[filter tracking] target tracking based on EKF, TDOA and frequency difference positioning with matlab code

1 Content introduction

Samsung TDOA passive location system mostly adopts the conversion of TDOA measurement value into distance difference based on elevation constraints

location , If the satellite moves relative to the radiation source , Then Doppler exists in the intercepted signal frequency of the same radiation source

frequency shift . Because the satellites are always in motion , The signals received by each observation station will produce different

What kind of Doppler shift , Thus, through multi satellite signal correlation , It is possible to obtain frequency difference information . Research in this chapter

The key point is after adding frequency difference information , What impact will it have on the positioning accuracy of Samsung TDOA positioning system ？ And for different time difference 、 The influence of frequency difference measurement error on positioning accuracy is compared and analyzed .​

1.1  Samsung TDOA positioning principle

TDOA location is one of the main location methods of Samsung passive location system . The emitter signal reaches different satellites   There are differences in the distance between the satellite observation stations , As a result, the arrival time of the signal at each observation station is different . Due to passive   The bit system works by passively receiving the emitter signal , It is usually difficult to directly observe the radiation source to the satellite   Distance of （ Or arrival time measurement ）. therefore , In Samsung passive location system , Often with radiation source signal   The time difference of arriving at different satellite observation stations is taken as the main observation , By observing the arrival time difference between stations   Locate the radiation source [50].  In 3D space , The same emitter signal arrives  2  Between satellite observation stations completely isolated in space   Arrival time difference , A half bilobal rotating hyperboloid with two observation stations as the focus can be determined . from  3  A satellite is true   Set the  2  A TDOA positioning curve is obtained by intersecting two rotating hyperboloids , Any point on the curve is radiation   Source location feasible solution . Because the radiation source to be located is usually located at a certain elevation on the earth's surface , Locate the curve by time difference   Intersect with the elevation constraint surface , The location of the radiation source can be uniquely determined . However , Samsung TDOA location usually exists   Vague questions , Instant difference positioning curve and elevation constraint surface usually exist  2  A point of intersection .

At a given position   Under the condition of checking information , The location of the radiation source can be uniquely determined , This is the principle of Samsung TDOA location . In practical application , For the arrival time of communication signal  TOA  Observation is difficult to obtain accurately . about   analog signal , Usually, the radiation signals arriving at each satellite observation station are used as a mutual ambiguity function , To extract  TDOA  Observation and measurement ; For radar signals , You can directly measure the rising edge time of the pulse as the signal arrival time .

1.2  Samsung frequency difference positioning principle

Due to the relative motion between the observation station and the target radiation source , Thus causing the signal received by the observation station

There is a difference between the signal frequency and the emission frequency of the radiation source , This difference is called Doppler shift . And for  2  Empty  

Isolated satellite observation stations , The Doppler frequency shift of the same emitter signal is also different , observation

There is also a Doppler frequency difference between stations . According to the frequency difference between satellite observation stations, an equal frequency can be determined

Difference surface , Using three observation stations, we can get  2  An equal frequency difference surface .2  The intersection of two equal frequency difference surfaces results in an equal

Frequency difference intersection , The radiation source is on the frequency difference curve . For earth surface targets , Using the earth model and so on

The frequency difference curve intersects , Thus, the Doppler frequency can locate the emitter .

