# US 11,994,598 B2 · Method and apparatus for performing joint channel and time estimation in a GNSS receiver

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- Number: US 11,994,598 B2
- Document ID: US11994598B2
- Status: Granted
- Kind: B2
- Application number: 17/058,219
- Filed: 2018-05-24
- Published: 2021-05-06
- Granted: 2024-05-28
- Earliest claimed: 2018-05-24
- Assignees: European Space Agency
- Applicants: European Space Agency
- Inventors: Jose Antonio Garcia Molina
- Web page: https://patentgrep.com/patent/US11994598B2

## CPC

- G01S 19/14: specially adapted for specific applications
- G01S 19/256: {relating to timing, e.g. time of week, code phase, timing offset}
- G01S 19/24: Acquisition or tracking {or demodulation} of signals transmitted by the system {(synchronisation aspects of direct sequence spread spectrum modulation H04B1/7073)}
- G01S 19/243: {Demodulation of navigation message}
- G01S 19/30: code related {(G01S19/246 takes precedence)}
- G01S 19/44: Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method
- G06N 7/01: Probabilistic graphical models, e.g. probabilistic networks
- H04B 1/7073: Synchronisation aspects
- G01S: RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- H04B: TRANSMISSION

## Abstract

A receiver is provided for use with a global navigation satellite system (GNSS) comprising multiple satellites. The receiver comprises a receiver clock and at least one antenna for receiving multiple signals over multiple respective channels, each channel being defined by a transmitting satellite and a receiving antenna at opposing ends of the channel. The receiver further comprises at least one correlator for calculating cross-correlation functions between (i) the signals received over the multiple channels and (ii) reference versions of the navigation signals provided by the receiver. The receiver is configured to use the calculated cross-correlation functions to perform a joint estimate of (i) a clock bias of the receiver clock relative to the time reference maintained by the GNSS, and (ii) a composite channel comprising the combined contribution of the multiple channels as a function of time-delay.

## Claims

### Claim 1

A receiver for use with a global navigation satellite system (GNSS) comprising multiple satellites, wherein each satellite transmits a respective navigation signal containing a spreading code, and wherein the GNSS maintains a time reference which is encoded into the navigation signals, the receiver comprising:
a receiver clock;
at least one antenna for receiving multiple signals over multiple respective channels, each channel being defined by a transmitting satellite and a receiving antenna at opposing ends of the channel; and
at least one correlator for calculating cross-correlation functions between (i) the signals received over the multiple channels and (ii) reference versions of the navigation signals provided by the receiver;
wherein the receiver is configured to use the calculated cross-correlation functions to perform a joint estimate of (i) a clock bias of the receiver clock relative to the time reference maintained by the GNSS, and (ii) a composite channel comprising the combined contribution of the multiple channels as a function of time-delay; and
wherein the clock bias of the receiver clock is estimated as an offset from an approximate clock bias.

### Claim 2 (depends on 1)

The receiver of claim 1, wherein the signals received over the respective channels include contributions from one or more of the navigation signals.

### Claim 3 (depends on 2)

The receiver of claim 2, wherein the receiver is configured to detect a given navigation signal included in a signal received over a given channel based on the calculated cross-correlation function between the signal received over the given channel and the reference version of the given navigation signal.

### Claim 4 (depends on 3)

The receiver of claim 3, wherein the receiver is further configured to use the calculated cross-correlation function between the signal received over the given channel and the reference version of the given navigation signal to determine a code-phase alignment between the received given navigation signal and the provided reference version of the given navigation signal.

### Claim 5 (depends on 4)

The receiver of claim 4, wherein the code-phase alignment is dependent upon: (i) the propagation time of the given navigation signal from the satellite to the receiver and (ii) the clock bias between the receiver clock and the time reference maintained by the GLASS.

### Claim 6 (depends on 4)

The receiver of claim 4, wherein the calculated cross-correlation functions used for performing the joint estimate are centered on the determined code-phase alignment for each satellite.

### Claim 7 (depends on 2)

The receiver of claim 2, wherein the contributions for the one or more navigation signals include multiple non-line-of-sight components.

### Claim 8 (depends on 1)

The receiver of claim 1, wherein the time-delay is referenced to arrival of a line-of-sight component.

### Claim 9 (depends on 1)

The receiver of claim 1, wherein the approximate clock bias is equal to an initial estimated clock bias having a typical accuracy (1-sigma) in the range 0.1-1 microseconds.

### Claim 10 (depends on 1)

The receiver of claim 1, wherein the receiver is configured to estimate the approximate clock bias, prior to performing the joint estimation, by using the calculated cross-correlation functions to determine a maximum of a composite cross-correlation function for the composite channel.

### Claim 11 (depends on 10)

The receiver of claim 10, wherein the composite cross-correlation function is defined by
Λ
ˆ
(
Φ
0
,
n
)
=
∑
j
=
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N
⁢
x
j
H
⁢
B
⁡
(
Φ
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,
n
-
Δ
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Φ
j
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⁢
(
B
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B
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B
H
(
Φ
0
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n
-
Δ
⁢
Φ
j
)
⁢
x
j
;
wherein:
Φ0,n comprises a state vector of the receiver;
Φ0,n−ΔΦj comprises a state vector per antenna;
xj comprises the signal received at antenna j; and
B(Φj) comprises a basis function matrix for the state vector Φj.

### Claim 12 (depends on 1)

The receiver of claim 1, wherein performing the joint estimate of the clock bias includes searching a predefined range of possible clock bias values.

### Claim 13 (depends on 1)

The receiver of claim 1, wherein the composite channel is specified by a set of coefficients, each coefficient corresponding to a particular time-delay, and representing the aggregate level of power transmission through the composite channel for that time-delay.

