Location estimation method

1. A location estimation method for locating a mobile station (MS) by a plurality of base stations (BS), comprising:

analyzing a geometric distribution of the BSs to provide a list of conditional equations;

allocating virtual BSs having virtual distances to the MS to provide constraint equations; and

estimating the MS location based on the conditional equations and the constraint equations;

wherein analysis of the geometric distribution comprises:

transmitting coordinates of each BS to the MS;

estimating time-of arrival (TOA) of signals transmitted to or from the BSs to obtain measured distances correspondingly;

measuring noise level of each transmission to calculate standard deviations of the measured distances;

generating the conditional equations based on the measured distances and the standard deviations;

calculating an initial estimate of the MS location based on the standard deviations and coordinates of the BSs;

determining the virtual distances based on the initial estimate of the MS location, the coordinates of the BSs and a plurality of virtual coefficients each corresponding to a BS; and

rendering a GDOP contour based on the analysis of the geometric distribution, statistically presenting measurement error distribution of the BSs;

wherein allocation of the virtual BS comprises:

observing peak values distributed in the GDOP contour; and

allocating the virtual BSs to the positions where at least one peak value is causally smoothed away.

2. The location estimation method as claimed in claim 1 , wherein the positions of the virtual BSs are determined by adjusting the virtual coefficients.

3. The location estimation method as claimed in claim 1 , wherein the constraint equations is formed by the coordinates of the virtual BS and the virtual distances.

4. The location estimation method as claimed in claim 1 , wherein estimation of the MS location comprises substituting the conditional equations and the constraint equations into a two-step least square algorithm.

5. The location estimation method as claimed in claim 4 , wherein estimation of the MS location further comprises:

for a first step of the two-step least square algorithm, providing a variable equivalent to the square sum of the MS location: β=x 2 +y 2 , where (x,y) are the coordinates of the MS location, and β is the variable;

generating a first linear vector from the variable and the coordinates of MS location;

performing a maximum likelihood search using the first linear vector, the conditional equation and the constraint equations; and

obtaining a preliminary solution comprising a preliminary coordinate of the MS location.

6. The location estimation method as claimed in claim 5 , wherein estimation of the MS location comprises:

for a second step of the two-step least square algorithm, providing a second linear vector from the preliminary coordinate of the MS location;

performing the maximum likelihood search using the second vector, such that a final solution is obtained.