## 1. Introduction

[2] Estimation of channel impulse response is an important ingredient in the design of reliable communication systems. The estimation process constitutes a first step in computation of scattering function, channel equalization, elimination of multipath, and optimum detection and identification of transmitted signals. The estimation of channel impulse response is a major challenge for noisy multipath channels that also vary both in spatial and temporal domains. The HF communication channel and underwater acoustic channel are the two examples where channel estimation has to performed adaptive to time variations of the channel. In HF band, due spatial and temporal variations at various scales, the channel response is usually obtained by controlled experiments conducted for specific links and frequency intervals of interest. In these experiments, typically, a predetermined narrowband input sequence is transmitted and the variability of the channel investigated based on the observed channel output sequence. This investigation requires the adaptive estimation of the channel response where the adaptation should be fast enough to capture the short term variations in the channel response.

[3] Kalman filter can be utilized as an ideal processing tool for estimation of the HF channel response [*Proakis*, 1995; *Haykin*, 1991; *Clark*, 1989]. However, Conventional Kalman Filters, as mentioned in *Clark* [1989], are operated with little or no adaptation to the physical structure of the channel. Since the performance of the Kalman Filter is very sensitive to the dynamics of the channel, careful initialization and proper adjustments of the operating parameters are required for improved performance [*Haykin*, 1991; *Arikan and Arikan*, 1998; *Miled and Arikan*, 2000]. In this paper, a robust method for the initialization of the Kalman filter is proposed. The measurement noise covariance matrix is modeled in an adaptive manner that represents the underlying varying physical structure of the ionosphere. The performance of the estimation algorithm is tested with the channel outputs obtained from simulated HF links under good, moderate and poor ionospheric conditions. With the new state-space model to capture the pulse-to-pulse variability of the channel impulse response and initialization, the tracking performance of the Kalman filter improved significantly compared to that of the Conventional Kalman Filter even under poor ionospheric conditions. According to *Clark* [1989], the major problems in application of conventional Kalman Filters can be summarized as the cost of implementation, computational complexity, tendency of a steady build-up of round-off errors compared with other possible estimators. All these problems can be overcome with new fast and cost-effective Digital Signal Processors.

[4] In Section 2, formulation of the state space model and the Kalman Filter will be presented. Also, the initialization of the Kalman filter parameters which considerably affects the performance of tracking will be discussed in detail. In Section 3, results for a computer simulated channel will be presented.