A Carrier Estimation Method Based on MLE and KF for Weak GNSS Signals

Abstract

Maximum likelihood estimation (MLE) has been researched for some acquisition and tracking applications of global navigation satellite system (GNSS) receivers and shows high performance. However, all current methods are derived and operated based on the sampling data, which results in a large computation burden. This paper proposes a low-complexity MLE carrier tracking loop for weak GNSS signals which processes the coherent integration results instead of the sampling data. First, the cost function of the MLE of signal parameters such as signal amplitude, carrier phase, and Doppler frequency are used to derive a MLE discriminator function. The optimal value of the cost function is searched by an efficient Levenberg–Marquardt (LM) method iteratively. Its performance including Cramér–Rao bound (CRB), dynamic characteristics and computation burden are analyzed by numerical techniques. Second, an adaptive Kalman filter is designed for the MLE discriminator to obtain smooth estimates of carrier phase and frequency. The performance of the proposed loop, in terms of sensitivity, accuracy and bit error rate, is compared with conventional methods by Monte Carlo (MC) simulations both in pedestrian-level and vehicle-level dynamic circumstances. Finally, an optimal loop which combines the proposed method and conventional method is designed to achieve the optimal performance both in weak and strong signal circumstances.

A Novel Carrier Loop Algorithm Based on Maximum Likelihood Estimation (MLE) and Kalman Filter (KF) for Weak TC-OFDM Signals

“…The MLE minimum variance unbiased estimation can be achieved by obtaining the maximum value of (10) to get the values A mp , Δ f and Δ φ . The diagonal elements of the diagonal matrix W are set as 1 to obtain the log-likelihood cost function of Equation (12) as in [ 31 , 32 ]: where Corr n = Corr ( n ), Corr N = [ Corr (0), Corr (1), ……, Corr ( N − 1)] is N consecutive coherent integration results. μ = [ A mp Δ f Δ φ ] T represents the signal parameters to be estimated, n = 0… N − 1, θ = 2 π Δ fnT coh + Δ φ , and represent the real and imaginary part respectively.…”

“…Tracking sensitivity is defined as the SNR at which tracking probability exceeds 50%. At present, the definition of tracking sensitivity can be divided into two types: the detection probability is 50% [ 31 ] and 90% [ 35 ]. In order to better illustrate the problem, this paper refers to [ 31 ] for the definition of tracking sensitivity.…”

“…At present, the definition of tracking sensitivity can be divided into two types: the detection probability is 50% [ 31 ] and 90% [ 35 ]. In order to better illustrate the problem, this paper refers to [ 31 ] for the definition of tracking sensitivity. According to the results of the detection probability of the proposed algorithm in Figure 11 , the SNR is adopted to be taken as the tracking sensitivity when the tracking probability is 50%, which can reflect the overall level of the performance of the algorithms.…”

A Novel Carrier Loop Algorithm Based on Maximum Likelihood Estimation (MLE) and Kalman Filter (KF) for Weak TC-OFDM Signals

“…The MLE minimum variance unbiased estimation can be achieved by obtaining the maximum value of (10) to get the values A mp , ∆f and ∆tϕ. The diagonal elements of the diagonal matrix W are set as 1 to obtain the log-likelihood cost function of Equation 12as in [31,32]:…”

A Two-Stage Kalman Filter-Based Carrier Tracking Loop for Weak GNSS Signals

“…Moreover, Ref. [10] assumed that the data bit sign had been eliminated before employing KF-based tracking because data bit reversals could cause incorrect KF estimations. Accordingly, it is necessary to achieve bit synchronization before KF-based tracking, especially when the coherent integration time should be extended for tracking weaker signals.…”