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Transmitter positions x₁, y₁, x₂, y₂ are known; the transmitter locations are typically provided by the GNSS satellites or known to be at a fixed surveyed location for a terrestrial source. Signal travel times ΔT₁, ΔT₂ are measured by the system. Initially, the user positions are assumed. Set position coordinates X, Y equal to their initial estimates:

Compute the range errors:

(2.15)

(2.16)

Compute the θ angle (see Figure 2.3):

(2.17)

Compute update to user position:

(2.18)

(2.19)

Compute a new estimate of position using the update:

(2.20)

Continue to compute θ, ΔR₁, and ΔR₂ from these equations with new values of . Iterate Eqs. (2.15)–(2.20) and stop when Δx and Δy become less than the desired accuracy: