多立方卫星编队飞行中的阵列信号检测相对位置与姿态确定

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"这篇研究论文探讨了在编队飞行中基于阵列信号检测的多方体（多颗立方体卫星，CubeSat）相对位置和姿态确定方法。高精度的相对位置和姿态测量对于多CubeSat编队飞行中的共识控制和碰撞避免至关重要。然而，传统的相对导航系统由于体积大、复杂度高和成本昂贵，不适用于CubeSat小型卫星。为此，作者提出了一种名为Multi-CubeSat relative State determination by Array Signal detection (MUSAS)的新方法。 MUSAS方法利用了 CubeSat 上现有的通信系统和天线阵列，无需额外组件。在MUSAS系统中，编队中的副车（Deputy Vehicle, DV）CubeSat同时广播正交扩频谱信号。两颗主车（Chief Vehicle, CV）CubeSat接收这些信号并进行分离，提取多个输入多个输出（Multiple-Input Multiple-Output, MIMO）信道信息。通过分析这些信道信息，可以精确地计算出DV CubeSat相对于CV CubeSat的相对位置和姿态。该方法的优势在于减少了硬件需求，降低了系统复杂性和成本，同时提高了测量精度。论文中可能会详细介绍MUSAS的工作原理，包括信号处理、信道估计、阵列信号检测算法以及姿态解算的具体步骤。此外，可能还会讨论这种方法的性能评估，如误差分析、抗干扰能力以及在不同飞行条件下的适用性。通过MUSAS技术，编队飞行的CubeSat可以实现更高效、低成本的相对导航，这对于推动小型卫星集群任务的发展具有重要意义，尤其是在地球观测、通信网络和空间科学实验等领域。论文可能还涉及了未来可能的研究方向和实际应用的潜在挑战，为立方体卫星编队飞行技术的进步提供了新的思路。"

nal transmission among CubeSats. Then, the signals to each

CV are detected by signal separation, and the directions of

the propagation paths (i.e., AoDs and AoAs) are estimated.

Finally the bi-directional LOS vectors between each CV

and DV with respect to the corresponding frame bodies are

deduced.

A. Array Signal Transmission and Detection

First, all of the DVs are allowed to transmit asyn-

chronously, and thus, the complicated synchronization and

coordination among the CubeSats are avoided. The multi-

CubeSat detection (i.e., separation of the signals from dif-

ferent DVs) is realized by the CDMA technology. Each DV

is assigned a predeﬁned spread spectrum sequence, i.e., pe-

sudonoise pseudo-noise (PN) sequence with the length of

L bits. Readers are referred to [39] and [40] for a detailed

explanation of the characteristics and generation of PN-

sequences. The spreading sequence assigned to the kth DV

is denoted by a

(τ ) and expressed as

(τ ) =



l=1

k,l

rect

(

τ − lT

)

k,l

∈

{

+1, −1

}

(1)

where rect

(

)

denotes a rectangular pulse with the dura-

tion of T

and power of P



rect

(τ )dτ. The duration

of the spreading sequence is T

= LT

. Please note that

the spread spectrum sequences of the K DVs are selected

such that their autocorrelation functions are pulse functions

and they are orthogonal to each other. The cross-correlation

functions of the spreading sequences are

a

(τ ),a

(τ )=a

(τ ) ∗ a

∗

(−τ ) =



= k

δ(τ ),k

= k

(2)

where < ·, · > denotes the sliding inner-production,

≈ 0 is a very small pesudorandom number, and δ(τ )

is the delta function.



(τ )dτ = LP

is the peak value

of the autocorrelation f unction of a

(τ ).

