To get a feeling for how well we can estimate the location of the stationary receiver in the presence of noisy range measurements from both satellites, the simulation of Listing 11.1 was slightly modified to account for the fact that the range measurements might not be perfect. The resultant simulation with the noisy range measurements appears in Listing 11.2. We can see from the listing that zero-mean, Guassian noise with a standard deviation 300 ft was added to each range measurement every second (i.e., T _s = 1). The formulas of the preceding section were used to estimate the receiver location from the noisy measurements, as shown in Listing 11.2. Changes to the original simulation of Listing 11.1 to account for the noisy range measurements are highlighted in bold in Listing 11.2.

The nominal case of Listing 11.2 was run. Figures 11.2 and 11.3 compare the actual and estimated downrange and altitude receiver locations based on the noisy range measurements. We can see that a 300-ft 1 ? noise error on range yields extremely large downrange location errors for this particular geometry. In this example the error in estimating the downrange location of the receiver was often in excess of 50,000 ft, whereas the error in estimating the altitude of the receiver was often in excess of 300 ft. The reason for the large downrange location errors is caused by poor geometry. In this example the initial angle between the two range vectors is only...