Algorithm 1: Compressive sensing-based target localization via energy-level jumping algorithm
	Input: A measurement matrix P, a measurement vector y, an error threshold $\delta$.
	Initialize: An initial point $x_0=P^{+}y$, an iterative index l.
	while Stopping criterion not met do
	1: Apply IRLS to reconstruct a locally optimal sparse solution $x_l^{*}$.
	2: Let $x_l^{*}$ jump to $u_l^0$ by absorbing the energy ${\epsilon }_l$.
	3: Apply the modified Euler’s forecast-Newton correction homotopy method to construct a homotopy curve between $u_l^0$ and $u_l^{*}$.
	4: Update $x_0=u_l^{*}$ and apply IRLS to find a sparser solution $x_{l+1}^{*}$.
	5: Increase iterative index l.
	end while if $|E^{\left(p\right)}\left(x_{l+1}^{*}\right)-E^{\left(p\right)}\left(x_l^{*}\right)|<\delta$.
	Output:
	1: The globally optimal sparse solution $x_g^{*}=x_{l+1}^{*}$.
	2: The grid locations of targets
	$id=\left\{i\right|x_g^{*}\left(i\right)\ne 0,i=1,\cdots ,n\}.$