- Open Access
Joint acquisition algorithm with assisted information for weak GNSS signals
© Tong et al.; licensee Springer. 2014
- Received: 17 September 2013
- Accepted: 28 April 2014
- Published: 19 May 2014
In this paper, we propose an enhanced joint acquisition scheme with satellite selection and assisted information to detect weak signals. The theoretical derivation of the joint acquisition is detailed in the principle of the generalized likelihood ratio test (GLRT) to evaluate detection performance. An approximate and simplified architecture is proposed to reduce the computation load. The traditional acquisition performs two-dimensional search over the delay and Doppler frequency per satellite, while the simplified joint acquisition adopts one statistic for all the available satellites to perform multi-dimensional search over the receiver motion parameters and the clock errors. Based on the simplified architecture, one novel strategy of the satellite selection is presented to enhance the robustness. The selection strategy removes the satellites which should be available but are possibly blocked by buildings or trees. Monte Carlo simulations are performed to verify the analytical results. Under the condition that 1-ms coherent integration is adopted in the simulation with 16 satellites, the sensitivity improvement of the enhanced joint acquisition is about 9 dB over those of conventional acquisition. Furthermore, experiments show that the joint acquisition with the satellite selection is more invulnerable to blocked satellites than that without the satellite selection.
- Assisted GNSS
- Weak signals
- Satellite selection
- Generalized likelihood ratio test
As new constellations become operational, global navigation satellite systems (GNSS) are expected to provide better positioning service in the fading environments (e.g., indoors, urban canyon, and flyover). Long integration time is always used in the conventional scalar-based acquisition and tracking for weak signals [1, 2]. Various methods on the coherent, noncoherent, and differential detectors were analyzed theoretically in [3–6]. However, the sensitivity improvement of the conventional acquisition is limited by the constraints, such as receiver movement and computational load. Due to each satellite signal that is processed individually, the correlations of the multi-satellite signals are neglected by the scalar-based acquisition and tracking. If the correlations of the GNSS signals from different satellites are exploited, the acquisition sensitivity will be improved further.
Instead of processing the signals separately, the vector delay/frequency lock loop (VDFLL) adopts a single Kalman filter to track the GNSS signals and determine the navigation solution simultaneously [7–9]. The spatial correlation between visible satellites and the positioning solution is exploited; consequently, the VDFLL performs better than conventional scalar loops, especially in environments with high dynamics and low signal power. However, the tracking sensitivity is still limited by the individual discriminators. In contrast to conventional two-step position, the direct position estimation (DPE) without discriminators was proposed in  and the Cramér-Rao bound was analyzed . Recently, the implementing loop called maximum likelihood vector tracking loop (MLVTL) was introduced in . The experiments in the indoor environment demonstrate that the benefits of the MLVTL are more pronounced than those of the VDFLL . Similar to the DPE and the MLVTL, the joint acquisition combining outputs of the individual satellite correlators is used to improve the acquisition sensitivity in . Both the simulation and outdoor experiments demonstrate the benefit of the joint acquisition [15, 16]. However, the detection performance is not evaluated detailedly, and the collective detection degrades greatly with some blocked satellites. There are some other joint acquisition algorithms, which focus on speeding up the correlator computation by combining the satellite replicas [17, 18]. As a result, the addition of the different code replicas affects the acquisition sensitivity.
In this paper, we introduce an approach to enhance the joint acquisition for detecting the weak GNSS signals. The enhanced algorithm is characterized by the simplified architecture and the satellite selection strategy. The simplified architecture adopts the approximate calculation of the detector, which is derived in the principle of the generalized likelihood ratio test (GLRT). In the stage of performance evaluation of the simplified architecture, we derive the closed-form expressions of the probabilities of the false alarm and detection. Moreover, a satellite selection strategy is proposed to deal with the case that some satellites are blocked.
