Cramér-Rao Bounds for a Coupled Mixture of Polynomial Phase and Sinusoidal FM Signals

Wang, Pu; Orlik, Philip V.; Sadamoto, Kota; Tsujita, Wataru; Sawa, Yoshitaka

doi:10.1109/sam.2018.8448983

Cited by 2 publications

(2 citation statements)

References 26 publications

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“…As a consequence, with respect to (w.r.t.) the single source CSM in (2a), in addition to

η

, precise positioning requires estimation of the signal amplitude and phase, and thus the following reparameterisation can be used

bold-italicx = bold-italica false(bold-italicη false) ρ e^{normalj φ} + bold-italicw, bold-italicx, bold-italicw \in C^{N}, bold-italica false(bold-italicη false) \in C^{N}, ρ \in R^{+} .

To the best of our knowledge, no compact CRB formula for the joint estimation of

ε^{⊤} = false(σ_{w}^{2}, ρ, φ, η^{⊤} false)

, where

σ_{w}^{2}

is the power of the white noise vector w (such that

bold-italicw \sim C N false(bold0, σ_{w}^{2} I_{N} false)

), seems to be available in the open literature [13–15, 17, 29–36, 39–46]. Only by assessing the performance of CMLE at the single source CSM, the stochastic modelling of PVT observables can be determined.…”

Section: Introductionmentioning

confidence: 99%

Compact CRB for delay, Doppler, and phase estimation – application to GNSS SPP and RTK performance characterisation

Medina

Ortega²,

Vilà‐Valls

et al. 2020

IET Radar, Sonar & Navigation

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The derivation of tight estimation lower bounds is a key tool to design and assess the performance of new estimators. In this contribution, first, the authors derive a new compact Cramér-Rao bound (CRB) for the conditional signal model, where the deterministic parameter's vector includes a real positive amplitude and the signal phase. Then, the resulting CRB is particularised to the delay, Doppler, phase, and amplitude estimation for band-limited narrowband signals, which are found in a plethora of applications, making such CRB a key tool of broad interest. This new CRB expression is particularly easy to evaluate because it only depends on the signal samples, then being straightforward to evaluate independently of the particular baseband signal considered. They exploit this CRB to properly characterise the achievable performance of satellite-based navigation systems and the so-called real-time kinematics (RTK) solution. To the best of the authors' knowledge, this is the first time these techniques are theoretically characterised from the baseband delay/phase estimation processing to position computation, in terms of the CRB and maximum-likelihood estimation.

show abstract

“…As a consequence, with respect to (w.r.t.) the single source CSM in (2a), in addition to

η

, precise positioning requires estimation of the signal amplitude and phase, and thus the following reparameterisation can be used

bold-italicx = bold-italica false(bold-italicη false) ρ e^{normalj φ} + bold-italicw, bold-italicx, bold-italicw \in C^{N}, bold-italica false(bold-italicη false) \in C^{N}, ρ \in R^{+} .

To the best of our knowledge, no compact CRB formula for the joint estimation of

ε^{⊤} = false(σ_{w}^{2}, ρ, φ, η^{⊤} false)

, where

σ_{w}^{2}

is the power of the white noise vector w (such that

bold-italicw \sim C N false(bold0, σ_{w}^{2} I_{N} false)

Section: Introductionmentioning

confidence: 99%

Compact CRB for delay, Doppler, and phase estimation – application to GNSS SPP and RTK performance characterisation

Medina

Ortega²,

Vilà‐Valls

et al. 2020

IET Radar, Sonar & Navigation

View full text Add to dashboard Cite

show abstract

“…to the best of our knowledge, no compact CRB formula for the joint estimation of T = σ 2 n , ρ, ϕ, η T , where σ 2 n is the white noise n power (n ∼ CN 0, σ 2 n I N ), seems to be available in the open literature [3]- [5], [7], [17]- [32]. This lack is all the more surprising that the derivation of such compact CRB is not difficult with the ad hoc approach, as proposed in Sec.…”

Section: Introductionmentioning

confidence: 99%

A Compact CRB for the Single Source Conditional Signal Model with Application to Delay-Doppler-Phase Estimation of Band-Limited Signals

Ortega¹,

Medina

Vilà‐Valls

et al. 2020

2020 59th IEEE Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

The derivation of tight estimation lower bounds is a key player to design and assess the performance of new estimators. In this contribution, we derive a new compact Cramér-Rao bound (CRB) for the conditional signal model, where the deterministic parameter's vector includes a real positive amplitude and the signal phase. Then, such CRB is particularized to the delay, Doppler, phase and amplitude estimation with bandlimited (narrowband) signals, where transmitter and receiver are in relative uniform radial movement. The latter expression is especially easy to use because it only depends on the signal samples. We provide illustrative results for a representative Global Navigation Satellite System positioning example.

show abstract

Cramér-Rao Bounds for a Coupled Mixture of Polynomial Phase and Sinusoidal FM Signals

Cited by 2 publications

References 26 publications

Compact CRB for delay, Doppler, and phase estimation – application to GNSS SPP and RTK performance characterisation

Compact CRB for delay, Doppler, and phase estimation – application to GNSS SPP and RTK performance characterisation

A Compact CRB for the Single Source Conditional Signal Model with Application to Delay-Doppler-Phase Estimation of Band-Limited Signals

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