## 1. Introduction

The positioning tecnique of global navigation satellite systm (GNSS) has become mature and also been applied to a variety of navigation vehicles, whether it be the application to ground vehicle ot aircraft. Nevertheless, the precision of GNSS is susceptible to intentional or unintentional factors such as interference or jammer, etc. The influences range from minor effect like the positioning precision of satellite signal to significant impact like the misleading information to users or malfunction of receivers. The ionosphere or troposphere in environment or the noise in receiver itself are the source of positioning error when satellite passes through ionosphere or troposphere, the change of media results in the delay of wave transmission rate and yields error. The adoption of dual frequency receiver can decrease error but it presents no significant improvement in terms of the error generated by multipath.

The effect of multipath is because the satellite signal is reflected or diffracted by obstacle prior to its receiption by antenna. Most of the time, it results in the decrease of signal propagation power and delay of time. In 1973, Hagerman employed conventional code tracking to analyze the effect of multipath on the coarse/acquire (C/A) code in carrier L1 using one chip of early-late spacing. He also estimated that under different delay, phase and signal magnitude, the effect may result in 70−80 m tracking error [Hagerman, 1973]. With the growing application of global positioning system (GPS), many researches investigating multipath effect have been proposed to effectively reduce its impact and have provided various estimation algorithms for implementation in hardware.

The most effctive solution for multipath effect is the location of antenna. Assume the antenna is placed above the highest source reflection, the reflected signal will not be received. In antenna design, it can reduce the gain of received signal coming through lower elevation. Generally, the receiver will setup up the minimum elevation capable of receiving satellite signal. The design of choke ring antenna is used to mitigate multipath. The choke ring antenna circles the antenna with vertical concentric rings, whose function is to reduce the gain of received reflected signal. However, such a function is strongly related to the location of antenna.

In additioon, the change of structure in internal correlator design of receiver is also a solution for multipath. The conventional GPS receiver typically adopts one chip early-late spacing of correlator. The use of narrow correlator to reduce chip spacing can effectively mitigate multipath and noise, which cuts down the error of 70−80 m to 8−10 m (van Dierendonck et al., 1992). Note that the use of narrow correlator technique in coherent discriminator may lead to the lock failure in code delay locked loop without the cooperation of phase locked loop (PLL).

The strobe correlator and edge correlator are both solutions for multipath mitigation (Garin et al., 1996). The strobe correlator is implemented using two different narrow correlator discriminators. The strobe correlator and edge correlator developed by Ashtech only provide code correlation for C/A code. The enhanced strobe correlator (Garin and Rousseau, 1997) offers carrier phase correction and code correction for C/A code. With the additional carrier phase correction in terms of multipath its real-time dynamic processing outperforms previous methods. Note that the narrow correlator and strobe correlator do not encompass carrier phase correction. Thus, their sensitivity approaches that of conventional correlator.

Another discriminator design is early 1/ early 2 (E1/E2) correlator (Mattos, 1996; van Dierendonck and Braasch, 1997). The method utillzes part of correlation coefficients not subject to multipath effect for multipath mitigation. That is, it employs two correlators with the spacing and location at the front end of correlation function. However, this method is a choice between noise mitigation and multipath mitigation.

The multipath estimation method initial estimates multipath signal and then subtracts it from received signal so that the signal approaches direct signal. Literature review that resembles this algorithm are MEDLL, MET. (van Nee, 1992; van Nee et al., 1994), which utilize maximum likelihood estimation technique and recursive least square method to estimate the magnitude, delay, phase and erase it from received signal. Though the above estimation methods can not completely eliminate multipath signal, they present significant improvment in terms of multipath delay within certain range.

Nevertheless, these techniques have difficulties in mitigating short-delay multipath signals (less than 0.1 PN code chip or approximately 30 m). Scholars have proposed methods on short-delay multipath mitigation (Sleewaegen et al., 2001; Stone and Chansarkar, 2004). However, these techniques still have drawbacks. The method proposed by Sleewaegen requires a scaling factor, depending on multipath environment, to link the signal amplitude with the range error. The method proposed by Stone and Chansarkar is to estimate the pseudorange error on the basis of a statistical model, which requires large numbers of collected data. Consequently, the performances of these two methods are significantly influenced by multipath environment.

