I am about to embark on a little project involving trilateration which is intended to find the originating point of a sonic wave using a microcontroller and several sound sensors.

I have seen sensor arrays arranged in an equally spaced triangular pattern, but I am wondering if it’s possible to achieve an accurate 2D trilateration result with 3 sound sensors which are aligned on the same axis? The goal would be to pinpoint the origin of a sonic wave on a 2D coordinate plane and identify the (x, y) coordinate of the source using time difference of arrival.

Also, is there a specific type of sensor that is best suited to detect a supersonic shock wave and shock waves created by the clap of hands or will one work for both?

Here are the known facts:

  1. Location of sensors. They are statically positioned and equally spaced on the x axis at (0,0), (0,10) and (0,20).

  2. Propagation speed of the of the sonic wave.

  3. For simplicities sake the static location of the sensors and the source of all sound occur within the positive coordinate plane or aka Quadrant I.

  4. Additionally, the source of the pulse shall be located within the bounds of the points of sensor 1 and sensor 2 which is between x (0) and x (20) and y (1) to y (∞).

  • \$\begingroup\$ What kind of supersonic shock wave... spherical or conical? (Alternately, what is it that creates the shock wave? \$\endgroup\$ Jan 7, 2022 at 19:06
  • \$\begingroup\$ Conical like supersonic aircraft. Not like an explosion. \$\endgroup\$
    – zig zag
    Jan 7, 2022 at 19:15
  • \$\begingroup\$ Although if I wanted to detect a large meteor in the atmosphere both may be useful. Not sure. \$\endgroup\$
    – zig zag
    Jan 7, 2022 at 19:23

1 Answer 1


No. If the sensors are collinear then you have symmetry with respect to the line they're on — you can't tell a source on one side of the line from one that's the same distance on the opposite side of the line.

  • \$\begingroup\$ What if you place them along the bottom of the 2D coordinate plane? \$\endgroup\$
    – ocrdu
    Jan 7, 2022 at 19:00
  • \$\begingroup\$ This problem is "quasi" the same that a "linear array" of antennas. A new sensor is needed to "remove doubt". \$\endgroup\$
    – Antonio51
    Jan 7, 2022 at 19:02
  • \$\begingroup\$ Agreed, there are two solutions (y positive and negative), however @zigzag says he knows y>=1 so it should work. \$\endgroup\$ Jan 7, 2022 at 19:08
  • \$\begingroup\$ Circular networks of sensors would be more appropriate, so at least 3. \$\endgroup\$
    – Antonio51
    Jan 7, 2022 at 19:09

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