Localization via Range Measurement: proof of intermediate resultLocalization > Outer Sphere Approximations > Proof
In the localization via range measurement problem, the application of Lagrange duality leads to the function of ![]() We can express the function The objective function of the maximization problem defining ![]() where for notational convenience we use the matrix The above immediately implies that the maximum in the definition of ![]() Assume that the first constraint holds. When this constraint is in place, computing ![]() Plugging that value of ![]() Assume now that the second constraint holds: ![]() |