GPS World, September 2013

Algorithms Methods INNOVATION This is reasonable if the antenna motion can be reasonably well predicted and this prediction is fed into the tracking loops as aiding information Then the prompt correlator output is given as 3 Again any noise contribution is not considered for the moment Here a t denotes the signal amplitude and d t a possibly present navigation data bit The carrier phase difference is given as 4 where ĳ t is the true carrier phase and is the NCO carrier phase used for correlation We now split the geometric line of sight distance into an absolute distance the satellite movement and a relative distance 5 For the example of the rotating antenna t 0 might be the epoch when the antenna is pointing in the north direction The term 0 t 0 is the conventional satellite to reference point distance for example to the rotation center and sat t 0 t accounts for the satellite movement during the beam forming interval The term ǻ μ t is the rotational movement and may depend on the parameter μ The parameter μ represents for the rotating antenna the absolute heading but may represent more complex motion parameters The absolute term 0 t 0 is constant but unknown in the beam forming interval We assume that approximate coordinates are available and thus ǻ μ t can be computed for a given set of μ that is the line of sight projection of the relative motion is assumed to be well predicted even with only approximate absolute coordinates The same applies also to sat t 0 t Lets assume that the NCOs are controlled in a way that the satellite movement is captured as well as the satellite clock drift and the atmospheric delays 6 Then 7 and 8 Thus the correlator output depends on the absolute distance of the reference point to the satellite at t 0 the relative motion of the antenna the receiver clock error the received amplitude and the broadcast navigation data bits Satellite movement and satellite clock drift are absent Let us now denote m as the index for the different satellites under consideration The index k denotes correlation values obtained during the beam forming interval at the epoch t k Then 9 I PXOWLSOH VLJQDO UHÀHFWLRQV DUH UHFHLYHG DQG LI WKH DUH denoted by the indices m 1 m 2 then the correlator output is the sum of those 10 For the following m or m 1 denotes the line of sight signal and m n with n 1 denoting multipath signals Estimation Principle It seems natural to choose receiver clock parameters dt rec and trajectory parameters μ in a way that they optimally represent the receiver correlation values This approach mimics the maximum likelihood principle The estimated parameters are FIGURE 5 Estimated relative user trajectory over 5 seconds outside the forest user walking horizontally FIGURE 6 Synthetic antenna aperture diagram for a walking user and beam forming interval of 2 seconds FIGURE 7 Estimated user trajectory with 02 1 and 2 seconds beamforming interval blue surveyed reference markers www gpsworld com September 2013 GPS World 45