The author has proposed an adaptive filter in 2008 (Chang and Juang, 2008), which adopts five tap-delay to effectively mitigate short-delay multipath. Though this method is efficient in short-delay multipath mitigation, it does not guarantee that the receiver will not receive multipath signal at different time delay under variable environment. Moreover, the correlator technique of coventional receiver is not quite capable of accurately describing the data distribution of correlated signal, which results in longer period of time to estimate multipath parameter. Thus, this paper utilizes multi-correlator technique in combination with proposed method to mitigate the mystical multipath signal. Simulation results show that the multi-correlator technique can clearly present the output distribution of correlator, make adaptive filter rapidly estimate multipath parameter and cope with multipath signal at different time delay.

## 2. Methodology

### 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

### 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:

(3) |

The makeup of

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

(4) |

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.

#### 2.4.1. Multi-correlators techniques

The concept of multi-correlator and the process of this method have been detailed in previous chapter. What we consider for the time being is that initial point of code delay of received signal and the local replica is not identical and multipath does not take place at the set correlator. Thus, paralell shift method is utilized to change the element of

#### 2.4.2. Adaline-based filter

The function of a multipath estimator is to estimate the multipath delay using Adaline-based filter, shown in Fig. 9. It adopts the tap-delay line with an Adaline network (Widrow and Hoff, 1960) to constitute this structure without a non-linear element. An adaptive algorithm such as the LMS algorithm or the Back-Propagation (BP) learning algorithm is often employed to adjust the weights of the Adaline so that it responds accurately to as many patterns as possible in a training set. It is the simplest and most intelligent self-learning system which adapts itself to achieve an optimal solution (Rumelhart, D. E. et al, 1986). In this paper, the BP with an adaptive learning rate algorithm serves as a substitute for the LMS algorithm so as to prevent inherent limitations in LMS and to improve filter convergence rate (Schalkoff, R. J., 1997). The multipath estimator offers the multipath delay profile. Suppose the estimated digital IF signal is given by:

Where the parameter with the symbol “

where

where

The filter minimizing the cost function is chosen by its tap weights to be the optimal solution to the normal equation (Haykin, S., 1986).

where

where

#### 2.4.3. Correlation extractor

After the use of adaptive filter, the estimated parameters can be obtained and the correlation decomposer divides the estimated parameters into multipath and direct signal. Besides, the autocorrelation function of multipath signals is subtracted from analog-to-digital (A/D) converter output of the received signal. In the decomposer process, it is assumed that the values of the first peak amplitude tap weight are the direct signal and the remainders are multipath signals. Fig. 5 presents an example where the direct signals refers to the first peak

where

Hence, the entire correlation value of the estimated multipath signal

#### 2.4.4. Multipath removal

The entire correlation values of multipath signal

In (12), the estimated correlation

The tracking error takes place in DLL and PLL due to the multipath effect. The effect primarily results from distortion of the correlation function receiving the IF signal, shown in Fig. 8(a), which illustrates the normalized correlation function with multipath effect. Fig. 8(a) presents that the symmetry is lost and the propagation delay is difficult to estimate. Thus, the range measurement accuracy is diminished. Nevertheless, the use of a subtractive method offers multipath mitigation in the tracking loop and the output

The above processes: the estimate process, the correlation extractor and the cancellation method can counteract the multipath effects regarding the autocorrelation function of the received signal, since the tracking errors in DLL and PLL are not completely eliminated. Provided that the reference signal acquires the multipath error, the estimated parameters do not present accurately that of the real multipath. So as to obtain the ideal estimated parameters, the BP learning process is recursively employed. The use of multi-correlator technique can speed up BP learning process and enhance its performance.

## 3. Performance analysis and simulation results

In this section, computer simulations are performed to evaluate the performance of proposed method. To compare with other published methods in performance, the multipath tracking error envelopes in code and carrier phase for a multipath signal amplitude of half the LOS amplitude is denoted as

### 3.1. Simulation parameter

The digital IF frequency of a GPS signal is

### 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

These figures indicates that through the use of proposed method in combination with multi-correlator technique with a delay element

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

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

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.

## 4. Conclusion

Multipath is the primary error source in high-precision-based GNSS applications and is also a significant error source in non-differential applications. Various receiver designs have been on the market and claim various multipath mitigation functions. Most of these techniques can be characterized either as discriminator function shaping or correlation function shaping. In this paper, an Adaline-based filter with multi-correlators method is adopted in multipath mitigation for GNSS application. A simplified direct plus multipath signal model is employed in this simulation. This approach enhances the performance of code phase and carrier phase errors compared with other published methods. Simulation results demonstrates that the proposed method is a viable and effective solution to increase the positioning accuracy for GNSS navigation in the presence of short-delay and medium-to-long-delay multipath environment.