Is it still data reconciliation?

The classic definition of the data reconciliation problem for the mass balance is:
minimizing J(y_hat) = (y-y_hat)^T * V^(-1) * (y-y_hat)
subject to A*y_hat = 0
where A is the incidence matrix containing the mass balance constraints, V - variance matrix, y - flow measurements vector, y_hat - reconciled flows vector

I'm wondering if a slightly changed approach where constraints are exchanged with minimization function as described below is still the correct data reconciliation?
minimizing J(y_hat) = (A*y_hat)^T * (A*y_hat)
subject to |y-y_hat| <= measurement uncertainty

I'm definitely loosing the information about standard deviations (no variance matrix) of the measurements but simultaneously I'm forcing in the constraint that the adjustment must fall into the measurement uncertainty. Also, I do not guarantee that the adjustments are as small as possible but still are within limits of measurement uncertainty which has sense. I see some advantages of such an approach: the uncertainty of the measurement is directly addressed (contrary to classic data reconciliation) and bias of measurements can be easily determined: if J is high and the adjustments are equal to uncertainty it means that algorithm cannot find the mass balance fulfiling all conditions and probably some measurements are faulty.

Am I reinventing the wheel? Does it have sense?