## 1 Introduction  
Passive forward scattering radars are a special class of passive bistatic radars (PBR), in which the bistatic angle \(\beta\) between the non-cooperating transmitter, the target and the receiver is \(\beta\approx 180^{\circ}\)[1; 2; 3]. In such kinds of passive radars, the illuminating signal can be a wave from a commercial transmitter of popular systems such as FM, DAB, DVB-T, GSM, and so forth [4; 5; 6; 7]. The simplified passive forward scattering radar (PFSR) geometry is presented in Figure 1.  
Unlike typical PBRs, the PFSR is characterized by the fact that objects cross the baseline, which has certain consequences. In such a case the PBR radar using classical PCL (Passive Coherent Location) processing is blind, as a target is crossing the line of sight between a receiver and a transmitter, and for PBR in this geometry there is no existing range resolution. Additionally, the target disturbs the reference signal, thus based on PCL principles it is difficult to detect the target at the line of sight to the transmitter as only the reference antenna is pointed in this direction, and surveillance beams are pointed in other directions. In bistatic radars a target moving at a velocity \(V\) provides the Doppler shift expressed as follows: [8]:  
\[f_{d}=\frac{2V}{\lambda}\cos(\alpha)\cos(\beta/2). \tag{1}\]As previously mentioned, in PFSR \(\beta\approx 180^{\circ}\), which makes \(f_{d}\approx 0\) (Hz). However, observing the object in a slightly wider range, that is \(\beta\in(180^{\circ}-\Delta,180^{\circ}+\Delta)\), where \(\Delta\) is a certain angle, it is possible to measure the Doppler rate (or equivalently the chirp rate (CR)). This parameter describes the kinematic properties of the measured object. The literature describes some methods of Doppler rate estimation in PFSR. [PERSON] et al. proposed in Reference [9] a four-step processing technique for the extraction of kinematic motion parameters of targets in forward scattering radar (FSR). The method is based on multiple matched filtration of the signal with simultaneous time-frequency analysis, resulting in the precise estimation of the motion parameters of a single object near the intersection of the baseline. However, a problem may be the analysis of several objects that intersect the baseline at the same time. In addition, due to multiple matched filtration and other processing operations, the complexity of the method is significant. The same authors developed this approach and described it in Reference [10]. Another solution is to use the Radon transformation to calculate the phase acceleration [11]. After transforming the signal into a two-dimensional distribution in the TF domain, the components responsible for the Doppler rate of objects are found. Analyzing the aforementioned papers, it can be noticed that the analysis in the TF domain is the proper approach to the PFSR signal's considerations. A waveform received by the radar can be treated as a non-stationary frequency modulated signal. In the vicinity of \(f_{d}\approx 0\) (Hz) the signal can be approximated as a linear frequency modulated waveform. This methodology was also presented in References [12; 13; 14]. This is due to the fact that the phase of the received signal can be described by the dependency:  
\[\phi(t)=-\frac{2\pi}{\lambda}\left[R_{1}(t)+R_{2}(t)-L\right], \tag{2}\]  
which can be approximated using Taylor expansion into the following formula [15]:  
\[\phi(t)\approx\frac{\pi}{\lambda}v_{p}\left(\frac{1}{L-D}+\frac{1}{D}\right)( t-t_{0})^{2}, \tag{3}\]  
where \(v_{p}\) is the velocity component perpendicular to the baseline \(L\), \(t_{0}\) is the moment when the target crosses the baseline and \(D\) is the range from the receiver to the crossing point (see Figure 1). As can be noted, Equation (3) describes the second order polynomial characteristic for the frequency modulated signals. The above considerations prompted the authors to use the CR estimation in the TF domain to analyze signals from PFSR.