Dead reckoning

In navigation, dead reckoning is the process of calculating one's current position by using a previously determined position, or fix, and advancing that position based upon known or estimated speeds over elapsed time and course. The corresponding term in biology, used to describe the processes by which animals update their estimates of position or heading, is path integration. Dead reckoning is subject to cumulative errors. Advances in navigational aids that give accurate information on position, in particular satellite navigation using the Global Positioning System, have made simple dead reckoning by humans obsolete for most purposes. However, inertial navigation systems, which provide very accurate directional information, use dead reckoning and are very widely applied. By analogy with their navigational use, the words dead reckoning are also used to mean the process of estimating the value of any variable quantity by using an earlier value and adding whatever changes have occurred in the meantime. Often, this usage implies that the changes are not known accurately. The earlier value and the changes may be measured or calculated quantities. The term 'dead reckoning' was not originally used to abbreviate 'deduced reckoning,' nor is it a misspelling of the term 'ded reckoning.' The use of 'ded' or 'deduced reckoning' appeared much later in history, no earlier than 1931; in contrast to 'dead reckoning' appearing as early as 1613 in the Oxford English Dictionary. The original intention of 'dead' in the term is not clear however. Whether it is used to convey 'absolute' as in 'dead ahead,' reckoning using other objects that are 'dead in the water,' or using reckoning properly 'you’re dead if you don’t reckon right,' is not known. Dead reckoning can give the best available information on position, but is subject to significant errors as both speed and direction must be accurately known at all instants for position to be determined accurately. For example, if displacement is measured by the number of rotations of a wheel, any discrepancy between the actual and assumed travelled distance per rotation, due perhaps to slippage or surface irregularities, will be a source of error. As each estimate of position is relative to the previous one, errors are cumulative, or compounding, multiplicatively or exponentially, if that is the co-relationship of the quanta.