Method for resolving sub-carrier ambiguities of a number of tracking channels of a navigation signal
A method for resolving sub-carrier ambiguities of a total number of tracking channels of a binary offset carrier (BOC) navigation signal is provided. For a simultaneously considered subset of at least four tracking channels, a set of sub-carrier candidate ambiguities is determined based on the sub-carrier modulation. Position and receiver clock error are calculated for each possible combination of sub-carrier ambiguities. Predicted delays are calculated based on each calculated position and receiver clock error. Differences between the predicted delays and the delay candidates originating from each specific combination of subcarrier ambiguities are calculated. A residual is calculated based on the differences and the set of sub-carrier ambiguities and the corresponding position and receiver clock error leading to the smallest residual are selected.
1. A method for resolving sub-carrier ambiguities of a total number of tracking channels of a binary offset carrier (BOC) navigation signal comprising a carrier modulated by a code modulation function of a given code rate and further modulated by a sub-carrier modulation function of a given sub-carrier rate, for each channel comprising:
generating a first estimate τ of delay based on the code modulation;
generating a second estimate τ* of delay based on the sub-carrier modulation,
wherein for a simultaneously considered subset of at least four tracking channels, the method further comprises
determining a set of sub-carrier candidate ambiguities N i,k based on the sub-carrier modulation by processing the first and the second estimate of delay by calculating
N
i
,
k
=
round
(
τ
i
-
τ
i
*
T
s
)
+
k
·
T
s
with i being a channel, k being the ambiguities, and T s being a sub-carrier chip duration;
calculating, for each possible combination of the sub-carrier candidate ambiguities, position error and receiver clock error;
calculating predicted delays based on each of the calculated position error and receiver clock error;
calculating differences between the predicted delays and delay candidates, wherein each of the delay candidates is based on a sub-carrier candidate ambiguity, of the set of sub-carrier candidate ambiguities, for a respective tracking channel;
calculating a residual for a specific combination of sub-carrier ambiguities based on the calculated differences by squaring and summing the differences between the predicted delays and the delay candidates, providing the residual for the specific combination of sub-carrier ambiguities;
selecting a set of sub-carrier ambiguities and corresponding position error and receiver clock error leading to the smallest residual; and
determining a position of a GNSS receiver corresponding to the position error and receiver clock error.
2. The method according to claim 1 , wherein k i residuals are calculated with k being the number of ambiguities and i being the number of channels.
3. The method according to claim 1 , wherein the subset of considered tracking channels comprises a good geometric dilution of precision (GDOP).
4. The method according to claim 3 , wherein predicted delays are calculated using the calculated position error and receiver clock error for remaining channels.
5. The method according to claim 4 , wherein sub-carrier ambiguities for the remaining channels are obtained using the calculated predicted delays for the remaining tracking channels.
6. The method according to claim 5 , wherein the sub-carrier ambiguities for the remaining channels are obtained by:
N
i
=
round
(
τ
^
i
-
τ
i
*
T
S
)
.
7. The method according to claim 5 , wherein the sub-carrier ambiguities for the remaining channels are obtained using Real Time Kinematic-technology for carrier phase ambiguity fixing.
8. The method according to claim 1 , wherein all tracking channels a considered simultaneously.