伪距定位算法

Posted 2022-11-30 者乎之类的

伪距定位算法：
1.准备数据与设置初始解：准备卫星位置（经地球自转校正后）和伪距值
设置接收机初始位置、接收机钟差
2.非线性方程线性化
3.求解非线性方程
4.更新非线性方程的根
5.迭代完毕

function [pos, el, az, dop] = leastSquarePos(satpos, obs, settings)
%satpos卫星坐标xyz;obs观测伪距
%Function calculates the Least Square Solution.
%
%[pos, el, az, dop] = leastSquarePos(satpos, obs, settings);
%
%   Inputs:
%       satpos      - Satellites positions (in ECEF system: [X; Y; Z;] -
%                   one column per satellite)
%       obs         - Observations - the pseudorange measurements to each
%                   satellite:
%                   (e.g. [20000000 21000000 .... .... .... .... ....])
%       settings    - receiver settings
%
%   Outputs:
%       pos         - receiver position and receiver clock error 
%                   (in ECEF system: [X, Y, Z, dt]) 
%       el          - Satellites elevation angles (degrees)
%       az          - Satellites azimuth angles (degrees)
%       dop         - Dilutions Of Precision ([GDOP PDOP HDOP VDOP TDOP])

%--------------------------------------------------------------------------
%                           SoftGNSS v3.0
%--------------------------------------------------------------------------
%Based on Kai Borre
%Copyright (c) by Kai Borre
%Updated by Darius Plausinaitis, Peter Rinder and Nicolaj Bertelsen
%
% CVS record:
% $Id: leastSquarePos.m,v 1.1.2.12 2006/08/22 13:45:59 dpl Exp $
%==========================================================================

%=== Initialization =======================================================
nmbOfIterations = 7;

dtr     = pi/180;
pos     = zeros(4, 1);
X       = satpos;
nmbOfSatellites = size(satpos, 2);

A       = zeros(nmbOfSatellites, 4);
omc     = zeros(nmbOfSatellites, 1);
az      = zeros(1, nmbOfSatellites);
el      = az;

%=== Iteratively find receiver position ===================================
for iter = 1:nmbOfIterations

    for i = 1:nmbOfSatellites
        if iter == 1
            %--- Initialize variables at the first iteration --------------
            Rot_X = X(:, i);
            trop = 2; % 对流层矫正值
        else
            %--- Update equations -----------------------------------------
            rho2 = (X(1, i) - pos(1))^2 + (X(2, i) - pos(2))^2 + ...
                   (X(3, i) - pos(3))^2;%伪距预测值，即r
            traveltime = sqrt(rho2) / settings.c ;

            %--- Correct satellite position (do to earth rotation) --------
            Rot_X = e_r_corr(traveltime, X(:, i));
            %X是(t-tao)(卫星发射信号)时刻的在WGS-84坐标系下的卫星位置；
            %Rot_X是t(接收机接收到信号)时刻在WGS-84坐标下的卫星位置
            %两者差别很大倒不是因为卫星绝对位置移动了多少，而是地球自转导致坐标系移动了
            %--- Find the elevation angel of the satellite ----------------
            [az(i), el(i), dist] = topocent(pos(1:3, :), Rot_X - pos(1:3, :));
            %根据接收机位置和伪距矢量计算方位角、高度角、距离
            if (settings.useTropCorr == 1)
                %--- Calculate tropospheric correction --------------------
                trop = tropo(sin(el(i) * dtr), ...
                             0.0, 1013.0, 293.0, 50.0, 0.0, 0.0, 0.0);
            else
                % Do not calculate or apply the tropospheric corrections
                trop = 0;
            end
        end % if iter == 1 ... ... else 

        %--- Apply the corrections ----------------------------------------
        omc(i) = (obs(i) - norm(Rot_X - pos(1:3), 'fro') - pos(4) - trop);
% n = norm(v) 返回向量 v 的欧几里德范数。此范数也称为 2-范数、向量模或欧几里德长度。
%omc就是b
        %--- Construct the A matrix ---------------------------------------
        A(i, :) =  [ (-(Rot_X(1) - pos(1))) / obs(i) ... %Rot_X是卫星的位置，pos是接收机大体位置
                     (-(Rot_X(2) - pos(2))) / obs(i) ...
                     (-(Rot_X(3) - pos(3))) / obs(i) ...
                     1 ];
    end % for i = 1:nmbOfSatellites

    % These lines allow the code to exit gracefully in case of any errors
    if rank(A) ~= 4
        pos     = zeros(1, 4);
        return
    end

    %--- Find position update ---------------------------------------------
    x   = A \\ omc;   %只用了4颗卫星，所以没有用最小二乘；
%     \\
%     对线性方程组 Ax = B 求解 x
% 
%     此 MATLAB 函数 对线性方程组 A*x = B 求解。矩阵 A 和 B 必须具有相同的行数。如果 A 未正确缩放或接近奇异值，MATLAB
%     将会显示警告信息，但还是会执行计算。
% 
%     x = A\\B
%     x = mldivide(A,B)
    %--- Apply position update --------------------------------------------
    pos = pos + x;
    
end % for iter = 1:nmbOfIterations

pos = pos';

%=== Calculate Dilution Of Precision ======================================
if nargout  == 4
    %--- Initialize output ------------------------------------------------
    dop     = zeros(1, 5);
    
    %--- Calculate DOP ----------------------------------------------------
    Q       = inv(A'*A);
    
    dop(1)  = sqrt(trace(Q));                       % GDOP    
    dop(2)  = sqrt(Q(1,1) + Q(2,2) + Q(3,3));       % PDOP
    dop(3)  = sqrt(Q(1,1) + Q(2,2));                % HDOP
    dop(4)  = sqrt(Q(3,3));                         % VDOP
    dop(5)  = sqrt(Q(4,4));                         % TDOP
end