| # Navigation by range measurement Matrices > Linear Maps > Example
| Navigation by range measurement.
In the plane, we measure the distances of an object located at an unknown position from points with known coordinates , . The distance vector is a non-linear function of , given by Now assume that we have obtained the position of the object at a given time, and seek to predict the change in position that is consistent with observed small changes in the distance vector . We can approximate the non-linear functions via the first-order (linear) approximation. A linearized model around a given point is , with a matrix with elements