The rest of this paper is organized as follows: Firstly, we introduce the linear model for the multi-satellite signals. Secondly, the GLRT for the joint acquisition is derived and the GLRT-based architecture is presented. Thirdly, we detail the enhanced joint acquisition and the satellite selection strategy. Then, the Monte Carlo simulations are performed to validate the theoretical analysis. Finally, we conclude the paper.
where x[ n] is the received digital signal, and fIF is the intermediate frequency. w[ n] is the zero-mean white Gaussian noise. The sampled signal is indexed by n. The subscript m is used to number the satellite. Ts is the sample interval. M is the total number of available satellites. The pseudorandom code of the m th satellite is g m (·). The unknown parameters are listed as follows:
A m : the data modulation amplitude of the m th satellite signal
ϕ m : the carrier phase of the m th satellite
σ2: the variance of the noise w[ n]
τ m : the signal delay of the m th satellite
: the Doppler frequency of the m th satellite
Hereafter, the synchronization parameters are τ m and .
In the open environment, the line-of-sight satellites are available. The total number M can be determined by the assisted information such as navigation data and the rough receiver position. Some satellites are blocked and become unavailable due to local conditions (trees, buildings) in the urban environment, while line-of-sight is maintained to other satellites. These blocked satellites can be removed using the satellite selection strategy, which will be presented later. The bit transition is not considered in the signal block. Although the navigation data transition could degrade the detection performance, a number of techniques have been studied to overcome this effect . Besides, the modern GNSS signals with data and pilot channels also reduce the effect of the bit transition.
Firstly, we derive the GLRT-based detector assuming that the synchronization parameters are known in this section. Secondly, we review the asymptotic maximum likelihood estimator (MLE) of the synchronization parameters based on the position searching. Finally, the implementing architecture of the joint acquisition is detailed.
Known synchronization parameters
with n=0,1,…,N−1 and m=0,1,…,M−1.
where F2M,N−2M is an F distribution with 2M and N−2M degrees of freedom. The is a noncentral F distribution with 2M and N−2M degrees of freedom and noncentrality parameter λ.
where IM−1(·) is the modified Bessel function of the first kind.
The detector in (10) is also termed as the constant false alarm rate (CFAR) detector. If M=1, it is easily obtained that the modified statistic test (10) is equivalent to the coherent detector in conventional acquisition . The conventional scalar acquisition searches the visible satellites separately, while the joint acquisition tries to combine the coherent integration results of different satellites noncoherently.
Unknown synchronization parameters
where c is the speed of light, p(m) is the Sagnac-corrected position of the m th satellite in ECEF coordinate system, δ t(m) is the clock bias in seconds for the m th satellite, and and are the tropospheric delay and ionospheric delay in seconds, respectively. In (16), fc is the carrier frequency, v(m) is the velocity of the m th satellite, and is the clock drift in units of hertz for the m th satellite. As the annotation in (1), τ m and refer to the code delay and carrier Doppler frequency, respectively.
for all possible Υ. The threshold γ′ is determined by (11). The number of the search bins depends on the quality of the initial user position provided by the assisted information. The resolutions of the position and velocity for acquisition can be lower than those for tracking. However, the computation load cannot be neglected. The 2M×2M dimensional inverse matrix is calculated in the individual statistic shown in (10), the computation load increases significantly if more satellites are available.
The implementing architecture
As shown in Figure 1, all the local signals are generated individually by the synchronization parameters τ and fd. As described in (15) and (16), these synchronization parameters are determined by the searching bin. The replica local signals appear in complex form in Figure 1. The real parts of the complex signals correspond to the even columns of the matrix H in (3), while the imaginary parts correspond to the odd columns. The coherent integration at individual channel is implemented after the carrier and code stripping process. Then, the integrated results, quadratic sum of signals, and the matrix H form the statistic in (10). The MLE of the Υ, is obtained by maximizing the statistics over the search space. The joint acquisition is successful if the maximum statistic exceeds the threshold γ′ in (17); then, the estimated synchronization parameters of all the available satellites are obtained, respectively. Some implementation losses may exist as a result of residual errors in the replicas of the estimated synchronization parameters. Thus, the detection probability in (12) should be viewed as the upper bound.
