Abstract: In a general aspect, a target is localized based on measurements from a measurement device array. In some aspects, range difference values (di) and coordinate vectors (ai) of devices in the measurement device array are obtained. The range difference values are generated based on time difference of arrival measurements of wireless signals between the target device and each of the devices in the measurement device array. A first matrix (A) and a first vector (b) are constructed. The first matrix (A) and the first vector (b) each includes the range difference values and the coordinate vectors. Whether a second vector (y) satisfies a condition set is determined. The condition set includes a first condition (ATA+?D)y=ATb and a second condition vT (ATA+?D)v?0. A numerical approximation of an optimal solution of the second vector is generated. The target device is localized according to the numerical approximation of the optimal solution.

Abstract: In a general aspect, a target is localized based on measurements from a measurement device array. In some aspects, range difference values (di) and coordinate vectors (ai) of devices in the measurement device array are obtained. The range difference values are generated based on time difference of arrival measurements of wireless signals between the target device and each of the devices in the measurement device array. A first matrix (A) and a first vector (b) are constructed. The first matrix (A) and the first vector (b) each includes the range difference values and the coordinate vectors. Whether a second vector (y) satisfies a condition set is determined. The condition set includes a first condition (ATA+?D)y=ATb and a second condition vT (ATA+?D)v?0. A numerical approximation of an optimal solution of the second vector is generated.