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    Re: Do We Still Need to Use Sextants?
    From: Don Seltzer
    Date: 2013 Mar 27, 11:46 -0700

    Sems wrote:
    Micro electro mechanical systems (MEMS) gyroscopes or gyro chips may create a revolution for sextants. In a routine daily life we are using those chips in our smart phones, video game controllers or in navigation systems. Gyroscope MEMS are an inertial sensing integrated circuit that measures the angle and rate of rotation in an object or system. This technology has been improved in the last 10 years and now, 3-axis gyroscope, 3-axis accelerometer and 3-axis compass are integrated in the same chip can be found on the shelf. With the advent of MEMS, gyroscopes and other inertial measurement devices can now be produced cheaply and in very small packages in the micro domain. So it can be fitted to a binocular or monocular.

    Brad replied;
    ...This device (mostly) exists already. The device is a Celestron Sky Scout.
    It has insufficient resolution for celestial navigation. I think its just a matter of paying for improved (read more expensive) electronics.

    It is an interesting idea. I am not sure about the utility of gyros, which measure angular acceleration, but I think that a MEMS 2-axis accelerometer would be effective in measuring tilt from a vertical axis as defined by gravity. This star sighting device suggested by Sems would directly measure zenith distance of an object, in slight contrast to a sextant which determines altitude from the horizontal. But as to Brad's point, can it be accurate enough for celestial navigation?

    In a 2 axis tilt sensor, the ratio of the outputs of the orthogonal x and y axis accelerometers is a measure of the tangent of the angle between the scope and vertical as defined by gravity. In order to resolve a .5 arc minute, the accelerometers must be able to each accurately resolve about .15 mG (thousandth of one G).

    Electrically, that is not a problem. Commercial MEMS accelerometers can have outputs on the order of a volt per G, and digitizing fractions of a mvolt is well within the capability of inexpensive electronics.

    However, accelerometers have two fundamental error sources. Bias offset is similar to a sextant's index error. It can be significant, but it can also be zeroed out through initial calibration. There is also Scale Factor error, the electrical output in Volts/G. The basic SF will vary from unit to unit, and there will also be linearity errors from an ideal straight line. Like bias offset, it is possible to initially calibrate each device by measuring its output in small steps throughout its entire range and applying either a correction function or lookup table for subsequent use.

    Unfortunately, these factory calibration values do not last. Both Bias and SF are subject to long term drift. But worse, they are also temperature sensitive. I have done some work with MEMS accelerometers, and it has been my experience that bias can drift on the order of a mG per degree centigrade. This level of variation would make it impractical for celestial navigation. A close analogy is a plastic Davis sextant, whose index error changes significantly with temperature changes, requiring the user to recheck the error against the horizon at frequent intervals. I do not see a comparable means of recalibrating an accelerometer in the field.

    There are ways to overcome temperature sensitivities. You can add a temperature sensor to the circuitry and calibrate each device for its full temperature range. This is what is done for some aerospace and military applications. However it is a very time intensive process, not suitable for the high volume commercial market that can produce cheap devices costing only a few dollars each.

    Don Seltzer

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