*2.1. Measurement Model*

We studied CMoN of a polynomial smooth scalar function *h* of a non-random variable *x* in [35], where

$$h(\mathbf{x}) = a\mathbf{x}^n,\tag{1}$$

and *a* is a non-zero scalar. In scenarios considered, *x* > 0 and *n* = 2, 3, 4, 5.

**Remark 2.** *For MoN of other forms of nonlinearity, such as the bearing-only [27], GMTI [32], and video filtering [34] problems in radar communities, we shall discuss in detail in the end of Section 3.*

The measurement model for the polynomial function is given by

$$z\_i = h(\mathbf{x}) + v\_{i\prime} \; i = 1, \ldots, N,\tag{2}$$

where *vi* is a zero-mean white Gaussian measurement noise with variance *σ*2,

$$
v\_i \sim \mathcal{N}(0, \sigma^2). \tag{3}$$

We assume that the measurement noises are independent. The measurement model can be written in the vector form

$$\mathbf{z} = \mathbf{h}(\mathbf{x}) + \mathbf{v},\tag{4}$$

where

$$\mathbf{z} := \begin{bmatrix} z\_1 & z\_2 & \dots & z\_N \end{bmatrix}'\_{\prime} \\ \tag{5}$$

$$\mathbf{v} := \begin{bmatrix} v\_1 & v\_2 & \dots & v\_N \end{bmatrix}',\tag{6}$$

$$\mathbf{h}(\mathbf{x}) := h(\mathbf{x})\mathbf{d},\tag{7}$$

$$\mathbf{d} := \begin{bmatrix} 1 & 1 & \dots & 1 \end{bmatrix}^{\prime}, \tag{8}$$

$$\mathbf{v} \sim \mathcal{N}(\mathbf{0}, \mathbf{R}), \quad \mathbf{R} = \mathbf{I}\_N \sigma^2. \tag{9}$$
