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⛄ 内容介绍
随着科技的发展,雷达对目标跟踪的精确度要求越来越高.但在实际应用中,系统所处的环境会受到各种各样的干扰,此时,卡尔曼滤波器凭借其优良的噪声处理能力而被应用到各种领域,是现阶段雷达跟踪中最常用的算法.文章在卡尔曼滤波算法的基础上,就如何将其应用于雷达目标跟踪系统的问题进行了研究与仿真;分析了卡尔曼滤波与常增益滤波的适用范围及优缺点;给出了极坐标系下卡尔曼滤波的计算及过程噪声方差的获取方法;最后以目标仿真结果证明了估计的有效性.
⛄ 部分代码
function [tem,tam] = helperPassiveRangingErrorMetrics(ownship,isMSC)
% This is a helper function for passive ranging example using a single sensor
% and may be removed in a future release without notice.
% Copyright 2018 The MathWorks, Inc.
tem = trackErrorMetrics;
tem.ErrorFunctionFormat = 'custom';
% The ownship is a handle object and refers to the same object as does
% scenario. This helps the function to calculate metrics, which are a
% function of ownship.
if ~isMSC
tem.EstimationErrorFcn = @(track,truth)rangeAndRateErrorCart(track,truth,ownship);
else
tem.EstimationErrorFcn = @(track,truth)rangeAndRateErrorMSC(track,truth,ownship);
end
tem.EstimationErrorLabels = {'deltaR','deltaRSigmaP','deltaRSigmaM','deltaRR','deltaRRSigmaP','deltaRRSigmaM'};
tam = trackAssignmentMetrics;
tam.DistanceFunctionFormat = 'custom';
tam.AssignmentDistanceFcn = @assignmentByAttribute;
end
function [rError, rSigmaPlusError, rSigmaMinusError, ...
rrError,rrSigmaPlusError,rrSigmaMinusError] = rangeAndRateErrorCart(track,truth,ownship)
% sigma values
sigmaValues = [0 -1 1];
n = numel(track.State); % State-size.
trackStateSigmas = track.State + chol(track.StateCovariance)*repmat(sigmaValues,[n 1]);
trackPos = trackStateSigmas(1:2:end,:);
trackVel = trackStateSigmas(2:2:end,:);
% truth
truthPos = truth.Position(:);
truthVel = truth.Velocity(:);
ownPose = pose(ownship);
% Error in range
rAct = norm(truthPos - ownPose.Position(:));
rEst = sqrt(dot(trackPos - ownPose.Position(:),trackPos - ownPose.Position(:),1));
rError = rEst(1) - rAct;
rSigmaMinusError = rEst(2) - rAct;
rSigmaPlusError = rEst(3) - rAct;
% Error in range-rate
rTruth = truthPos - ownPose.Position(:);
rrTruth = dot(truthVel - ownPose.Velocity(:),rTruth)/rAct;
rTracks = trackPos - ownPose.Position(:);
vTracks = trackVel - ownPose.Velocity(:);
rrTracks = dot(vTracks,rTracks,1);
rrError = rrTracks(1)/rEst(1) - rrTruth;
rrSigmaMinusError = rrTracks(2)/rEst(2) - rrTruth;
rrSigmaPlusError = rrTracks(3)/rEst(3) - rrTruth;
end
function [rError, rSigmaPlusError, rSigmaMinusError, ...
rrError,rrSigmaPlusError,rrSigmaMinusError] = rangeAndRateErrorMSC(track,truth,ownship)
% range is available as 5th state and range-rate is a function of 6th
% state.
[rAct,rrAct] = trueRangeAndRate(truth,ownship);
% 1 std-dev of states.
deltainvR = sqrt(track.StateCovariance(5,5));
deltadRByR = sqrt(track.StateCovariance(6,6));
% Range and range-rate estimate
range = 1/track.State(5);
rangeRate = track.State(6)/track.State(5);
% Convert 1 std-dev of state to 1 std-dev of range and range-rate using
% linearization
deltaStateValues = [0 -deltainvR deltainvR;0 -deltadRByR deltadRByR];
H = [-range^2 0;-rangeRate*range range];
deltaRandRR = H*deltaStateValues;
deltaR = deltaRandRR(1,:);
deltaRR = deltaRandRR(2,:);
% Formulate outputs
rError = range - rAct;
rSigmaPlusError = range + deltaR(3) - rAct;
rSigmaMinusError = range + deltaR(2) - rAct;
rrError = rangeRate - rrAct;
rrSigmaPlusError = rangeRate + deltaRR(3) - rrAct;
rrSigmaMinusError = rangeRate + deltaRR(2) - rrAct;
end
function [range,rangeRate] = trueRangeAndRate(truth,ownship)
ownPose = pose(ownship);
r = truth.Position(:) - ownPose.Position(:);
range = norm(r);
v = truth.Velocity(:) - ownPose.Velocity(:);
rangeRate = dot(v,r)/range;
end
function distance = assignmentByAttribute(track,truth)
trackOriginationID = track.ObjectAttributes.TargetIndex;
if trackOriginationID == truth.PlatformID
distance = 0;
else
distance = inf;
end
end
⛄ 运行结果
⛄ 参考文献
[1]陶洪久, 高俊, 吴巍. 基于卡尔曼滤波的多目标检测与跟踪[C]// 全球化制造高级论坛暨21世纪仿真技术研讨会. 2004.
