Anti-Multipath Filter with Multiple Correlators in GNSS Receviers

2.1. Multipath overview

Multipath effect is caused by the reflection of satellite siganl by obstacles when the receiver receives the reflected signal, it leads to positioning error and the lock failure of signal for receiver, which renders positioning funciton void. In GPS, the desired signal consist of only the direct path signal. All other signals distort the desired signal and result in ranging measurement errors. To understand the effect of multipath in measurement process, let’s consider the heart of the GPS code tracking loop. The pseudorange measurement originates from a locally generated pseudorandom noise (PRN) code which is kept phase-locked to the received code. The discriminator is formed based on the difference between early correlator output and late correlator output. The output of the discriminator is fed back to the local code generator to keep synchronism between the local code and incoming code. This generatess the so-called delay-locked loop (DLL). When multipath is present, the incoming code, correlation function and discriminator functions are distorted. Analytically, the direct and multipath components may be conducted separately. Note that for the direct-path case, the discriminator function passes through zero when the code-tracking error (local-code delay) is zero. This is the ideal case. However, when multipath is present, the distorted function has a zero-crossing at non-zero code tracking error. Fig. 1 demonstrates the tracking errors of the early-late discriminator output due to multipath in the DLL. The tracking errors result from distortion of the correlation function with the received IF signal. In the direct-path case, the ideal case is when the discriminator function passes through zero while the code tracking error is zero. However, with the presence of multipath, the distorted function has a zero-crossing at a non-zero code tracking error. With the direct signal, when the relative multipath phase is 0 radians, the multipath component is ‘in-phase’. With pi radians, the multipath component is ‘out-of phase’.

Thus, pseudorange multipath analysis encompasses simulation of direct and indirect path signals and determination of zero-crossing of distorted discrimintator function. There are three multipath parameters to consider: strength, delay and phase. The absolute value of each parameter is irrelevant. The upper and lower bounds of the multipath error can be determined, for a given multipath-to-direct ratio, by fixing the relative multipath phase at 0 and pi radians, respectively, and varying the relative multipath delay. At each delay point, the distorted discriminator curve is determined and the resulting zero-crossing point and pseudorange error are calculated. The result of an example is presented in Fig. 2, which illustrates result of the theoretical multipath error envelope versus the multipath delay. The code autocorrelation sidelobes have been ignored. This simulation is offered in the case of 24 MHz bandwidth receiver filter, 1-chip, 0.5-chip, and 0.2-chip early-late (E-L) spacing and unaltered multipath amplitude. A conventional GPS receiver adopts a delay-lock loop with a 1-chip spacing between early and late correlators. The smaller E-L spacing is regarded as narrow-correlator architecture. Narrow-correlator receivers typically utilize spacings in the range of 0.05 to 0.2 PRN chips.

2.2. Signal model

A GPS receiver may receive a number of reflected signals and direct signal from the satellite. The error source of GPS consist of ionosphere delay, troposphere delay, receiver noise and multipath effect. Except for multipath, the other errors can be significantly decreased through advanced prediction and differential correction method. It is hard to depict the statistical model of the received signal in the presence of multipath. However, many hypotheses can still be proposed. One hypothesis describes that the multipath signals are delayed with respect to direct GPS signal. Thus, let’s consider only these reflected signals with a delay of less than one chip. This is because signals with a code delay larger than one chip are uncorrelated with the direct signals. Otherwise, the multipath signal is assumed to have the lower power than the direct one. The composite baseband signal, ignoring the navigation data bit, is given by

where α k , θ k and τ k denote amplitude, carrier phase, and code delay of k- th delayed signal. M represents the number of multipath component. p ( · ) indicates spread-spectrum code. ω denotes the IF angular frequency. The notation z [ n ] = z ( n T s ) is employed to denote a digital sequence sampled at the frequency f s = 1 / T s where T s indicates period of sampling and n is the discrete time index. The 0-th delayed signal corresponds to the direct signal. ν [ n ] is modeled as white Gaussian noise distribution. The positioning error caused by the reception of multipath and direct signal is not only associated with the hardware design of receiver but also the detection algorithm. The literature review has provided several solutions for multipath effect. The following chapter will describe the proposed algorithm to counteract multipath.

2.3. Multiple correlator concept

The design of multi-correlator is seldom implemented due to the consideration of processing speed of hardware and cost. Owing to the promotion of hardware speed, decrease of cost and emergence of software wireless, the application of multi-correlator technique to receiver has become more prevalent. In fact, the strobe correlator described above is one of multi-correlator technique, which utilizes the linear combination of two correlators as discriminator output and adjusts chip spacing to track signal. Multi-correlator technique can depict the signal distribution after correlation process. In other words, this technique can present the process of correlation output in detail. Fig. 3 demonstrates the correlation output using 1 and 32 correlators, respectively. This figure illustrates that the multipath component can not be apparent if it adopts one set of correlator (early, prompt, and late). On the contrary, the 32 sets of correlator can better present the distribution of correlation output. Assume there are five correlators and the correlation of received signal is known. The linear combination of the five correlators can constitute received signal, which is expressed as:

v denotes each measurement value of correlator, Q indicates the number of correlator, r is corresponding correlation value and u is the scaled value of correlation center itself. Take the five correlators as example. Assume five correlators are located at -0.5, -0.25, 0, 0.25, 0.5, respectively. The combination of five correlators can be employed to accomplish the measurement value of each correlator. Equation (1) is rewritten as follows:

