Method and apparatus of GNSS receiver heading determination

A GNSS receiver apparatus :

• a processor configured to perform the following operations:
• (A) generating a primary estimate of an absolute value of a velocity vector using current estimates of velocity vector projections;
• (B) generating an extrapolated absolute value of the velocity vector using previous estimates of the absolute value of the velocity vector obtained at step (A);
• (C) generating a primary estimate of a velocity vector orientation angle determined in a range of either [0 . . . 2π] or [−π . . . +π] using current estimates of velocity vector projections;
• (D) generating a variance estimate of the primary estimate of the velocity vector orientation angle as follows:
• (i) if the primary estimate of the absolute value of the velocity vector at step (A) is smaller than a preset minimum value, a variance estimate of the primary velocity vector orientation angle equals a preset maximum value, and
• (ii) otherwise, a variance estimate of the primary estimate of the velocity vector orientation angle calculated as a ratio of a preset variance estimate of the velocity vector's absolute value to a square of primary estimate of velocity vector's absolute value generated at step (A);
• (E) if the extrapolated estimate of the absolute value of the velocity vector generated at step (B) is greater than a preset minimum value, then performing step (G), otherwise, performing step (F);
• (F) setting a next smoothed estimate of the velocity vector orientation angle equal to its previous value;
• and
• (G) generating a smoothed estimate of the velocity vector orientation angle based on non-linear recurrent filtering of the primary estimate of the orientation angle obtained at step (C), wherein filter parameters, at every clock cycle, are based on the variance estimate from step (D).

A method of determining a heading of a GNSS receiver comprising, at each clock cycle n:

• (A) using a processor, generating primary estimates of a velocity vector's vn absolute value using current estimates of velocity vector projections VE and VN , as follows:
• V=√{square root over (VE2+VN2)};
• (B) generating an extrapolated velocity vector's absolute value V pred using Vn from step (A) from a second previous, or earlier, clock cycle;
• (C) generating a primary estimate of a velocity vector orientation angle Θ as follows:
• Θ
• =
• arctg
• ⁡
• (
• V
• E
• V
• N
• )
• ,
• where Θ is in a range [0. . .2π];
• (D) generating a variance estimate σΘ2 of Θ as follows:
• σ
• Θ
• 2
• =
• {
• σ
• Θ
• ⁢
• ⁢
• MAX
• 2
• if
• ⁢
• ⁢
• 〈
• V
• n
• <
• V
• min
• 〉
• σ
• V
• 2
• V
• n
• 2
• if
• ⁢
• ⁢
• 〈
• V
• n
• ≥
• V
• min
• 〉
• ,
• where σΘMAX2, σV2, Vmin are preset values, and Vn is obtained at step (A);
• (E) if Vpred>Vmin, then performing step (G), otherwise performing step (F), using Vpred;
• (F) setting a next smoothed estimate of the velocity vector orientation angle {tilde over (Θ)}n equal to its previous value {tilde over (Θ)}n-1:
• {tilde over (Θ)}n={tilde over (Θ)}n-1;
• (G) generating a smoothed estimate of {tilde over (Θ)}n by Kalman filtering adapted to filter the primary estimate of Θn obtained at step (C) and using σΘ2 from step (D), as follows:
• θnpred=F2[Φn·{tilde over (θ)}n-1],
• Ψnpred=Φn·(Ψn-1+Ψ0)·ΦnT,
• Kn=Ψnpred·HnT·(Hn·Ψnpred·HnT+Rn)−1,
• {tilde over (θ)}n=F2[θnpred+Kn·F1[Yn−Hn·θrpred]],
• Ψn=Ψnpred−Kn·Hn·Ψnpred,
• where Yn=Θn is the primary estimate of the velocity vector orientation angle Θ from step (C),
• Rn=σΘn2 is the variance estimate from step (D),
• θnpred is the extrapolated estimate,
• {tilde over (θ)} to is the smoothed estimate,
• F1[ . . . ] and F2[ . . . ] are nonlinear transformations to modify Kalman filter for filtering cyclic values,
• Ψ0 is a preset value of a parameter limiting a bandwidth of the Kalman filter,
• matrix Φn is based on a chosen model of angle change,
• matrix Hn is based on a chosen filter order.