The following is claimed:

1. A method for operating a satellite navigation receiver, the method comprising:

receiving one or more satellite signals;

measuring a carrier phase of the received satellite signals;

receiving a real-time kinematic (RTK) signal encoded with RTK correction data;

determining, by a real-time kinematic (RTK) position estimator, a real-time kinematic position based on the measured carrier phase of the received satellite signals and the received RTK correction data in an RTK correction mode;

receiving a precise signal encoded with precise correction data;

determining, by a precise positioning estimator, a precise position based on the measured carrier phase of the received satellite signals and the received precise correction data in a precise correction mode;

determining a reference frame bias or offset vector between the precise position and the RTK position for the same measurement time or epoch; and

upon loss, interruption or corruption of the RTK signal, switching a mobile receiver to a relative position mode based a last available RTK position, wherein the next position estimate is compensated by an offset vector or reference frame bias to avoid a jump or discontinuity in the next position estimate;

detecting a cycle slip in the tracking of the received carrier signal in the relative position mode; and

supporting a relative position estimation framework that allows relative navigation over a time interval exceeding multiple epochs or an arbitrarily long time interval by establishing a series of chained relative position vectors from a next initial position that is established or coextensive with a last known relative position of the relative position estimator prior to detection of the cycle slip.

2. The method according to claim 1 wherein determining the reference frame bias comprises estimating the bias in the mobile receiver by monitoring the difference between the RTK and precise position solutions (expressed in position or carrier phase) when both are available and when the precise position solution has converged.

3. The method according to claim 1 wherein the determining the reference frame bias comprises:

estimating the bias observed via an RTK reference station by its monitoring a difference between the RTK and precise position solutions at an RTK reference station while operating in the RTK mode; and further comprises:

transmitting the reference frame bias to the mobile receiver.

4. The method according to claim 1 wherein the determining of the reference frame bias is determined in accordance with the following equation:

b = XRTK.t - Xref.t. where

^{x}RTK,t is ^{tne} RTK position estimate of an antenna of the mobile receiver at measurement time t;

x_{re}f,t is the relative position estimate or precise position estimate of the antenna of the mobile receiver at measurement time t;

and b is the reference frame bias.

5. The method according to claim 1 wherein the determining of the reference frame bias is determined based on computing relative position based on a prior last available RTK position and a relative position update to a prior last available RTK position solution if the PPP solution has not converged or if the reference frame bias has not been estimated within a certain maximum time period that is greater than a threshold time period.

6. The method according to claim 1 wherein a relative position is determined based on computing relative position based on the a prior last available RTK position and a relative position update to the prior last available RTK position in accordance with the following equation:

^{x}RTKX,t ^{= x}RTK,tO + A^{x}t,tO

^{x}RTKx,t is a virtual RTK position estimate, by the relative position estimator, of an antenna of the mobile receiver at time t after loss of the RTK correction signal;

^{x}RTK,to is the RTK position estimate of an antenna of the mobile receiver at time to or a last available RTK position in the RTK mode that is used to initialize the relative position estimator; and

Ax_{tit0} represents the change in position from time to to time t.

7. The method according to claim 1 wherein the determining of the reference frame bias is determined based on computing the relative position with respect to a prior last available RTK position as an initial position for the mobile receiver in the relative position mode, and a relative position update to the prior last available RTK position until the reference frame bias can be determined based on estimating the bias in the mobile receiver in the RTK mode by monitoring the difference between the RTK and PPP solutions when both are available.

8. The method according to claim 1 wherein the determining the reference frame bias between the PPP reference frame and the RTK reference frame further comprises filtering position differences between an RTK position determined by the RTK estimator and a relative position estimate determined by the PPP estimator to transition from a relative reference frame bias based on prior last available RTK position and a relative position estimate to a reference frame bias based on the bias in the mobile receiver in the RTK mode by monitoring the difference between the RTK and PPP solutions when both are available.

9. The method according to claim 8 wherein the filtering is based on the following difference: ^{x}RTK,t - Xref,t> ^{where}

^{ x}RTK,t is ^{tne} RTK position estimate of an antenna of the mobile receiver at time t; and x_{re}f_{it} is the position along the reference trajectory at time t.

10. The method according to claim 8 wherein the filtering is based on using a learned reference frame bias from the relative position estimator or loaded from data storage of the receiver data processing system in the case it was previously calculated, wherein the learned reference frame bias is determined in accordance with the following equation:

b « XRTK.to ^{~~ x}ref,to ^{~~ x}bias,to . where

^{x}RTK,to is ^{tne} RTK position estimate, by the RTK position estimator, of an antenna of the mobile receiver at time tO;

x_{re}f_{,t} is the relative position estimate or PPP estimate, by the relative positon estimator, of the antenna of the mobile receiver at time t;

Xbias.to is the initial position bias, expressed in position, of the antenna of the mobile receiver at tO;

and b is the reference frame bias.

