Home > src > demos > eimm_demo > bot_dh_dx.m

# bot_dh_dx

## PURPOSE

Jacobian of the measurement model function in BOT demo.

## SYNOPSIS

function dY = bot_dh_dx(x,s)

## DESCRIPTION

``` Jacobian of the measurement model function in BOT demo.

dh_dx = -(y-sy) / (x-sx)^2 * 1 / (1 + (y-sy)^2 / (x-sx)^2)
= -(y-sy) / ((x-sx)^2 + (y-sy)^2)
dh_dy = 1 / (x-sx) * 1 / (1 + (y-sy)^2 / (x-sx)^2)
= (x-sx) / ((x-sx)^2 + (y-sy)^2)```

## CROSS-REFERENCE INFORMATION

This function calls:
This function is called by:
• botm_demo EIMM_DEMO2 Bearings Only Tracking of a Manouvering Target demonstration

## SOURCE CODE

```0001 % Jacobian of the measurement model function in BOT demo.
0002 %
0003 %  dh_dx = -(y-sy) / (x-sx)^2 * 1 / (1 + (y-sy)^2 / (x-sx)^2)
0004 %        = -(y-sy) / ((x-sx)^2 + (y-sy)^2)
0005 %  dh_dy = 1 / (x-sx) * 1 / (1 + (y-sy)^2 / (x-sx)^2)
0006 %        = (x-sx) / ((x-sx)^2 + (y-sy)^2)
0007 %
0008
0009 % Copyright (C) 2003 Simo S�kk�%
0011 % Licence (version 2 or later); please refer to the file
0012 % Licence.txt, included with the software, for details.
0013
0014 function dY = bot_dh_dx(x,s)
0015   % Reserve space for the Jacobian.
0016   dY = zeros(size(s,2),size(x,1));
0017
0018   % Loop through sensors
0019   for i=1:size(s,2)
0020     dh = [-(x(2)-s(2,i)) / ((x(1)-s(1,i))^2 + (x(2)-s(2,i))^2);...
0021        (x(1)-s(1,i)) / ((x(1)-s(1,i))^2 + (x(2)-s(2,i))^2);...
0022       zeros(size(x,1)-2,1)]';
0023     dY(i,:) = dh;
0024   end
0025```

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