A DV (transmitter) modulates a carrier with its spread-

ing sequence circularly (e.g., via BPSK). The modulated

signal is transmitted on its M antennas in a time division

multiplexing manner. By using a microwave switch, the an-

tennas transmit the modulated signal one-by-one, and each

transmits at least 2N spreading sequences. Meanwhile, con-

trolled by a microwave switch, the N antennas of the array

on a CV (receiver) receive the signals from the DVs se-

quentially. Each antenna keeps receiving for the duration of

such that it can capture at least one complete spreading

sequence from a DV. After all the antennas on the DVs have

transmitted their spreading sequences, every pair of the DV

and CV antennas have transferred a complete spreading

sequence. The MIMO links between a DV and CV are il-

lustrated in Fig. 1.

Determined by the relative positions and attitudes of

the CubeSats, the signal over the link from the mth (m =

1, 2,...,M) antenna on DV

to the nth (n = 1, 2,...,N)

antenna on CV

k,m,i,n

(τ ) = g

k,i

k,m

(φ

k,i

,θ

k,i

i,n

(φ



k,i

,θ



k,i

(τ − τ

k,i

)

(3)

where

k,i

is the free-space path loss depending on the dis-

tance between DV

and CV

and a

(τ − τ

k,i

) is the circular

shift of a

(τ )byτ

k,i

, the propagation delay from DV

.In(3),t

k,m

(φ

k,i

,θ

k,i

) is the complex gain of the mth

Tx antenna, including the antenna radiation pattern at the

AoD of (φ

k,i

,θ

k,i

) and the phase shift with respect to the

reference antenna for its position. Similarly, r

i,n

(φ



k,i

,θ



k,i

)

is the complex gain of the nth Rx antenna, including the

antenna pattern at the AoA of (φ



k,i

,θ



k,i

) and the phase shift

with respect to the reference antenna.

As all of the K DVs are broadcasting simultaneously,

the signals received on the CVs’ antennas are the superpo-

sition of all the DVs’ signals. The received signal on the

nth antenna of CV

i,n

(τ ) =



k=1

k,m,i,n

(τ ) + w

i,n

(τ )(4)

where

k,m,i,n

(τ ) is the signal from the mth antenna on

as given in (3) and w

i,n

(τ ) is the noise through the nth

receiving chain on CV

We can then separate and detect each DV’s signal based

on the orthogonality among the spreading sequences. Each

CV performs sliding correlation between the received

signal

i,n

(τ ) and the spreading sequence a

(τ ) in the delay

domain to extract the signal from DV

. The result is given

in (5) shown at the bottom of the next page. By plugging (2)

into (5), we can obtain (6) shown at the bottom of the next

page, where A

k,m,i,n

 LP

k,i

k,m

(φ

k,i

,θ

k,i

i,n

(φ



k,i

,θ



k,i

)

is the complex amplitude of the delta func-

tion in the cross-correlation function and ε

i,n







=1,k



=k



(φ



,θ



i,n

(φ



,θ



)ε

k,k



≈ 0isthe

inter-CubeSat interference received on the nth antenna

of CV

. Because of the orthogonality property of the

spreading sequences, the cross-correlation result in (6)

generates a peak at the excess delay of τ

k,i

with the

complex amplitude of A

k,m,i,n

, which is called the link

impulse response (LIR). Please note that the amplitude of

the LIR is ampliﬁed by LP

and the interference from

other DVs is removed by the sliding correlation, which is

the spread spectrum gain. Therefore, employing spread

spectrum sequences provides the advantages of mitigating

inter-CubeSat interference and high signal-to-interference

ratio (SIR).

Although the following derivation is based on an ideal

signal model with the Gaussian noise ignored for easy pre-

sentation, important insights can be obtained. As shown in

Fig. 1, the spreading sequence from a DV is transmitted

over the MIMO links to both CVs. CV

uses the spread-

ing sequence for DV

, a

(τ ), to perform sliding correlation

with the received signals on its N antennas,

i,n

(τ )for

n = 1, 2,...,N. Thus, it obtains the LIR between each

pair of antennas on DV

and CV

, A

k,m,i,n

. The LIRs are

organized in an M × N matrix as given in (7) shown at the

WANG ET AL.: MULTI-CUBESAT RELATIVE POSITION AND ATTITUDE DETERMINATION 3381

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