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The LAV general formulation is

(2.32a)

subject to

(2.32b)

(2.32c)

Figure 2.3 depicts the objective function for LAV estimator in the case of one single error. The violet and green curves correspond to a high and low weighting factor ω_i, respectively. Note that the weighted measurement error y_i(x) = w_i ⋅ (h_i(x) − z_i) appears as ∣y_i(x)∣ in the objective function J(x ).

Figure 2.3 Objective function for the LAV estimator as a function of the error (one measurement).

For the sake of generality, problem (2.32) is formulated by considering weighted measurement errors (see (2.30)). Note that some references label this estimator as WLAV (weighted least absolute value).

The objective function (2.32a) comprises the absolute value of vector y(x). This function is nonlinear but can be linearized straightforwardly, resulting in the mathematical programming formulation in Section 2.5.2.2.