2 Simulation code

<span style="color:#333333"><span style="background-color:rgba(0, 0, 0, 0.03)"><code><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span></code><code><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span>% TDOA location analysis     Can run  </code><code><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span></code><code>clear all;</code><code>clc;</code><code>c=<span style="color:#0e9ce5">3</span>e5;% The speed of light </code><code>w=<span style="color:#0e9ce5">10</span>;% error ns</code><code><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span> Aircraft distance </code><code>x=-<span style="color:#0e9ce5">200</span><span style="color:#dd1144">:</span><span style="color:#0e9ce5">2</span><span style="color:#dd1144">:</span><span style="color:#0e9ce5">200</span>;</code><code>y=-<span style="color:#0e9ce5">200</span><span style="color:#dd1144">:</span><span style="color:#0e9ce5">2</span><span style="color:#dd1144">:</span><span style="color:#0e9ce5">200</span>;</code><code>z=<span style="color:#0e9ce5">5</span>;</code><code><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span> Square type </code><code><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span> Loading stations <span style="color:#0e9ce5">1.1</span>（ Machine spacing ：<span style="color:#0e9ce5">15</span>km）</code><code>% x<span style="color:#0e9ce5">0</span>=[<span style="color:#0e9ce5">0</span>,<span style="color:#0e9ce5">15</span>,<span style="color:#0e9ce5">0</span>,<span style="color:#0e9ce5">15</span>]<span style="color:#dd1144">';</span></code><code>% y0=[0,15,15,0]';</code><code>% z<span style="color:#0e9ce5">0</span>=[<span style="color:#0e9ce5">1</span> ,<span style="color:#0e9ce5">0</span>.<span style="color:#0e9ce5">9</span>,<span style="color:#0e9ce5">0</span>.<span style="color:#0e9ce5">9</span> ,<span style="color:#0e9ce5">0</span>.<span style="color:#0e9ce5">9</span>]<span style="color:#dd1144">';</span></code><code>%%%%%%%%%%%%%%%%%%%%%%%%%1.2 （30km, The carrier layout is square ）</code><code>% x0=[0,30,0,30]';</code><code>% y<span style="color:#0e9ce5">0</span>=[<span style="color:#0e9ce5">0</span>,<span style="color:#0e9ce5">30</span>,<span style="color:#0e9ce5">30</span>,<span style="color:#0e9ce5">0</span>]<span style="color:#dd1144">';</span></code><code>% z0=[1 ,0.9,0.9 ,0.9]';</code><code><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span>Y type </code><code><span style="color:#dd1144">%%%</span><span style="color:#dd1144">%%%</span> Loading stations <span style="color:#0e9ce5">2.1</span>（<span style="color:#0e9ce5">15</span>km、 Lord Y middle ）</code><code>% x<span style="color:#0e9ce5">0</span>=[<span style="color:#0e9ce5">0</span>,<span style="color:#0e9ce5">13</span>,-<span style="color:#0e9ce5">13</span>,<span style="color:#0e9ce5">0</span>]<span style="color:#dd1144">';</span></code><code>% y0=[0,7.5,7.5,-15]';</code><code>% z<span style="color:#0e9ce5">0</span>=[<span style="color:#0e9ce5">1</span> ,<span style="color:#0e9ce5">0</span>.<span style="color:#0e9ce5">9</span>,<span style="color:#0e9ce5">0</span>.<span style="color:#0e9ce5">9</span> ,<span style="color:#0e9ce5">0</span>.<span style="color:#0e9ce5">9</span>]<span style="color:#dd1144">';</span></code><code>%%%%%% Loading stations 2.2（30km、 Lord Y middle ）</code><code>x0=[0,26,-26,0]';</code><code>y<span style="color:#0e9ce5">0</span>=[<span style="color:#0e9ce5">0</span>,<span style="color:#0e9ce5">15</span>,<span style="color:#0e9ce5">15</span>,-<span style="color:#0e9ce5">30</span>]<span style="color:#dd1144">';</span></code><code>z0=[1 ,0.9,0.9 ,0.9]';</code><code>dt=zeros(<span style="color:#0e9ce5">1</span>,<span style="color:#0e9ce5">3</span>);</code><code>dR=zeros(<span style="color:#0e9ce5">1</span>,<span style="color:#0e9ce5">3</span>);</code><code><span style="color:#ca7d37">for</span> n=<span style="color:#0e9ce5">1</span><span style="color:#dd1144">:</span><span style="color:#0e9ce5">3</span></code><code>    dR(n)=w*<span style="color:#0e9ce5">1</span>e-<span style="color:#0e9ce5">9</span>*c;      </code><code><span style="color:#ca7d37">end</span></code><code>dr2=dR.^<span style="color:#0e9ce5">2</span>;</code><code>Pn=diag([dr2(<span style="color:#0e9ce5">1</span>) dr2(<span style="color:#0e9ce5">2</span>) dr2(<span style="color:#0e9ce5">3</span>)]);</code><code><span style="color:#ca7d37">for</span> i=<span style="color:#0e9ce5">1</span><span style="color:#dd1144">:length</span>(x)</code><code>    <span style="color:#ca7d37">for</span> j=<span style="color:#0e9ce5">1</span><span style="color:#dd1144">:length</span>(y)</code><code>        <span style="color:#ca7d37">for</span> k=<span style="color:#0e9ce5">1</span><span style="color:#dd1144">:length</span>(z)</code><code>%         k=<span style="color:#0e9ce5">1</span>;</code><code>            r1=sqrt((x(i)-x<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">1</span>))^<span