1? *Z* >

Shrunk search space

Valid Zk+1 found?

No

*Z Z* <sup>2</sup> = *<sup>k</sup>* 

2 2 2

χ =*C Z*( ) 

χ

Set the initial search space 2 0 0 χ, *Z*

Set Ω2 { } 2 2 2 2 ( ) | () *mN n*

> Search in Ω2 12 1 2 |( ) () *Z CZ CZ kk k* + + <

*k* = 0

*k k Z CZ* <sup>×</sup> Ω =∈ ≤

 χ

χ

Fig. 7. The *Expansion* approach: flow chart.

single-frequency case is of interest for many aerospace applications, where limits on weight and power consumption must often be respected.

In both tests the same receiver (Septentrio PolaRx2@) was connected to three antennas, placed on the middle of the fuselage, on the wing and on the nose (see Figure 9). In the first 20 Will-be-set-by-IN-TECH

Yes

Yes

*k k* = +1

EXPAND

ENUMERATE

MINIMIZE

Expand the space to 2 2 χ χ*k k* <sup>+</sup><sup>1</sup> = +Δ

Enumerate all the integer matrices in Ω1

Compute C(Z) for all the enumerated matrices in Ω1

*k k Z CZ* <sup>×</sup> Ω =∈ ≤

{ } 2 2 1 1 ( ) | () *mN n*

 χ

No

Evaluate the minimizer of C(Z) among the enumerated matrices in Ω1

() ()

Fig. 7. The *Expansion* approach: flow chart.

and power consumption must often be respected.

*ZR* 

*R R <sup>R</sup> <sup>Q</sup> R Z RZ R* <sup>×</sup> <sup>∈</sup> = − o

( )( ) <sup>3</sup> ˆ ˆ <sup>2</sup> <sup>ˆ</sup> arg min*<sup>p</sup>*

*RZRZ*

single-frequency case is of interest for many aerospace applications, where limits on weight

In both tests the same receiver (Septentrio PolaRx2@) was connected to three antennas, placed on the middle of the fuselage, on the wing and on the nose (see Figure 9). In the first

No

<sup>2</sup> ( ) is empty? *<sup>C</sup>* Ω χ*k*

Set the initial search space 2 0 0 χ, *Z*

Set Ω1 { } 2 2 1 1 ( ) | () *mN n*

> Search in Ω1 2

<sup>1</sup> | () *ZC Z* ≤ χ*k*

2 1( ) is empty? Ω χ*k*

*k* = 0

*k k Z CZ* <sup>×</sup> Ω =∈ ≤

 χ

χ

χ

Fig. 8. The *Search and Shrink* approach: flow chart.

test analyzed (*T* − *I*) the nose antenna was placed on the extremity of a boom, whereas in second test (*T* − *I I*) it was directly placed on the aircraft body. The two tests largely differ by the flight dynamic. Test *T* − *I* was conducted with aggressive maneuvering and few zero-gravity parabolas, whereas *T* − *I I* was performed as part of a gravimetry campaign, with very few smooth maneuvers, as shown in Figure 10. During test *T* − *I I*, the aircraft

<sup>0</sup> <sup>1000</sup> <sup>2000</sup> <sup>3000</sup> <sup>4000</sup> <sup>5000</sup> <sup>6000</sup> <sup>0</sup>

Epoch

(a) *T* − *I*

**5.1 Instantaneous ambiguity resolution**
