基于非线性最小二乘法 (NLLS) 实现伪距数据的 UAV 轨迹跟踪附matlab代码

最新推荐文章于 2025-02-08 18:12:13 发布

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最新推荐文章于 2025-02-08 18:12:13 发布

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分类专栏：无人机文章标签：最小二乘法 matlab 算法

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该项目使用非线性最小二乘法分析来确定UAV轨迹，并通过匹配真实轨迹进行验证。同时，计算了包括几何DOP、位置DOP、水平DOP、垂直DOP和时间DOP在内的五种DOP值，这些值反映了GPS定位数据的精度。低DOP值意味着更好的定位测量。文章还涉及了GPS定位问题的解决方案，如通过增加卫星数量来提高定位准确性。

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⛄ 内容介绍

This project consists of two primary tasks. The ﬁrst is to use non-linear least squares (NLLS) analysis to ﬁnd a UAV trajectory given pseudorange data and validating this result by matching them to the true UAV trajectory (also given). The second is to calculate the dilution of precision (DOP) of the calculated UAV trajectory.

The DOP is a measure of the accuracy of any given GPS position data. Five diﬀerent types of 1 DOPs will be calculated: Geometric DOP, Position DOP, Horizontal DOP, Vertical DOP and time DOP. They are a function of the variances in x,y,z,t (clock bias) components: Vx , Vy , Vz & Vt .Geometric DOP is the error due to the geometric orientation of the satellites in space. Position DOP is the error in the 3D position of the UAV. Horizontal DOP is the error in the horizontal position of the UAV while Vertical DOP is the error in the altitude of the UAV. Time DOP is the error due to the time accuracy.

The lower the DOP values, the better the instantaneous position measurement of the UAV. A good GDOP or PDOP is considered to be <5 while values >10 for PDOP are very poor. HDOP is expected to be between 2-3. VDOP is expected to be higher than HDOP as a result of all the satellites being above the receiver whereas for the horizontal coordinates, data is received from all sides of the UAV.

GPS Positioning Problem

Suppose a receiver is located on a ﬂat 2D earth. Two GPS satellites can be used to pinpoint its location on earth, provided that if the range of the two satellites is represented by a circle there will be two intersections, of which only one will be located on earth. This is given no range error. Suppose there is a range error in GPS gps satellites, the intersection of the two range circles will now have shifted, resulting in an incorrect position estimation of the receiver on the earth.

This issue can be resolved by having a third GPS satellite resolve the location of the receiver. Provided that all GPS satellites have the same clock/range error, all three range circle will intersect at the receiver position. This can be used to calculate the clock bias, hence the range error. Similarly in 3D space, we need four satellites to pinpoint receiver location.

⛄ 部分代码

% Clear workspace, close all open figure & clear the command windowclear allclose all;clc;% Extract the data from the text file% Add other folders to pathaddpath('../data', '../lib/', '../lib/conversion');% Load constantsconstants();% Initialise Ground Station Position% Defining Sydney Ground Station Coordinateslat        = deg2rad(-34.76);long       = deg2rad(150.03);alt        = 680;pos_llh_gs = [lat;long;alt];% File Nameuav_data_fpath = 'UAVPosition_F1.txt';% Import pseudorange datapseudo_data = importdata('GPS_pseudorange_F1.txt');% Load ECEF position values of satellitesload ECEFPos%% Categorising time values% Vernal Equinox timeequinox_time = 7347737.336;% Store time datatimes     = pseudo_data(:,1) - equinox_time;% Obtain the unique time values% nTimes is an array containing the total number of occurences of single time% value% timeVal is an array containing all unique timevalues[total_occurences time_values] = hist(times(:),unique(times));% Cummulative Time Arraycummulative_times = cumsum(total_occurences);% Increment time values% timeVal = timeVal + 1;%% Observed UAV Positions% Obtain the polar coordinates of UAV w.r.t Ground Station[pos_UAV_Cart_obs,pos_UAV_Pol_Obs, pos_ECEF_gs, UAVVel, UAVPos] = UAVpolarCoor(time_values,...                                         cummulative_times, pseudo_data, ECEFPos, pos_llh_gs);%% Extract true UAV Position data from text files% % Obtain polar coordinates of true measurements[pos_UAV_Pol_True, pos_UAV_Cart_True] = extractUAVtrue(uav_data_fpath,equinox_time);%% Catalog the position of the satellites during UAV Tracking% Find satellite position w.r.t ground station[pos_Sat_Pol_Obs] = findSatPos(ECEFPos, pos_ECEF_gs, pos_llh_gs);%% Calculate the DOP for each time value% Calculate the best and worst satellite configurations according to DOP[bestSatConfig, worstSatConfig, DOP, maxDOPIndex, minDOPIndex] = findDOP(UAVVel, pos_Sat_Pol_Obs);%% Save relevant data as a structured array for plottingplotData.timeArray         = times;plotData.pos_UAV_Cart_obs  = pos_UAV_Cart_obs;plotData.pos_UAV_Pol_Obs   = pos_UAV_Pol_Obs;plotData.pos_ECEF_gs       = pos_ECEF_gs;plotData.UAVVel            = UAVVel;plotData.UAVPos            = UAVPos;plotData.pos_UAV_Pol_True  = pos_UAV_Pol_True;plotData.pos_UAV_Cart_True = pos_UAV_Cart_True;plotData.pos_Sat_Pol_Obs   = pos_Sat_Pol_Obs;plotData.bestSatConfig     = bestSatConfig;plotData.worstSatConfig    = worstSatConfig;plotData.DOP               = DOP;plotData.maxDOPIndex       = maxDOPIndex;plotData.minDOPIndex       = minDOPIndex;plotData.nTimes            = total_occurences;plotData.pseudo_data       = pseudo_data;plotData.cumArray          = cummulative_times;%% Plot graphsplotq1B(plotData)