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Marcus Müller
Marcus Müller
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I have a question about the CRB when considering NLOS cultters interference.

Let $x[0] = A + w[0]$ where $w[0]\sim \mathcal N(0,\sigma^2)$, we would first define it's pdf and then calculate the logarithm of it, which is $$\log f_{x[0]}=-\frac{(x[0] - A)^2}{2\sigma^2}.$$

Here, $A$ is the unknwon parameter for a given value of $x[0]$.

However, according to papers I studied, e.g. Power allocation strategies for target localization, it seems the CRB calculation only LOS condition that no clutters exist.

When the model is NLOS, for example there are multiple targets required localization, and the waveform transmitted to target $A$ and reflected to receiver, might also be firstly reflected to target $B$ and then reflected from target $B$ to receiver, how do I consider this kind of interference in the CRB calculation?

For what I think is, the sample $x[0] = A + w[0]$ would be turned into $x[0] = A + w[0+1]$ where $w[0]\sim \mathcal N(0,\sigma ^2+ \Sigma^2)$, where $\Sigma^2$ is caused by the NLOS clutters.

Therefore the CRB calculation would be $$-\frac{(x[0] - A)^2}{2(\sigma^2+\Sigma^2)}.$$$$\log f_{x[0]}=-\frac{(x[0] - A)^2}{2(\sigma^2+\Sigma^2)}.$$

But I am not sure if this idea is correct for the CRB calculation when considering NLOS clutters.

I have a question about the CRB when considering NLOS cultters interference.

Let $x[0] = A + w[0]$ where $w[0]\sim \mathcal N(0,\sigma^2)$, we would first define it's pdf and then calculate the logarithm of it, which is $$\log f_{x[0]}=-\frac{(x[0] - A)^2}{2\sigma^2}.$$

Here, $A$ is the unknwon parameter for a given value of $x[0]$.

However, according to papers I studied, e.g. Power allocation strategies for target localization, it seems the CRB calculation only LOS condition that no clutters exist.

When the model is NLOS, for example there are multiple targets required localization, and the waveform transmitted to target $A$ and reflected to receiver, might also be firstly reflected to target $B$ and then reflected from target $B$ to receiver, how do I consider this kind of interference in the CRB calculation?

For what I think is, the sample $x[0] = A + w[0]$ would be turned into $x[0] = A + w[0+1]$ where $w[0]\sim \mathcal N(0,\sigma ^2+ \Sigma^2)$, where $\Sigma^2$ is caused by the NLOS clutters.

Therefore the CRB calculation would be $$-\frac{(x[0] - A)^2}{2(\sigma^2+\Sigma^2)}.$$

But I am not sure if this idea is correct for the CRB calculation when considering NLOS clutters.

I have a question about the CRB when considering NLOS cultters interference.

Let $x[0] = A + w[0]$ where $w[0]\sim \mathcal N(0,\sigma^2)$, we would first define it's pdf and then calculate the logarithm of it, which is $$\log f_{x[0]}=-\frac{(x[0] - A)^2}{2\sigma^2}.$$

Here, $A$ is the unknwon parameter for a given value of $x[0]$.

However, according to papers I studied, e.g. Power allocation strategies for target localization, it seems the CRB calculation only LOS condition that no clutters exist.

When the model is NLOS, for example there are multiple targets required localization, and the waveform transmitted to target $A$ and reflected to receiver, might also be firstly reflected to target $B$ and then reflected from target $B$ to receiver, how do I consider this kind of interference in the CRB calculation?

For what I think is, the sample $x[0] = A + w[0]$ would be turned into $x[0] = A + w[0+1]$ where $w[0]\sim \mathcal N(0,\sigma ^2+ \Sigma^2)$, where $\Sigma^2$ is caused by the NLOS clutters.

Therefore the CRB calculation would be $$\log f_{x[0]}=-\frac{(x[0] - A)^2}{2(\sigma^2+\Sigma^2)}.$$

But I am not sure if this idea is correct for the CRB calculation when considering NLOS clutters.

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Marcus Müller
Marcus Müller
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How to do the cramér–rao bound Cramér–Rao Bound (CRB) calculation when considering NLOS interference whenw/ multiple targets/clutters existclutter

I have a question about the CRB when considering NLOS cultters interference. Like for a sample x[0] = A + w[0]

Let $x[0] = A + w[0]$ where w[0]~N(0,σ²)$w[0]\sim \mathcal N(0,\sigma^2)$, we would first define it's pdf and then calculate the logarithm of it, which $-\frac{(x[0] - A)^2}{2\sigma^2}$.is $$\log f_{x[0]}=-\frac{(x[0] - A)^2}{2\sigma^2}.$$

Here A, $A$ is the unknwon parameter for a given value of x[0]$x[0]$.

