Applications of Kalman filter in WAAS

d_ion = a_f I         (2)

where I is the integrated electron density along the propagation path.

a_f = 40.3/ f² , f is the frequency of the signal

We can group the frequency-dependent and the non-dispersive terms separately in equations (1) . Grouping the non-dispersive terms together we get:

pⁱ_j = rⁱ_j + c(dtⁱ–dt_j) + dⁱ_{trop j}         (3)

Now eqn(1) can be written as:

Lⁱ_kj = pⁱ_j - a_kIⁱ_j-l_kbⁱ_kj
Pⁱ_kj = pⁱ_j + a_kIⁱ_j+qⁱ_kj         (4)

where a_k ºa_fk and qⁱ_kj = dq_kj+dqⁱ_k includes both the receiver and satellite instrumental group delay biases for each pair station j and satellite i.

However, in this system, the number of unknowns is greater than the number of equations. So we distribute the effect of instrumental delays among other terms defining other variables as:

The term I_jⁱ is called as the biased ionospheric term and it contains information about the ionospheric delay I_jⁱ and the receiver and satellite differential group delay biases k_j, kⁱ .

The cycle-slip detection and estimation of the modified initialization constant terms b_kjⁱ is made using the P code pseudorange measurements as discussed in Blewitt [1990]. Thus, after the removal of ambiguities, we will only consider the more precise carrier phase observables, with the ambiguities removed.



Now, the next step is the separation of the contribution _of the ionospheric delay I_jⁱ and that of the differential instrumental biases k_j and k_i in I_jⁱ .

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