The makeup of v is consitituted by third correlation (location as 0) because the Λ of the rest correlators is 0. The makeup of R is based on the location of selected correlator. With the v and R matrix known apriori, the magnitude of the signal in terms of the distribution set up by correlator can be known based on Λ = R − 1 v . The more the correlators, the clearer the distribution of the signal.

It is known that the muti-correlator can depict the makeup of signal. Thus, we will see if multi-correlator can estimate direct signal with the direct signal plus multipath signal. Assume the multipath delay as 0.25 chip, signal magnitude as 0.5 and five correlators are shown as Fig. 4. Based on Λ = R − 1 v , the distribution of signal is known. Apparently, a correlation value exists between third and fourth correlator and the Λ of fourth correlator is lower. Using the negative correlation value form fourth correlator, we can elminate multipath. Fig. 5 illustrates the multipath mitigation when the location of time delay is at the location of set multi-correlator.

When the multipath delay is not at the set correlator, the calculated value after the above deduction approximates direct signal with little gap. Fig. 6 demonstrates the scenario when the location of multipath time delay is not at the location of set correlator.

2.4. Anti-multipath filter with multiple correlator

The previous chapter has clearly presented the advantage of multi-correlator method and its operation process. This chapter will elaborate how to constitute an anti-multipath filter based on multi-correlator. Fig. 5 shows the block diagram of the multipath mitigation system. The received signal is processed in a RF filter, then downconverted and sampled to a digital IF signal.

The tracking module consists of multiple correlator, code/carrier generator, discriminator and filter. The purpose of this module is to acquire accurate code phase and the carrier phase from PLL and DLL. The multipath estimator is used to estimate the correlation parameter of multipath, on the basis of the adaptive filter by employing duplicated signal and digital IF signal. Fig. 7 demonstrates that the estimated signal parameters are sent to the correlation decomposer and the correlation value of multipath signal is determined in the multipath cancellation area.

The estimated delayed signal is recreated at the Adaline-based filter and is subtracted from the correlation value of the received signal. The process of multi-correlators, multipath estimator, correlation value decomposer, and multipath cancellation will be elaborated in the following subsections.

3.1. Simulation parameter

The digital IF frequency of a GPS signal is ω / 2 π =1.25 MHz and the sampling rate is 5 MHz. The delay chip of the multipath signal varies from 0 to 1.5 chips with the phase of 0 and π radians with regard to the direct signal. In conventional correlator simulations, code phase error and carrier phase error are computed with 1 chip early-late discriminator. The chip spacing of a narrow correlator is less than 1 chip. A spacing of 0.2 chips utilized to serve the discriminator functions. Two different narrow correlator discriminators are adopted in a strobe correlator and the chip spacing of the two narrow correlators can be adjusted to 0.1 and 0.2 chip. The same parameters are also adopted in both enhanced strobe and edge correlators. The E1/E2 tracker of the two correlators is located at E 1 =- 0.55 and E 2 =- 0.45 with 0.1 chip spacing (Irsigler, M. et al, 2003). The Adaline-based adaptive filter method with the parameter of tap delay d τ = 0.01 chip, 0.1 chip, 0.5 chip and its 5 delayed tap is employed as the input to the filter. The number of multi-correlator is set as five. The initial learning rate is 0.05, the number of training samples is 5000 at 1ms C/A code period and the weights are initialized to 1. The performance is assessed on a separate test set of 100ms samples measured at intervals of 1ms samples during the adaptive process.

3.2. Performance analysis and comparison

With regard to crucial multipath mitigation techniques of internal receiver, the multipath performance of these correlation techniques will be compared with each other, including the proposed method. Thus, the envelopes of all techniques described above are plotted into the same diagram to make a comprehensive comparison of multipath mitigation performance

Figs. 10-12 compare the error envelopes of the code phase and carrier phase for all of the multipath mitigation techniques. Simulation results show that the proposed method with multipath delay at the location of set correlator as d τ = 0.5 chip case has both the best multipath mitigation performance. Assume the location of correlator is not at multipath delay ( d τ = 0.1 chip), it also presents good performance. The conventional PLL has a maximum 0.52 radians in carrier phase error. Therefore, the use of the conventional correlator can yield very large maximum multipath errors and reveals the worst mitigation performance. The same results hold true for both narrow and edge correlators. Note that since the narrow, the MEDLL, the edge and strobe correlators do not provide any carrier phase elimination, their sensitivity to multipath is almost the same as the 1-chip early-late correlator. Only slight differences can be observed due to differences in their code multipath mitigation.

