Assumung your XY data are smooth, you can find the normal vector at each point, and then offset in that direction, like the code below. If your position data is not smooth, then you'll need to smooth it before you differentiate and get the normals or otherwise you'll get a bunch of noise.
%%%%%%%%%%Step 0. Just making some random data... %%%%%%%%%%
% Position
rng(16);
x = interpft(3*rand(1,4),1000);
y = interpft(3*rand(1,4),1000);
x = x(1:200);
y = y(1:200);
% Measurement
m = 0.1*interp1(1:20,rand(1,20),linspace(1,20,200),'pchip');
% Plot it
subplot(211);
plot(x,y,'r','linewidth',2);
hold on;
plot(x(1),y(1),'rx','markersize',10);
title('XY position');
axis equal;
grid on;
subplot(212);
plot(m,'k','linewidth',2);
title('Measurement');
%%%%%%%%%%Step 1. Find the normal vectors %%%%%%%%%%
% First find the velocity using finite differences
dx = conv(x,[-0.5 0 0.5],'valid'); % Same as (x(3:end) - x(1:end-2)) / 2
dx = [dx(1) dx dx(end)]; % Take care of the endpoints
dy = conv(y,[-0.5 0 0.5],'valid');
dy = [dy(1) dy dy(end)];
% Normalize it to unit length
V = [dx; dy];
Vmag = sqrt(sum(V.^2)); % Magnitude of velocity
V1 = bsxfun(@rdivide, V, Vmag); % Velocity vector normalized to 1
% Swap the components to get the normals
N1 = [V1(2,:); -V1(1,:)];
subplot(211)
quiver(x,y,N1(1,:),N1(2,:),0.5);
%%%%%%%%%%Step 2. Shift the measurement to the new axes %%%%%%%%%%
m_shifted = [x;y] + bsxfun(@times,m,N1);
plot(m_shifted(1,:),m_shifted(2,:),'k','linewidth',2);
hold off;
legend({'XY Path', 'Start pt.', 'Normals', 'Measured'})
