Algorithm 1 Gradient descent-based sequential waveform inversion.
Input: {gm}, {sm}, c(0)
Output: ĉ
1:	k ← 0 {k is the number of algorithm iteration.}
2:	while stopping criterion is not satisfied do
3:	k ← k + 1
4:	J ← 0
5:	for m := 0 to M − 1 do
6:	${\mathbf{p}}_m^{\mathrm{a}}\leftarrow {\mathbf{H}}^{\mathrm{c}}{\mathbf{s}}_m$ {m is the index of the emitter.}
7:	${\mathbf{q}}_m^{\mathrm{a}}\leftarrow {\mathbf{H}}^{\mathrm{c}}{\mathit{\tau }}_m$ {τm is calculated via Eqn. (12).}
8:	J ← J + Jm {Jm is calculated via Eqn. (10).}
9:	end for
10:	J ← J + βJR
11:	Determine step size λ via a line search
12:	c(k) ← c(k−1) − λJ
13:	end while
14:	ĉ = c(k)