This is incorrect. (I assure you: I *use* this technology in depth.:) )
The confusion arises from thinking about just the spatial component of the problem you are trying to solve, and not also the temporal. A GPS receiver has a generally *inaccurate* internal clock (which means it can be cheap, one of the brilliant parts of the design, IMO). Think of the "pseudorange" from a single satellite as providing a single equation with *four* unknowns: the three dimensions of position, and the *error* in your internal clock. To solve for all four unknowns, four equations (and thus four measurements) are needed.
Almost-- AC's figure of about 39% is assuming that these events occur as a Poisson *process*, so that the length of the interval between consecutive events has an *exponential* (continuous) distribution. In other words, 0.39 is the probability that this particular exponentially distributed random variable has a value less than 1500.
(The Poisson *distribution*, on the other hand, is a *discrete* distribution-- in this case, non-negative integer-valued-- that in this case would describe the probability of a *number* of these events occurring within a given length of time.)
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This is incorrect. (I assure you: I *use* this technology in depth. :) )
The confusion arises from thinking about just the spatial component of the problem you are trying to solve, and not also the temporal. A GPS receiver has a generally *inaccurate* internal clock (which means it can be cheap, one of the brilliant parts of the design, IMO). Think of the "pseudorange" from a single satellite as providing a single equation with *four* unknowns: the three dimensions of position, and the *error* in your internal clock. To solve for all four unknowns, four equations (and thus four measurements) are needed.
Almost-- AC's figure of about 39% is assuming that these events occur as a Poisson *process*, so that the length of the interval between consecutive events has an *exponential* (continuous) distribution. In other words, 0.39 is the probability that this particular exponentially distributed random variable has a value less than 1500. (The Poisson *distribution*, on the other hand, is a *discrete* distribution-- in this case, non-negative integer-valued-- that in this case would describe the probability of a *number* of these events occurring within a given length of time.)