精度衰减因子DOP
Dilution of precision (GPS)
'Dilution of precision' or 'DOP' is a GPS term used in geomatics engineering to describe the geometric strength of satellite configuration. When visible satellites are close together in the sky, the geometry is said to be weak and the DOP value is high; when far apart, the geometry is strong and the DOP value is low.
Factors that affect the DOP are, besides the satellite orbits, the presence of obstructions which make it impossible to use satellites in certain sectors of the local sky.
We speak of HDOP, VDOP, PDOP and TDOP respectively, for Horizontal, Vertical, Position (3-D) and Time Dilution of Precision. These quantities follow mathematically from the positions of the useable satellites on the local sky. GPS receivers allow the display of these positions ("skyplot") as well as the DOP values.
Note that this situation is not restricted to GPS, but occurs in electronic-counter-counter-measures (electronic warfare) when computing the location of enemy emitters (radar jammers and radio communications devices). Using such an interferometry technique can provide certain geometric layout where there are degrees of freedom that cannot be accounted for due to inadequate configurations
### Geometric Dilution of Precision (GDOP)
GPS devices calculate your position using a technique called “3-D multilateration,” which is the process of figuring out where several spheres intersect. In the case of GPS, each sphere has a satellite at its center; the radius of the sphere is the calculated distance from the satellite to the GPS device. Ideally, these spheres would intersect at exactly one point, causing there to be only one possible solution to the current location, but in reality, the intersection forms more of an oddly-shaped area. The device could be located within any point in the area, forcing devices to choose from many possibilities. Figure 2-1 shows such an area created from three satellites (using part one’s $GPGSV sentence). The current location could be any point within the gray-colored area. Precision is said to be “diluted” when the area grows larger, which leads to this article’s focus: dilution of precision. The monitoring and control of dilution of precision (or DOP for short) is the key to writing high-precision applications.
DOP values are reported in three types of measurements: horizontal, vertical, and mean. Horizontal DOP (or HDOP) measures DOP as it relates to latitude and longitude. Vertical DOP (or VDOP) measures precision as it relates to altitude. Mean DOP, also known as Position DOP (PDOP), gives an overall rating of precision for latitude, longitude and altitude. Each DOP value is reported as a number between one and fifty where fifty represents very poor precision and one represents ideal accuracy. Table 2-1 lists what I believe to be an accurate breakdown of DOP values.
DOP Rating Description
1 Ideal This is the highest possible confidence level to be used for
applications demanding the highest possible precision at all times.
2-3 Excellent At this confidence level, positional measurements are considered
accurate enough to meet all but the most sensitive applications.
4-6 Good Represents a level that marks the minimum appropriate for making
business decisions. Positional measurements could be used to make
reliable in-route navigation suggestions to the user.
7-8 Moderate Positional measurements could be used for calculations,
but the fix quality could still be improved. A more open view
of the sky is recommended.
9-20 Fair Represents a low confidence level. Positional measurements
should be discarded or used only to indicate a very rough
estimate of the current location.
21-50 Poor At this level, measurements are inaccurate by half a football
field or more and should be discarded.
##### Table 2-1: An interpretation of dilution of precision values.
%****************************************************************************
% This program calculates Dilution of Precision with respect to a GPS *
% receiver given its Cartesian ECEF position and the positions of four or *
% more visible GPS satellites. It is a validation of the DOP algorithm and *
% contains reference positions for which the DOP results are known. *
%****************************************************************************
% Written by Scott Burnside, United States Air Force, 4/30/2003 *
% Phone: (661) 277-4282 Email: richard.burnside@edwards.af.mil *
%****************************************************************************
% Reference: "Fundamentals of Astrodynamics": Bate, Mueller, White *
% *
% "Geometric Dilution of Precision, Bounds and Properties": *
% GE Research and Development, Technical Information Series *
% Yarlagadda, Ali, Al-Dhahir, Hershey *
% *
% "Linear Algebra and its Applications": Gilbert Strang *
% *
% "The Geographer's Craft Project": Peter H. Dana *
% Department of Geography, University of Colorado at Boulder *
%****************************************************************************
clear all
clc
format long g
%
% Test Values of 4 satellites contributing to DOP (ECEF coordinates)
veh(1,1:3) = [15524471.175, -16649826.222, 13512272.387]; % meters
veh(2,1:3) = [-2304058.534, -23287906.465, 11917038.105]; % meters
veh(3,1:3) = [16680243.357, -3069625.561, 20378551.047]; % meters
veh(4,1:3) = [-14799931.395, -21425358.240, 6069947.224]; % meters
%
%
% Test Value of GPS receiver for whom DOP is being calculated (ECEF coordinates)
rcvr(1,1:3) = [-730000, -5440000, 3230000]; % meters
%
%***************************Validation Block**********************************
% The test values provided should produce the following resultant DOP values *
% as calculated by Peter H. Dana, Department of Geography, University of *
% Texas at Austin, 1994: *
% *
% GDOP = 6.80612116250504 *
% PDOP = 6.17100492780574 *
% HDOP = 2.70785829792709 *
% VDOP = 1.7736928882298 *
% TDOP = 2.87088548355665 *
%*****************************************************************************
%
% Pseudo-Range and Directional Derivative Loop
for i = 1:4
% Calculate pseudo-ranges from reciever position to other vehicles
r(i) = sqrt((veh(i,1)-rcvr(1,1))^2 + (veh(i,2)-rcvr(1,2))^2 + (veh(i,3)-rcvr(1,3))^2);
% Calculate directional derivatives for X,Y,Z, and Time
Dx(i) = (veh(i,1)-rcvr(1,1))/r(i);
Dy(i) = (veh(i,2)-rcvr(1,2))/r(i);
Dz(i) = (veh(i,3)-rcvr(1,3))/r(i);
Dt(i) = -1;
end
%
% Produce the Covariance Matrix from the Directional Derivatives
A = zeros(4);
for n = 1:4
A(n,1) = Dx(n);
A(n,2) = Dy(n);
A(n,3) = Dz(n);
A(n,4) = Dt(n);
end
B = transpose(A);
C = B*A;
D = inv(C)
% Calculate DOPs from the diagonal elements of the Covariance Matrix
GDOP = sqrt(D(1,1) + D(2,2) + D(3,3) + D(4,4))
PDOP = sqrt(D(1,1) + D(2,2) + D(3,3))
HDOP = sqrt(D(1,1) + D(2,2))
VDOP = sqrt(D(1,1))
TDOP = sqrt(D(4,4))
%----------End of Code--------------------------------------------------------------------
精度衰减因子DOP |