GNSS error sources and satellite geometry

Which errors can affect a satellite measurement?

The same displayed position can contain several physical error contributions.

Propagation and signal errors

Ionospheric delay depends on electron content and frequency; suitable multi-frequency measurements can estimate much of it. Tropospheric delay comes from the neutral atmosphere and needs different modelling. Satellite clock and orbit errors affect predicted transmission time and position. Multipath adds reflected copies of a signal, disturbing the measurement at the receiver.

These effects need not be constant or equal for every satellite. Common-mode receiver clock bias is only one unknown; solving it does not remove every measurement error. The laboratory lets you vary a common bias separately from a differential range error so the distinction is visible.

Independence and error budgets

Independent random errors are often combined statistically in an appropriate model; systematic biases cannot simply be assumed to cancel. A synthetic user-equivalent range-error value can support a sensitivity calculation, but it is not a certified bound. The lesson’s numbers demonstrate mechanisms rather than predicting a particular receiver’s operational performance.

Separate a bias from random scatter

For a supplied statistical exercise, two independent zero-mean range-error contributions have standard deviations of 3 m and 4 m. Their combined standard deviation is √(3² + 4²) = 5 m, not 7 m. This root-sum-square calculation relies on the independence and statistical assumptions; it is not automatically an appropriate way to combine unknown systematic errors.

Now add a constant +10 m bias to one satellite measurement. Repeating measurements may reduce uncertainty about random scatter but will not average that fixed bias to zero. A receiver must model, monitor, correct or exclude unsuitable measurements according to its design. Multipath can be correlated with the local environment, making simple independent-error assumptions particularly questionable. State the assumptions before using a tidy error-budget formula to justify confidence in the resulting position.

Why can the same range error produce different position errors?

Geometry determines how the constraints intersect.

Dilution of precision

Widely spread satellites generally constrain position more effectively than satellites clustered in a small part of the sky. Dilution of precision summarises geometric amplification under the model’s assumptions. HDOP concerns horizontal position, VDOP vertical position, and PDOP three-dimensional position. The values are not measured errors by themselves.

A rough illustrative relation is position standard deviation ≈ DOP × range-error standard deviation, when the statistical model and units match. With range error 4 m, a DOP of 1.5 yields 6 m; DOP 5 yields 20 m. This is an uncertainty illustration, not an integrity protection level or guaranteed maximum error.

Count is not geometry

Six clustered satellites can give poorer geometry than a well-spread set. Losing one well-placed satellite can degrade a solution more than losing one redundant member of a cluster. The laboratory’s two-dimensional constraints use their crossing angle as a transparent geometry proxy; it labels the result as an analogy rather than calculating real constellation DOP.

Do not turn a standard deviation into a guarantee

With a supplied 4 m range-error standard deviation, changing the illustrative geometry factor from 1.5 to 5 raises the approximate position standard deviation from 6 m to 20 m. The measurement noise has not worsened. The spatial arrangement makes it harder to determine the weakly constrained coordinate from those same observations.

Neither 6 m nor 20 m is a guaranteed maximum error. Statistical distributions can have tails, measurement assumptions can fail, and integrity threats require separate treatment. A protection-level algorithm must account for its specified fault hypotheses and integrity risk. Keep three questions separate: what measurement quality is assumed, how geometry amplifies it, and whether the system can bound and warn about misleading information for the intended operation. The laboratory answers only the transparent geometry question.

Can you explain and apply the mechanism?

Four original questions. Work from the stated facts, then compare your reasoning with the explanation.