### Claim 14 (depends on 13)

The receiver of claim 13, wherein the receiver includes at least one probability distribution function for each coefficient in the set of coefficients.

### Claim 15 (depends on 14)

The receiver of claim 14, wherein the provided probability distribution functions are based on an estimate of the composite channel obtained using received signals from a previous epoch.

### Claim 16 (depends on 15)

The receiver of claim 15, wherein the receiver is configured to update the probability distribution functions based on the estimated composite channel.

### Claim 17 (depends on 14)

The receiver of claim 14, wherein receiver performs the joint estimate using a Monte Carlo search based on trial values of the composite channel, generated in accordance with the probability density functions, to find the trial values and clock bias that best fit the calculated cross-correlation functions.

### Claim 18 (depends on 1)

The receiver of claim 1, wherein performing the joint estimate is defined by:
h
^
l
,
β
^
f
=
arg
min
h
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β

Λ
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∑
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❘
"\[LeftBracketingBar]"
β
❘
"\[RightBracketingBar]"
<
W
;
wherein
ĥl comprises a composite channel vector estimated under the l-th hypothesis for the channel PDFs {p([h]m)}m=1D{pl,m}m=1D, with ĥl=[ĥl,1 . . . ĥl,D]T∈D×1,
{circumflex over (β)}l comprises an integer offset estimated under the l-th hypothesis;
W∈ constrains the values evaluated for the integer offset β based on an expected error of an intermediate clock bias {circumflex over (δ)}tint;
{circumflex over (Λ)}=[{circumflex over (Λ)}(δt1) . . . {circumflex over (Λ)}(δtQ)]T∈Q×1 comprises an estimated cross-correlation vector with uniform sampling, with a time-delay resolution Tδ, of a composite cross-correlation function Λ(δt) at Q clock offset values, being centered at the intermediate clock bias estimation {circumflex over (δ)}tint such that δtn|n=(Q+1)/2={circumflex over (δ)}tint; and
s({circumflex over (δ)}tint−(β−m+1)Tδ)∈Q×1 comprises a vector containing samples of the reference correlation function centered at the clock bias {circumflex over (δ)}tint−(β−m+1)Tδ.

### Claim 19 (depends on 1)

The receiver of claim 1, wherein the receiver includes multiple antennas, and the joint estimate takes advantage of spatial correlation between the signals received by different antennas.

### Claim 20 (depends on 19)

The receiver of claim 19, wherein the performing the joint estimate is defined by:
h
^
i
,
β
^
l
=
arg
min
h
,
β
γ
⁡
(
h
,
β
)
wherein
γ
⁡
(
h
,
β
)
=
1
N
⁢
∑
j
=
1
N
⁢
γ
^
j
(
h
,
β
)
(
∏
j
=
1
N
⁢
γ
^
j
⁡
(
h
,
β
)
)
1
/
N
,
where {circumflex over (γ)}j(h,β) comprises the j-th eigenvalue associated with a spatial covariance matrix of multipath mis-modelling errors estimated as Ĉε(h,β)=Ê(h,β)Ê(h,β)T;
Ê(h,β)=[{circumflex over (ε)}1(h,β) . . . {circumflex over (ε)}N(h,β)]T∈Q×N comprises a matrix containing vectors with estimated multipath mis-modelling errors {circumflex over (ε)}j, defined as
Ê(h,β)={circumflex over (θ)}j−Kj(h)Σm=1D[h]m|s({circumflex over (δ)}tint−(β−m+1) Tδ|2, with
{circumflex over (K)}j(h)=∥{circumflex over (θ)}j∥/∥Σm=1D[h]m|s({circumflex over (δ)}tint+(m−1) Tδ|2∥;
{circumflex over (θ)}j=[{circumflex over (θ)}j(δt1) . . . {circumflex over (θ)}j(δtQ)]T∈Q×1 comprises an estimated cross-correlation vector for the i-th antenna, which is uniformly sampling, with a time-delay resolution Tδ, the composite cross-correlation function θj (δt) at Q clock offset values, being centered at the intermediate clock bias estimation {circumflex over (δ)}tint such that δtn|n=(Q+1)/2={circumflex over (δ)}tint; and
{circumflex over (θ)}j(δtn){circumflex over (θ)}j(δtn, {dot over (δ)}t, p0T)={circumflex over (θ)}j(Φ0,n) is estimated as
{circumflex over (θ)}j(Φ0,n)=xjH B(Φ0,n−ΔΦj)(BH(Φ0,n−ΔΦj)B(Φ0,n−ΔΦj))−1 BH(Φ0,n−ΔΦj)xj.

### Claim 21 (depends on 1)

The receiver of claim 1, wherein the estimated clock bias has an accuracy of less than 100 nanoseconds.

### Claim 22

A method of operating a receiver for use with a global navigation satellite system (GNSS) comprising multiple satellites, wherein each satellite transmits a respective navigation signal containing a spreading code, and wherein the GNSS maintains a time reference which is encoded into the navigation signals, the receiver comprising a receiver clock and at least one antenna for receiving multiple signals over multiple respective channels, each channel being defined by a transmitting satellite and a receiving antenna at opposing ends of the channel, the method comprising:
calculating cross-correlation functions between (i) the signals received over the multiple channels and (ii) reference versions of the navigation signals provided by the receiver;
performing a joint estimate of (i) a clock bias of the receiver clock relative to the time reference maintained by the GLASS, and (ii) a composite channel comprising the combined contribution of the multiple channels as a function of time-delay, using the calculated cross-correlation functions;
wherein the clock bias of the receiver clock is estimated as an offset from an approximate clock bias.

### Claim 23 (depends on 22)

The method of claim 22, wherein the receiver is located in an indoor environment.