International Journal of Antennas and Propagation

Volume 2015, Article ID 864327, 11 pages

http://dx.doi.org/10.1155/2015/864327

## BDS Multipath Parameter Estimation in the Presence of Impulsive Noise

College of Automation, Harbin Engineering University, Harbin 150001, China

Received 25 September 2014; Accepted 18 January 2015

Academic Editor: Ding-Bing Lin

Copyright © 2015 Jicheng Ding et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This study focuses on mitigating the multipath, especially the short-delay multipath of the BeiDou navigation satellite system under impulsive noise conditions. A modified least mean -norm (LMP) algorithm is developed to reduce the convergence time with the same steady-state error by predicting the updating trend of weights. The modified normalized power and the normalized polynomial least mean th power are also directly provided according to a similar principle. According to the research work, an average filter has been utilized to improve the processing gain of designed mitigation scheme. Some significant simulation results verified the performance of the proposed adaption algorithm. Multipath parameter estimation tests have been conducted under different noise levels. Some comparative statistics performance assessments are quantified and verified under impulsive and additional white Gaussian noise environments. Results with various window widths of the average filtering and carrier-to-noise ratios indicate that the proposed scheme is able to improve the performance of the short-delay multipath mitigation under normal and degraded environments.

#### 1. Introduction

The BeiDou navigation satellite system (BDS), which currently covers the Asia Pacific region, is aimed at entering the global network stage and becoming a global navigation satellite system (GNSS) in 2015. The BDS will eventually operate in the ocean, urban, and indoor environments, similar to the global positioning system (GPS) [1].

The multipath problem has received considerable attention in recent years as the dominant error source in the preceding applications. Traditional techniques suffer from a common drawback in their ineffectiveness to suppress short-delay multipath signals (i.e., less than approximately 20 m) with respect to the line-of-sight (LOS) signal [2]. This situation is a big limitation because the real-life multipath tends to be the close-in, short-delay type. The a posteriori multipath estimation (APME) [2], swarm intelligence optimization algorithms [3], and adaptive filtering techniques [4, 5] are the approaches used to suppress the short-delay multipath. The APME has improved in order to suppress the short-delay multipath signal, but its rejection of the medium-delay multipath is unsatisfactory. The swarm intelligence optimization method is difficult to be implemented for practical applications because of its computational complexity. The adaptive filtering method is a practical technology which includes the recursive least squares (RLS) adaptive filtering algorithm and is mostly based on Gaussian assumptions. The RLS using the minimum mean square error criterion completes the inverse and iterative adaptive operation by using a simplified matrix and provides a small steady-state error. Accordingly, the limitations of the RLS are defined by the optimal assumptions. This condition ensures an analytical solution for the detection of a known signal in additional white Gaussian noise (AWGN) [4–6] in most cases.

The GNSS signal is buried in noise due to limitedly transmitted power from the satellites. Some effective algorithms mostly are based on the signal despreading to obtain enough processing gain. Compared with the signal-to-noise ratio (SNR), the carrier-to-noise ratio (CNR) is more easily accepted by lots of literatures to assess the performance of a GNSS receiver. It is defined according to the noise power in a 1 Hz bandwidth. In fact, in the context of digital modulations, digitally modulated signals are usually referred to as carriers. Therefore, the term CNR, instead of SNR, is preferred to express the signal quality when the signal has been digitally modulated. Moreover, the traditional adaptive filter has to be applied before the signal despreading, which leads to a limited processing gain. However, this problem has apparently not been discussed in [4–7].

As mentioned previously, the growing need for indoor GNSS and the increasing demand for satellite-based navigation in manned and autonomous ground, aerial, and surface vehicles have to be addressed. Hence, the GNSS receivers are operated in close proximity to various noise sources with Gaussian and non-Gaussian characteristics. Such non-Gaussian random signals contain a large number of outliers. These outliers disturb the receiver’s performance by impeding the baseband signal processing phase and increase the ranging error and bit error rates [8]. References [8–11] have thoroughly analyzed these non-Gaussian impulsive sources and the effect on the receiver, which operates in the GNSS operating band. For instance, the impulsive signal source is the ultrawideband signals which cover the GNSS operating band and are adopted more and more in outdoor and indoor environments. The model for these signals cannot be justified because of the Gaussian noise. Accordingly, an important class of distributions (i.e., a-stable distributions) is used to model this type of impulsive noises [11–14].

In order to overcome these problems, many variations of the least mean squares (LMS) have been proposed over the past decades. These LMS methods include the variable step-size approach [15], the affine projection algorithms [16], and the higher- or lower-order statistics method [17]. The third method yields many robust algorithms with improved convergence rate and robustness against the impulsive interference. The higher- or lower-order statistics method includes the least mean -norm (LMP) and its normalized version (NLMP algorithm), which have been reported in [17, 18]. Additionally, [19] has proposed the normalized polynomial least mean th power (NPLMP) to improve the algorithm convergence rate by extending the LMP algorithm. Moreover, some variable step-size sign algorithms similar to the extended LMS are also effective to accelerate the convergence process [20]. This study introduces another method to accelerate the LMP algorithm convergence process by using a self-tuned weighted term, which is an extension from other classic algorithms.

The structure of the paper is as follows. In Section 2, a BDS multipath parameter estimation scheme based on adaptive filter with an average filter is designed. Section 3 presents the derivation and analysis of the modified LMP adaptive filter and some extended algorithms which use the self-tuned weighted term. A variety of comparable tests are conducted in Section 4. The interesting results and analysis are also presented in this section. The conclusions are provided in Section 5.

#### 2. BDS Multipath Parameter Estimation

##### 2.1. BDS B1 Signal Model in Multipath Environments

The description of the statistical model of the received signal in the presence of a multipath is difficult in the case of a BDS. Nevertheless, many hypotheses are made. One of these hypotheses assumes that the multipath signals are delayed with respect to the direct BDS signal. The reflected signals with a delay of less than one chip will usually be considered because the signals with a code delay which is larger than one chip are uncorrelated with the direct signals; otherwise, the multipath signal is assumed to have lower power than the direct one. The baseband signal model is represented as follows: where represents the LOS component; is the ranging code, which modulates the Neumann-Hoffman code; is the sampling period; is the immediate frequency; is the noise; and , , and are, respectively, the amplitude, carrier phase, and code delay of the th delay component.

Unlike GPS signals, the NH code period is selected according to the duration of a navigation data bit [21]. The bit duration of the NH code is equal to bit period of the ranging code. The duration of one navigation data bit is 20 ms, while that of the ranging code is 1 ms (Figure 1). The NH code (0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0) with a length of 20 bits, a rate of 1 kbps, and a bit duration of 1 ms is synchronously modulated on the ranging code with the navigation data bit.