However, according to papers I studiesstudied, e.g.Power allocation strategies for target localization Power allocation strategies for target localization, it seems the CRB calculation only LOS condition that no clutters exist. What my question is, when

When the model is NLOS, for example there are multiple targets required localization, and the waveform transmitted to target A$A$ and reflected to receiver, might also be firstly reflected to target B$B$ and then reflected from target B$B$ to receiver, how do I consider this kind of intereference of this situationinterference in the CRB calculation?

For what I think is, the sample x[0] = A + w[0]$x[0] = A + w[0]$ would be turned into x[0] = A + w[0+1]$x[0] = A + w[0+1]$ where w[0]~N(0,σ²+Σ²)$w[0]\sim \mathcal N(0,\sigma ^2+ \Sigma^2)$, that Σ²where $\Sigma^2$ is caused by the NLOS clutters. 

Therefore the CRB calculation would be $-\frac{(x[0] - A)^2}{2(\sigma^2+\Sigma^2)}$. $$-\frac{(x[0] - A)^2}{2(\sigma^2+\Sigma^2)}.$$

But I am not sure if this idea is correct for the CRB calculation when considering NLOS clutters. Thank you!

How to do the cramér–rao bound(CRB) calculation when considering NLOS interference when multiple targets/clutters exist

I have a question about the CRB when considering NLOS cultters interference. Like for a sample x[0] = A + w[0] where w[0]~N(0,σ²), we would first define it's pdf and then calculate the logarithm of it, which $-\frac{(x[0] - A)^2}{2\sigma^2}$. Here A is the unknwon parameter for a given value of x[0].

However, according to papers I studies, e.g.Power allocation strategies for target localization, it seems the CRB calculation only LOS condition that no clutters exist. What my question is, when the model is NLOS, for example there are multiple targets required localization, and the waveform transmitted to target A and reflected to receiver, might also be firstly reflected to target B and then reflected from target B to receiver, how do I consider this kind of intereference of this situation in the CRB calculation?

For what I think is, the sample x[0] = A + w[0] would be turned into x[0] = A + w[0+1] where w[0]~N(0,σ²+Σ²), that Σ² is caused by the NLOS clutters. Therefore the CRB calculation would be $-\frac{(x[0] - A)^2}{2(\sigma^2+\Sigma^2)}$. But I am not sure if this idea is correct for the CRB calculation when considering NLOS clutters. Thank you!

Cramér–Rao Bound (CRB) calculation when considering NLOS interference w/ multiple targets/clutter

I have a question about the CRB when considering NLOS cultters interference.

Let $x[0] = A + w[0]$ where $w[0]\sim \mathcal N(0,\sigma^2)$, we would first define it's pdf and then calculate the logarithm of it, which is $$\log f_{x[0]}=-\frac{(x[0] - A)^2}{2\sigma^2}.$$

Here, $A$ is the unknwon parameter for a given value of $x[0]$.

However, according to papers I studied, e.g. Power allocation strategies for target localization, it seems the CRB calculation only LOS condition that no clutters exist.

When the model is NLOS, for example there are multiple targets required localization, and the waveform transmitted to target $A$ and reflected to receiver, might also be firstly reflected to target $B$ and then reflected from target $B$ to receiver, how do I consider this kind of interference in the CRB calculation?

For what I think is, the sample $x[0] = A + w[0]$ would be turned into $x[0] = A + w[0+1]$ where $w[0]\sim \mathcal N(0,\sigma ^2+ \Sigma^2)$, where $\Sigma^2$ is caused by the NLOS clutters. 

Therefore the CRB calculation would be $$-\frac{(x[0] - A)^2}{2(\sigma^2+\Sigma^2)}.$$

But I am not sure if this idea is correct for the CRB calculation when considering NLOS clutters.

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Loco Citato
Loco Citato
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How to do the cramér–rao bound(CRB) calculation when considering NLOS interference when multiple targets/clutters exist

I have a question about the CRB when considering NLOS cultters interference. Like for a sample x[0] = A + w[0] where w[0]~N(0,σ²), we would first define it's pdf and then calculate the logarithm of it, which $-\frac{(x[0] - A)^2}{2\sigma^2}$. Here A is the unknwon parameter for a given value of x[0].

However, according to papers I studies, e.g.Power allocation strategies for target localization, it seems the CRB calculation only LOS condition that no clutters exist. What my question is, when the model is NLOS, for example there are multiple targets required localization, and the waveform transmitted to target A and reflected to receiver, might also be firstly reflected to target B and then reflected from target B to receiver, how do I consider this kind of intereference of this situation in the CRB calculation?

For what I think is, the sample x[0] = A + w[0] would be turned into x[0] = A + w[0+1] where w[0]~N(0,σ²+Σ²), that Σ² is caused by the NLOS clutters. Therefore the CRB calculation would be $-\frac{(x[0] - A)^2}{2(\sigma^2+\Sigma^2)}$. But I am not sure if this idea is correct for the CRB calculation when considering NLOS clutters. Thank you!