1 1. The method according to claim 1 such that the mobile receiver can operate in the relative position mode indefinitely after loss of the RTK correction mode without material degradation of accuracy.

12. The method according to claim 1 further comprising:

estimating and accumulating time-varying tropospheric bias associated with the chained relative position vectors across one or more cycle slips.

13. A mobile receiver comprising:

a relative position estimator for determining an estimated relative position based on time-differenced phase measurements by the mobile receiver in the relative position mode;

a real-time kinematic (RTK) position estimator for determining an RTK position in an RTK mode based on correction data received by a wireless device via an RTK correction signal; a reference frame compensator for determining a reference frame bias between precise point positioning (PPP) reference frame and an RTK reference frame, where the PPP reference frame is associated with relative position estimates generated by the relative position estimator and where the RTK reference frame is associated RTK position estimates generated by the RTK position estimator;

upon loss of the RTK correction signal, a controller for switching to a relative position mode based a last available RTK position;

the reference frame compensator offsetting the estimated relative position in the relative position mode by the determined reference frame bias to avoid a jump or discontinuity in the relative position estimates;

a cycle slip detector for detecting a cycle slip in the tracking of the received carrier signal in the relative position mode; and

a continuity module for supporting a relative position estimation framework that allows relative navigation over a time interval exceeding multiple epochs or an arbitrarily long time interval by establishing a series of chained relative position vectors from a next initial position that is established or coextensive with a last known relative position of the relative position estimator prior to detection of the cycle slip.

14. The receiver according to claim 13 wherein the reference frame compensator bias estimates the reference frame bias in the mobile receiver in the RTK mode by monitoring the

difference between the RTK and PPP solutions (expressed in position or carrier phase) when both are available.

15. The receiver according to claim 13 wherein the reference frame compensator determines the reference frame bias in accordance with the following equation:

b = XRTK.t - Xref.t. where

^{x}RTK,t is ^{tne} RTK position estimate of an antenna of the mobile receiver at time t;

x_{re}f,t is the relative position estimate or PPP estimate of the antenna of the mobile receiver at time t;

and b is the reference frame bias.

16. The receiver according to claim 13 wherein a relative position estimator determines is the relative position based on the a prior last available RTK position and a relative position update to the prior last available RTK position in accordance with the following equation:

^{x}RTKX,t ^{= x}RTK,tO + A^{x}t,tO

^{x}RTKx,t is a virtual RTK position estimate, by the relative position estimator, of an antenna of the mobile receiver at time t after loss of the RTK correction signal;

^{x}RTK,to is the RTK position estimate of an antenna of the mobile receiver at time to or a last available RTK position in the RTK mode that is used to initialize the relative position estimator; and

Ax_{tit0} represents the change in position from time to to time t.

17. The receiver according to claim 13 wherein the reference frame compensator determines reference frame bias based on computing the relative position with respect to a prior last available RTK position as an initial position for the mobile receiver in the relative position mode, and a relative position update to the prior last available RTK position until the reference frame bias can be determined based on estimating the bias in the mobile receiver in the RTK mode by monitoring the difference between the RTK and PPP solutions when both are available.

18. The receiver according to claim 13 wherein reference frame compensator comprises a filter for filtering position differences between an RTK position determined by the RTK estimator and a relative position estimate determined by the PPP estimator to transition from a relative

reference frame bias based on prior last available RTK position and a relative position estimate to a reference frame bias based on the bias in the mobile receiver in the RTK mode by monitoring the difference between the RTK and PPP solutions when both are available.

19. The receiver according to claim 18 wherein the reference frame compensator filters in accordance with the following difference:

^{x}RTK,t - Xref,t> ^{where}

^{ x}RTK,t is ^{tne} RTK position estimate of an antenna of the mobile receiver at time t; and x_{re}f_{it} is the position along the reference trajectory at time t.

20. The receiver according to claim 18 wherein reference frame compensator filters based on using a learned reference frame bias from the relative position estimator or loaded from data storage of the receiver data processing system in the case it was previously calculated, wherein the learned reference frame bias is determined in accordance with the following equation:

b « XRTK.to ^{~~ x}ref,to ^{~~ x}bias,to . where

^{x}RTK,to is ^{tne} RTK position estimate, by the RTK position estimator, of an antenna of the mobile receiver at time tO;

x_{re}f_{,t} is the relative position estimate or PPP estimate, by the relative positon estimator, of the antenna of the mobile receiver at time t;

Xbias.to is the initial position bias, expressed in position, of the antenna of the mobile receiver at tO;

and b is the reference frame bias.

21. The receiver according to claim 13 further comprising:

an atmospheric bias estimator for estimating and accumulating time-varying tropospheric bias associated with the chained relative position vectors across one or more cycle slips, the atmospheric bias estimator associated with the relative position estimator.