These figures indicates that through the use of proposed method in combination with multi-correlator technique with a delay element d τ = 0 .5 chip, both code and carrier phase errors are reduced in the range of delay from 0 through 1.5 chip. In contrast, through the adoption of the proposed method with a tap delay d τ = 0 .5 , the code and carrier phase error decrease significantly in the range of delay from 0 to 1.5 chip. The figure shows that the use of multi-correlator technique can effectively reduce code phase error. Nevertheless, for carrier phase error, its performance remains the same. The reason is because carrier phase error is not related to multi-correlator. In the case of the tap delay d τ = 0 .5 , multipath mitigation performance degrades in comparison with the case of d τ = 0.1 . This is because to the accuracy of the estimated delay profile in the Adaline-based filter depends on the tap delay d τ . The smaller the d τ the better the performance of multipath mitigation. In the case of the d τ = 0 .5 chip, the multipath mitigation performance degrades in code phase error and the carrier phase error also exceeds that of the conventional tracking loop. Though the use of a small tap delay can yield high performance in multipath mitigation, it also takes large computation cost to estimate delay profiles. However, the use of multi-correlator can save computation cost to estimate delay profiles.

Note that Fig. 11 reveals that every DLL structure lacks of performance enhancement for short delay multipath signals. Nevertheless, the proposed method with multi-correlators can perform better in short delay and medium-to-long-delay multipath environment. Suppose a given application involves short delay and medium-to-long-delay multipath, then the best correlation techniques such as the enhanced strobe correlator will not outperform the proposed method of this paper.

To accomplish estimated performance of proposed method, the desired correct of multipath delay profiles are set α 0 = 1 . 0 , α 1 = 0 . 5 , τ 0 = 0 , τ 1 = 0 .7 5 , θ 0 = 0 ∘ and θ 1 = 0 ∘ . The delay element number is five and the number of multi-correlator is set as five. An estimated multipath delay versus the true multipath delay curve for three considered algorithms, the MEDLL and the Adaline-based filter with and without multiple correlators, is shown in Fig. 13. Note that the proposed method with and without multi-correlator technique of d τ = 0.01 has the faster convergence rate than the MEDLL. The Adaline-based filter without multi-correlator technique is rapid in convergence rate with d τ = 0.1 . However, it suffers from a steady state error 0.03 chip in delayed estimation. Nevertheless, the use of five multi-correlators with shift 0.1 chip, the error approximates zero.

Several concessions exist in these architectures such as: noise performance, code versus carrier performance, a priori information needed as input, short delay performance and hardware/software complexity. These factors are compared in Table 1. This performance comparison is on the basis of the published methods and simulation results of this paper. The research analysis is shown in the following:

Concerning the noise mitigation performance, when SNR =-10dB, the simulation result presents that the narrow correlator and proposed method with multi-correlators are the best in performance with the code tracking error of about 0.034 chip and 0.04 chip, respectively. The proposed method without multi-correlators in this paper is medium in performance with the tracking error of around 0.05~0.1 chip, which equals the medium noise performance of the edge and E1/E2 correlator. In contrast, the conventional correlator, strobe, enhanced strobe correlator and the MEDLL are inferior in noise performance, with the tracking error around 0.2 chip.

In term of the GPS mobile applications, high precision is required even at the expense of slightly increased complexity. The best options are the enhanced strobe correlator and the Adaline-based filter. The proposed method has the best performance in multipath mitigation. Nevertheless, its hardware complexity, such as the number of required multiplications per delay estimate is on the order of O [ N i t e r ( K d τ ) 3 ] where N i t e r is the number of filter iterations and K d τ is an estimate of the maximum delay spread of the channel in the samples. The high complexity of this method is principally due to the matrix inversion operations. However, in short-delay and medium-to-long delay multipath environments, the number of delay samples K d τ are smaller. Thus, the complexity of the Adaline-based filter is not very high. The enhanced strobe correlator has lower complexity, on the order of O [ ( K d τ ) 2 ] , but it does not perform as well as Adaline-based filter. With regard to design perspective, the best tradeoff between accuracy and complexity should be determined based on estimated maximum delay spread of the channel.

Concerning the conventional receiver design for civilian application, the lowest complexity solutions of the 1-chip E-L correlator and the narrow correlator, appear to be the best choice. What is more, complexity is the top priority and is emphasized more than performance in the design of a receiver provided that no significant degradation in performance occurs. All of the conventional, strobe and narrow correlator designs have least medium performance and reduced complexity in multipath scenarios. Hence, they are viable options for a low complexity receiver. In comparison, even though the edge, the E1/E2 and the MEDLL designs are higher in cost, they are better than the conventional, narrow, and strobe correlators in performance.

In fact, there are inherent limitations in almost every technique. Note that the combined features of proposed method prevails over those of other techniques. In addition, the condition of short-delay and medium-to-long-delay multipath renders the effect of hardware complexity in Adaline-based filter insignificant. Consequently, the proposed method is a well-suited and well-balanced application in multipath mitigation.