, it is mathematically impossible to
distinguish which locations are correct, if only the current measurement is taken into account.
Thus, the first problem to be solved is connecting ranges to targets. This is done using target association.
After this is done, one-dimensional tracking can track people at lower computational cost.
The tracking is both in one dimension (per-radar) and in two dimensions. The Hungarian algorithm
is used for keeping track of people using a Kalman filter. The Kalman filter considers the predicted
next location and the measured next location, and makes a best guess. A neural network was used for
the optimisation of location-specific noise parameters, something that has not been done before in this
context. Single person tracking and two person tracking works as expected. The tracking is relatively
cheap in terms of computational complexity. While the tracking has no limits on the maximum number
of people present, the localisation gets increasingly difficult with a complexity of O (n^n). Detecting
the correct peaks is a non-trivial problem because of multi-path reflections. In combination with UWB
radar detections, single and dual person tracking in a room is achieved. More people can be handled by
the tracking algorithm, which is detection-method-agnostic, but not by the localisation. There is some
room for improvement in the dual and triple-person case. However, going further than this is currently
unfeasible, because of the many reflections that occur. Furthermore, the large amount of possible person
locations also has an effect. This is a problem that scales with O (n^n) where n is the amount of
targets.