CramÉr–Rao Bound Analysis of Positioning Approaches in GNSS Receivers

Closas, Pau; Fernández‐Prades, Carles; Fernandez–Rubio, Juan A.

doi:10.1109/tsp.2009.2025083

Cited by 61 publications

(39 citation statements)

References 20 publications

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“…In order to evaluate the estimation performance for multipath propagation, Cramer‐Rao bound, the theoretical lower bound of accuracy of any unbiased estimator, is adopted to show the potential performance of ML estimation. For a single‐path case, it is not difficult to derive that the CRB of propagation time delay τ is

{CRB}_{1} ((), τ) = \frac{σ^{2}}{4 π^{2} A^{2} \int_{- B}^{B} f^{2} S ((), f) normald f} .

…”

Section: Cramer‐rao Bound For Multipath Propagationmentioning

confidence: 99%

Unambiguous and precise correlation receiver for binary offset carrier modulated signal

Zhang

Zuo

2019

Int J Communication

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Summary The binary offset carrier (BOC) modulated signal can improve the positioning accuracy and increase the multipath resistance in global navigation satellite system (GNSS), and it may cause potential ambiguity in the process of signal acquisition and code tracking. In this paper, a simple but efficient unambiguous receiver is firstly proposed for multiple side‐peaks mitigation by implementing correlation of the received BOC signal with local sine wave instead of square wave used at the transmitter. Moreover, the potential degradation of sharpness of the nonlinear correlation induced by the sine wave is well compensated by optimizing the early‐to‐late spacing. The other reason leading to ambiguity is the multipath propagation, so we further propose a maximum likelihood (ML) estimator with Newton iteration method, where the received GNSS signal is modeled via the line‐of‐sight (LOS) component and the first‐arrived non‐line‐of‐sight (NLOS) component. Finally, the analytical expression of multipath propagation Cramer‐Rao bound is derived for the designed ML estimator. Simulation results indicate that compared with the conventional BOC modulation, the proposed sine wave receiver can achieve unambiguous and more precise code tracking performance and thus turns out to be more robust to multipath propagation.

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{CRB}_{1} ((), τ) = \frac{σ^{2}}{4 π^{2} A^{2} \int_{- B}^{B} f^{2} S ((), f) normald f} .

…”

Section: Cramer‐rao Bound For Multipath Propagationmentioning

confidence: 99%

Unambiguous and precise correlation receiver for binary offset carrier modulated signal

Zhang

Zuo

2019

Int J Communication

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“…It is shown that this method can mitigate multipath and jamming interferences. A Cramér-Rao Bound of position for both conventional and DPE approaches is presented in [22] in order to show DPE is better compared to the conventional one. Despite the effectiveness of the DPE technique, its implementation within a GNSS receiver remains a great difficulty since these works are still theoretical and very general.…”

Section: Collective Detectionmentioning

confidence: 99%

Efficient and Innovative Techniques for Collective Acquisition of Weak GNSS Signals

Andrianarison¹,

Sahmoudi²,

Landry³

2017

JCC

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Navigation and positioning in harsh environments is still a great challenge for many applications. Collective Detection (CD) is a powerful approach for acquiring highly attenuated satellite signals in challenging environments, because of its capacity to process all visible satellites collectively taking advantage of the spatial correlation between GNSS signals as a vector acquisition scheme. CD combines the correlator outputs of satellite channels and projects them onto the position/clock bias domain in order to enhance the overall GNSS signal detection probability. In CD, the code phase search for all satellites in view is mapped into a receiver position/clock bias grid and the satellite signals are not acquired individually but collectively. In this concept, a priori knowledge of satellite ephemeris and reference location are provided to the user. Furthermore, CD addresses some of the inherent drawbacks of the conventional acquisition at the expenses of an increased computational cost. CD techniques are computationally intensive because of the significant number of candidate points in the position-time domain. The aim of this paper is to describe the operation of the CD approach incorporating new methods and architectures to address both the complexity and sensitivity problems. The first method consists of hybridizing the collective detection approach with some correlation techniques and coupling it with a better technique for Doppler frequency estimate. For that, a new scheme with less calculation load is proposed in order to accelerate the detection and location process. Then, high sensitivity acquisition techniques using long coherent integration and noncoherent integration are used in order to improve the performance of the CD algorithm.

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“…The covariance matrix of θ is constrained by the Cramer-Rao bound (CRB), which can be expressed as [11] …”

Section: Joint Navigation State Error Discriminatormentioning

confidence: 99%

“…Moreover, the element of H k in the ith row and jth column simply depends on the ith and jth elements of θ. Thus, because the x-axis, y-axis, and z-axis operate in the same way, it is reasonable to choose G 11 and H 11 as representatives for the analysis of the characteristics of the position estimation error, and to choose G 15 and H 55 to probe the characteristics of the velocity estimation error. In the case of observing four satellites, the cost function, gradient, and Hessian values for position and velocity estimation errors in the x-direction are shown in Figure 2, where all the values have been normalized.…”

Section: Iterative Maximum Likelihood Estimationmentioning

confidence: 99%

A novel joint navigation state error discriminator based on iterative maximum likelihood estimation

Wang

Luo

Wang

2015

Sci. China Inf. Sci.

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To break through the limitations of traditional discriminators used in vector tracking loops, this paper presents an iterative maximum likelihood estimation (IMLE) method for extracting navigation state errors from multi-satellite signals. The IMLE method takes into account both computational cost and estimation accuracy. The associated gradient vector and Hessian matrix of the MLE cost function are derived. The characteristics of the proposed joint discriminator are analyzed based on the properties of the MLE cost function, gradient vector, and Hessian matrix. The effectiveness of IMLE is verified by Monte Carlo simulation.Keywords global navigation satellite system (GNSS), iterative maximum likelihood estimation (IMLE), joint navigation state error discriminator, Cramer-Rao bound (CRB), vector tracking loop CitationWang Y Q, Luo Y, Wang P, et al. A novel joint navigation state error discriminator based on iterative maximum likelihood estimation.

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CramÉr–Rao Bound Analysis of Positioning Approaches in GNSS Receivers

Cited by 61 publications

References 20 publications

Unambiguous and precise correlation receiver for binary offset carrier modulated signal

Unambiguous and precise correlation receiver for binary offset carrier modulated signal

Efficient and Innovative Techniques for Collective Acquisition of Weak GNSS Signals

A novel joint navigation state error discriminator based on iterative maximum likelihood estimation

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