# Optimal Order of Time-Domain Adaptive Filter for Anti-Jamming Navigation Receiver
###### Abstract  
Adaptive filtering algorithms can be used on the time-domain processing of navigation receivers to suppress interference and maintain the navigation and positioning function. The filter length can affect the interference suppression performance and hardware utilization simultaneously. In practical engineering, the filter length is usually set to a large number to guarantee anti-jamming performance, which means a high-performance receiver requires a high-complexity anti-jamming filter. The study aims at solving the problem by presenting a design method for the optimal filter order in the time-domain anti-jamming receiver, with no need for detailed interference information. According to interference bandwidth and jam-to-signal ratio (JSR), the approach designed a band-stop filter by Kaiser window for calculating the optimal filter order to meet interference suppression requirements. The experimental results show that the time-domain filtering processing has achieved good interference suppression performance for engineering requirements with optimal filter order in satellite navigation receivers. Global Navigation Satellite System (GNSS) receiver; time-domain anti-jamming; adaptive filter processing; Kaiser window; optimal filter order +
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prediction. The former obtains the power spectrum of the received signal and then designs a transverse filter to significantly attenuate the interference signal's frequency band [12; 13]. While the latter directly estimate the pole position of the filter through the signal and suppresses the interference signal through linear prediction [14]. The adaptive algorithms based on linear prediction, such as least-mean-square (LMS) algorithm [15], Recursive-least-square (RLS) algorithm [16], Levinson-Durbin algorithm [17], Burg algorithm [18], can be used in the time-domain anti-jamming navigation receivers and have achieved good results in anti-narrowband interference [19]. The four kinds of algorithms are all based on the MMSE (Minimum Mean Square Error) criterion to calculate the inverse of the sampling matrix to obtain the optimal weight vector. Although the inversion methods are different, the weight vectors after convergence are all close to the Wiener solution [20]. The LMS algorithm is often used in practical engineering applications due to its simple algorithm, small calculation amount, and easy convergence [15]. The interference suppression performance can usually be improved by increasing the filter length, but more calculations are required for the hardware [10]. Based on the LMS algorithm, the variable-tap-length algorithm based on optimal order selection is derived to solve the high complexity caused by undetermined filter order. Segmented Filter LMS algorithm and Gradient Descent LMS algorithm searched for the optimal filter order adaptively by the iteration step [21; 22]. Fractional Tap-length LMS removed the restriction that the filter length must be an integer, adding flexibility to the filter order variation [23]. Refs. [24; 25] proposed algorithms for updating both the iteration step and filter order. However, when the anti-jamming performance is very categoric, such as 5 dB, the existing algorithm cannot adjust the filter length adaptively according to the actual requirements. Therefore, it is usually set to a large number to guarantee anti-jamming performance. This study presents an optimal design method for adaptive filter order in time-domain anti-jamming processing based on the Kaiser Window. This paper introduces a design method of the optimal adaptive filter order based on prior interference knowledge. Section 2 introduces the mathematical model of time-domain anti-jamming filters, and an improved LMS algorithm is used in time-domain adaptive processing to suppress the interference. The analysis of filter order deduced from the Kaiser window is detailed in Section 3.