## 3 Multipath Interference Suppression
Step 2: Perform matching filtering as [27]

\[S_{out}(v_{m},H_{m})=\int_{-\frac{T}{2}}^{\frac{T}{2}}y^{*}(t)\cdot f(t)dt, \tag{32}\]

where \(T\) is the observation time, \(*\) represents the conjugate operation, \(S_{out}(v_{m},H_{m})\) stand for the output result, and \(y(t)\) is the received signal after interference suppression. Substituting the known relationship between \(v\) and \(H\) into (32), we can obtain

\[S_{out}(H_{m})=\int_{-\frac{T}{2}}^{\frac{T}{2}}y^{*}(t)\cdot f(t)dt. \tag{33}\]

Step 3: To obtain more accurate estimates. In this process, \(\Delta v\) and \(\Delta H\) are shortened to obtain a more accurate estimate according to the estimated \(v\) and \(H\) values. ### Parameter Estimation Based on MF+LCT

Since the LCT can achieve effective separation of signal and noise by reducing the influence of noise on matched filtering, the LCT process is performed on the matched filtering. The target parameter estimation system diagram based on MF+LCT is shown in Figure 11.

After matching filtering, the signal is transformed into the LCT domain, and the target parameters are estimated by searching for the peak value. The steps of parameter estimation based on MF+LCT are as follows:

Step 1: Construct the feature function as

\[f(t)=a_{F}e^{\jmath 2\pi\ell_{c}q(v,H)t^{2}}, \tag{34}\]

Figure 11: Target parameter estimation system diagram based on MF+LCT. where \(a_{F}\) represents the amplitude of the characteristic function, \(f_{c}\) is the carrier frequency, and \(q(v,H)\) stands for a function about the parameters \(v\) and \(H\) with \(q(v,H)=\frac{v^{2}\cos\delta_{SV}\big{(}1-\cos^{\theta}\theta_{v}\sin^{2} \theta_{SV}\big{)}}{2 CH}\). Step 2: Perdom matching filtering and transform it to LCT domain as

\[SL_{out}(v_{m},H_{m})=\frac{1}{\sqrt{2\pi b}}\int_{-\frac{T}{2}}^{\frac{T}{2}} y^{*}(t)\cdot f(t)e^{i\frac{\theta}{2b}t^{2}-j\frac{t}{b}t+j\frac{\theta b^{2}}{2 b}}dt, \tag{35}\]

where \(T\) represents the observation time, \(*\) denotes the conjugate operation, \(S_{out}(v_{m},H_{m})\) is the output result, and \(y(t)\) stands for the received signal after interference suppression. ## 7 CRLBs of Target Parameter Estimators

Assume that \(y(t)\) is the signal after interference suppression and contains only echo signals and noise, and thus \(y(t)\) can be rewritten as:

\[y(t)=a_{Tt}e^{i2\pi f_{0}(\tau_{d}-\tau_{t})}+m(t), \tag{36}\]

where \(a_{Tt}\) represents the amplitude of the echo signal, \(m(t)\) is Gaussian noise with mean zero and \(\Delta\tau=\tau_{t}-\tau_{d}\). The power spectral density of the noise is

\[E\big{[}m(t)m\big{(}t^{\prime}\big{)}\big{]}=0, \tag{37}\]

\[f(t)=a_{F}e^{\jmath 2\pi\ell_{c}q(v,H)t^{2}}, \tag{31}\]0

The vector form of the estimation speed and the estimation height can be expressed as

\[f(t)=a_{F}e^{\jmath 2\pi\ell_{c}q(v,H)t^{2}}, \tag{31}\]1

The probability density function (PDF) of the echo signal can be expressed as [28; 29]:

\[f(t)=a_{F}e^{\jmath 2\pi\ell_{c}q(v,H)t^{2}}, \tag{31}\]2

Accordingly, the natural logarithmic of PDF is given by

\[f(t)=a_{F}e^{\jmath 2\pi\ell_{c}q(v,H)t^{2}}, \tag{31}\]3

By differentiating the logarithmic PDF, one has

\[f(t)=a_{F}e^{\jmath 2\pi\ell_{c}q(v,H)t^{2}}, \tag{31}\]4

and

\[f(t)=a_{F}e^{\jmath 2\pi\ell_{c}q(v,H)t^{2}}, \tag{31}\]5

According to the parameter estimation theory, the CRLB is

\[f(t)=a_{F}e^{\jmath 2\pi\ell_{c}q(v,H)t^{2}}, \tag{31}\]6

where \(\big{[}I^{-1}(\theta)\big{]}_{ii}\) is the \((i,i)\)-th element of the inverse matrix of the FIM matrix, and the FIM matrix is

\[f(t)=a_{F}e^{\jmath 2\pi\ell_{c}q(v,H)t^{2}}, \tag{31}\]7Define the following variables

\[f(t)=a_{F}e^{\jmath 2\pi\ell_{c}q(v,H)t^{2}}, \tag{31}\]8

\[f(t)=a_{F}e^{\jmath 2\pi\ell_{c}q(v,H)t^{2}}, \tag{31}\]9

and

\[S_{out}(v_{m},H_{m})=\int_{-\frac{T}{2}}^{\frac{T}{2}}y^{*}(t)\cdot f(t)dt, \tag{32}\]0

The elements of the available FIM matrix are

\[