IEEE - Aerospace and Electronic Systems - July 2022 - 9

Kassas et al.
Figure 3.
DT NAVFEST GPS jamming laydown: (a) highway taken toward Edwards AFB, (b) photo of Edwards AFB, CA, (c) location of the experiment,
(d) photo of one of the jammers used in the experiment, (e) heat map showing the jamming power and jammers' location, (f) photo of
the 58 Highway, where the ground vehicle experiment was performed. Map data: Google Earth.
where wclk is a discrete-time zero-mean white noise
sequence with covariance Qclk, and
Fclk ¼
1 T
01
; Qclk ¼
T þ S~w _dt
S~w _dt
T2
2
T3
3
S~w _dt
S~w _dt
T2
2
:
T
measurement noise, which is modeled as a discrete-time
zero-mean white Gaussian sequence with variance s2
fðkÞ.
" # Note that the termN in (9) is not necessarily an integer
S~wdt
(7)
SOP MEASUREMENT MODEL
A specialized receiver could produce a pseudorange measurement
to an SOP, which after discretization and mild
approximations discussed in the work of Kassas and Humphrey
[26], can be modeled as
rðkÞ¼ krrðkÞ rsk2
þ c dtrðkÞ dtsðkÞ½þ vrðkÞ (8)
where c is the speed of light and vr is a DT zero-mean
white Gaussian sequence with variance s2
rðkÞ.
Another, more precise navigation observable that can
be produced is the carrier phase, which can be modeled as
fðkÞ¼ rrðkÞ rskk2
þ c dtrðkÞ dtsðkÞ½þN þ vfðkÞ
(9)
where is the wavelength ofthe carrier signal, N represents
the carrier phase ambiguity (namely, the initial phase difference
between the receiver and the SOP), and vfðkÞ is the
JULY 2022
RADIO SLAM EKF FORMULATION
The observables to all SOPs in the environment, whether
pseudoranges and/or carrier phases are augmented into
IEEE A&E SYSTEMS MAGAZINE
9
[42]. Single- or double-difference carrier phase measurements
will have integer ambiguities. Ifthe SOP carrier phase
measurements are used in a differential framework, the
Least-squares AMBiguity Decorrelation Adjustment
(LAMBDA) method [43], or its variants, e.g., the modified
LAMBDA method [44], could be used to resolve the integer
ambiguities. If SOP carrier phase measurements are
used in a nondifferential framework, the carrier phase
ambiguity is treated as a real-valued constant offset
that can be assimilated into the SOP's initial clock
bias [45]. In both differential and nondifferential
frameworks, cycle slips in carrier phase tracking may
occur, which could introduce integer " jumps " in N.In
such cases, cycle slip detection and mitigation methods
may be used to reduce their effects on carrier phase
measurements [46]. The rest of this article focuses on
a pseudorange-based navigation solution.

IEEE - Aerospace and Electronic Systems - July 2022

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