Today I was talking with David Christensen about a project of his, and I had some ideas about tracking styluses on drawing tablets using ultrasound. In his project, which is not a drawing tablet, they're tracking a point of contact on a surface using an array of piezoelectric contact microphones on the back of the surface, using the relative intensity of the conducted sound at different microphones to estimate the location.
It occurred to me that by cross-correlating the signals at the different microphones, you can do a much better job of localizing the sound, and this could be useful for an inexpensive large-area drawing tablet. (This is related to Measuring submicron displacements by pitch bending a slide guitar.)
A stylus scratching on a rough surface such as paper or MDF produces broad-spectrum noise, and broad-spectrum noise is wonderful at having very low autocorrelation at any shift other than zero; it's very nearly orthogonal to itself at other shifts.
Echoes from the edges of the tablet can set up Chladni-plate-like standing waves, which could complicate the situation substantially (like some stupid Hollywood action movie that ends in a hall of mirrors) so using a highly attenuating material like leather might be a good idea, or perhaps cutting the edges of the material in a sunburst-like zigzag pattern so that the high frequencies we want are strongly attenuated and their coherence destroyed as they reflect from the edge. (This is related to the Q of acoustic resonators such as music-box tines cut from the material, although I don't know if we can talk about an acoustic Q of the material itself; but clearly for this purpose MDF is dramatically superior to plastics, which are dramatically superior to metals, which are mostly somewhat superior to ceramics.)
With only two microphones you would have an ambiguity about which side of the line through them the stylus is on (whose importance could be minimized by putting them along the same edge of the tablet); three microphones would avoid this problem, and more than three microphones would help to reduce errors and latency further. Latency of under 10 milliseconds is critical for musical use and strongly desirable for drawing; anything over 1 millisecond is detectable and undesirable.
The localization precision and interaction latency are both limited by the speed of sound in the material, but unfortunately in opposite directions: a higher speed of sound means less interaction latency but lower precision. Using higher frequencies alleviates this problem. Suppose you have three microphones in an equilateral triangle one meter on a side; the center is 661 mm from the corners, and that's as far as you can get from the corners inside the triangle or indeed anywhere near it. With a speed of sound of 2000 m/s, a reasonable estimate for many solids, that works out to an intrinsic acoustic latency of 331 microseconds, not counting processing time. If there are significant 10-kHz components of the noise being tracked, they will narrow the autocorrelation peak to around 100 microseconds --- but at 2km/s, that's 200 mm of position uncertainty! That's no good for drawing, which needs submillimeter precision. A lower speed of sound would reduce the positional uncertainty proportionally.
However, correlation and intensity aren't the only sources of information we have. Solids actually carry two different kinds of sound, longitudinal and transverse, and transverse waves are slower and have polarization. If the microphones are able to detect the direction of vibration, for example by coupling them to points on the board through taut UHMWPE or glass-fiber threads near tangent to the board, they will first detect the longitudinal waves moving the board towards and away from the point of contact, then later the transverse waves moving it in some direction normal to the vector towards the pencil.
This still depends on getting substantial phase separation of the two waves --- I haven't measured yet but I think they'll tend to be strongly correlated, though perhaps longitudinal impulses going in one direction will be strongly associated with transverse impulses propagating at right angles to it.
Raising the frequency would help a lot, but you need to raise it by a factor of 500 or so, to about 5 MHz. It may be the case that pencils scraping on paper or MDF intrinsically produce 5-MHz noise, but I doubt it. 5-MHz ultrasound doesn't travel very far in air, but it has no difficulty with most solids and liquids. You could attach a small sound transmitter to the pencil that transmits a 10Mbps LFSR signal, which would be transmitted to the board whenever the pencil was touching it. (Or touching paper taped to it.) You could transmit this signal intermittently --- a 40-bit burst, taking 4 microseconds, every 100 microseconds or more, would be adequate.
Alternatively you could couple ultrasonic vibrations into the board from a piezoelectric, magnetostrictive, or electromagnetic actuator mounted on the back of it and see how they scatter; this might be adequate but would probably work better for large, hard contact points than for a pencil point. Or, as described for the one-dimensional case in Measuring submicron displacements by pitch bending a slide guitar, you could attach the detector to the stylus (or the person's finger) and pick up vibrations injected into the surface.
Periodicity in the sound injected would be problematic, since the autocorrelation of periodic waveforms has many peaks, creating ambiguity about the stylus position. It's easy enough to avoid with an LFSR in the electronic case, but for acoustically produced sounds there is the risk of resonances.
Vibration transducers attached to the board could also, at sub-kilohertz frequencies, provide haptic feedback like the piezoelectric click pioneered by Nokia for some of their cellphones years ago; and if the tablet is horizontal and isn't very well damped at the edges, they could also make Chladni figures to move small objects around on it, also a technique demonstrated some years ago by a research group using a single actuator to vibrate a metal plate.