style="color:#0e9ce5">2</span>+(y(j)-y<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">1</span>))^<span style="color:#0e9ce5">2</span>+(z(k)-z<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">1</span>))^<span style="color:#0e9ce5">2</span>);</code><code>            r2=sqrt((x(i)-x<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">2</span>))^<span style="color:#0e9ce5">2</span>+(y(j)-y<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">2</span>))^<span style="color:#0e9ce5">2</span>+(z(k)-z<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">2</span>))^<span style="color:#0e9ce5">2</span>);</code><code>            r3=sqrt((x(i)-x<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">3</span>))^<span style="color:#0e9ce5">2</span>+(y(j)-y<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">3</span>))^<span style="color:#0e9ce5">2</span>+(z(k)-z<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">3</span>))^<span style="color:#0e9ce5">2</span>);</code><code>            r4=sqrt((x(i)-x<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">4</span>))^<span style="color:#0e9ce5">2</span>+(y(j)-y<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">4</span>))^<span style="color:#0e9ce5">2</span>+(z(k)-z<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">4</span>))^<span style="color:#0e9ce5">2</span>);</code><code>            R=[r1,r2,r3,r4];</code><code>​</code><code>            cx=[(x(i)-x<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">1</span>))/r1,(x(i)-x<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">2</span>))/r2,(x(i)-x<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">3</span>))/r3,(x(i)-x<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">4</span>))/r4];</code><code>            cy=[(y(j)-y<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">1</span>))/r1,(y(j)-y<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">2</span>))/r2,(y(j)-y<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">3</span>))/r3,(y(j)-y<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">4</span>))/r4];</code><code>            cz=[(z(k)-z<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">1</span>))/r1,(z(k)-z<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">2</span>))/r2,(z(k)-z<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">3</span>))/r3,(z(k)-z<span style="color:#0e9ce5">0</span>(<span style="color:#0e9ce5">4</span>))/r4];</code><code>            C=[cx(<span style="color:#0e9ce5">2</span>)-cx(<span style="color:#0e9ce5">1</span>),cy(<span style="color:#0e9ce5">2</span>)-cy(<span style="color:#0e9ce5">1</span>),cz(<span style="color:#0e9ce5">2</span>)-cz(<span style="color:#0e9ce5">1</span>);</code><code>               cx(<span style="color:#0e9ce5">3</span>)-cx(<span style="color:#0e9ce5">1</span>),cy(<span style="color:#0e9ce5">3</span>)-cy(<span style="color:#0e9ce5">1</span>),cz(<span style="color:#0e9ce5">3</span>)-cz(<span style="color:#0e9ce5">1</span>);</code><code>               cx(<span style="color:#0e9ce5">4</span>)-cx(<span style="color:#0e9ce5">1</span>),cy(<span style="color:#0e9ce5">4</span>)-cy(<span style="color:#0e9ce5">1</span>),cz(<span style="color:#0e9ce5">4</span>)-cz(<span style="color:#0e9ce5">1</span>)];</code><code>            B=inv(C.<span style="color:#dd1144">'*C)*C.'</span>;</code><code>            Pd=B*Pn*B.<span style="color:#dd1144">';</span></code><code>            Gxy(i,j)=abs(sqrt(Pd(1,1)+Pd(2,2)));</code><code>            Gz(i,j)=abs(Pd(3,3));</code><code>        end</code><code>    end</code><code>end</code><code>figure(1);  %GDOP</code><code>M=0.02:0.2:1.25;</code><code>fig=contour(x,y,Gxy,M);clabel(fig);</code><code>xlabel( 'x/km<span style="color:#dd1144">');</span></code><code>ylabel('y/km<span style="color:#dd1144">');</span></code><code>hold on;</code><code>grid on;</code><code>title('<span style="color:#0e9ce5">4</span> Station TDOA location GDOP(x,y) Figure simulation <span style="color:#dd1144">');</span></code><code>figure(2);  %GDOP</code><code>M=0.1:0.2:2.5;</code><code>fig1=contour(x,y,Gz,M);clabel(fig1);</code><code>xlabel( 'x/km<span style="color:#dd1144">');</span></code><code>ylabel('y/km<span style="color:#dd1144">');</span></code><code>hold on;</code><code>grid on;</code><code>title('<span style="color:#0e9ce5">4</span> Station TDOA location GDOP(z) Figure simulation <span style="color:#dd1144">');</span></code><code>​</code></span></span>

3 Running results

4 reference

[1] Zhu Guohui . Research on multi station passive location and tracking algorithm based on time difference and frequency difference . Diss. Xi'an University of Electronic Science and Technology .

[2] Zhang Yan . Research on joint target location and tracking algorithm of time difference and frequency difference of Samsung [D]. Xi'an University of Electronic Science and Technology .

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