The implementing architecture depicted in Figure 1 is similar to the MLE-based tracking architecture named MLVTL in . There are, however, two differences. One is that the resolution of the search bins in Figure 1 is lower than that in the MLVTL. Besides, the scope of the search space for the joint acquisition is wider than that for the MLVTL. As a result, the joint acquisition produces the approximate MLE of the receiver motion parameters and clock errors while the MLVTL generates the refined estimates. The other one is that the joint acquisition decides whether the signals are strong enough to detect. If all the signals are degraded seriously or even blocked, the MLE of the receiver motion parameters still can be obtained by the joint acquisition and the MLVTL. The joint acquisition declares that the estimated values are noneffective by checking the statistic while the MLVTL generates the distorted results. It is suggested that the statistic T′(x) be used as an indicator for the lock state of the MLE-based tracking loop.
Acquiring the GNSS signals together, rather than individually, improves the acquisition sensitivity. However, the drawbacks of the joint acquisition are obvious. As discussed above, the calculation of the matrix inverse is extensive and the computation load is heavy. When some satellites are blocked, the final statistic reduces dramatically while the threshold is invariable. Thus, the performance of the joint acquisition is degraded. To overcome these drawbacks, a simplified architecture of the joint acquisition with the satellite selection strategy is proposed.
A simplified implementing architecture
where Leff,dB is the effective signal power loss in decibels, Q=1.5 and R c =1.023 MHz with the C/A code, and (C m /N0)eff is the effective signal power to noise density of the m th satellite. Both C m /N0 and (C m /N0)eff are in decibel hertz.
where I2M×2M denotes the 2M×2M identity matrix.
It can be concluded from (21) that the is the coherent integration results of the m th satellite signals, while I M (τ,fd) is the noncoherent sum of .
where Tcoh is the coherent integration time.
Satellite selection strategy
In the conventional acquisition, there is a binary hypothesis test per satellite signal with associated probabilities of false alarm and detection. The two-dimensional search over the Doppler and delay is performed to form the detector individually. The conventional acquisition is still effective with and without a priori information, such as ephemeris, initial receiver position, and so on. When these information are available in the reacquisition or the assistant GNSS, the limited process gain can be obtained by reducing the search scope and fining the searching solution in the conventional acquisition. Furthermore, the joint acquisition combines all these binary hypothesis tests into a single test to obtain more process gain. In the open ground, the line-of-sight satellites to be acquired are easily determined by the ephemeris and initial position. However, the set of available satellites cannot be directly determined by a priori information in the cases where some satellite signals are blocked by the buildings, mountains, or trees. Under this condition, the blocked satellites are still regarded as available in the joint acquisition. It is concluded from (22) that the probability of detection decreases considerably with the blocked satellites. To deal with the degraded or blocked satellites, the satellite selection is proposed in this section.
where M is the total satellite number used in the search process and γ′ is determined by (11).
All the maximum values of the individual statistics are consistent with the true PVT in the normal circumstance without interference signals. However, the multipath interference may exist in the blocked environments. The multipath will distort the consistence between the individual statistics and the true PVT, which can result in the outliers of the estimated Doppler and delay. How to detect and remove the multiple outliers may refer to . We only focus on the direct-path signals in this paper.
Validation and comparison of the detection performance
The Monte Carlo simulations are conducted to validate the analytic results. Through all simulations, the intermediate frequency (IF) fIF is 4.068 MHz and the sampling frequency fs is 6.140625 MHz. The IF bandwidth is fs/2. The GPS C/A codes are used as the PRN codes of satellites. The number of the available satellites in different scenarios are 1, 4, 8, 12, and 16, respectively. The front-end filter has been neglected. The coherent integration time is 1 ms. The navigation data and rough receiver position are provided as a priori information.
Demonstration of the benefits of satellite selection
The joint acquisition combining GNSS signals has been derived from a statistical point of view. The acquisition performance is detailedly analyzed in terms of the probabilities of false alarm and detection. A simplified implementing architecture is presented to reduce the computation load. In order to improve the robustness against the blocked satellites, the satellite selection strategy is proposed. Simulation results have validated the analytic expressions and demonstrated the benefit of the satellite selection strategy. The assisted joint acquisition also can be used in the reacquisition after lost tracking loop.
HT is a Ph.D. candidate of the School of Electronic Science and Engineering at the National University of Defense Technology. His research interests include the GNSS signal acquisition and vector tracking.
This work has been supported by the China’s Ministry of Education (NCET-08-0144).
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