Radio ranging using sequential time-difference-of-arrival estimation

Abstract

A method determines a position of a target object. A window function is applied repeatedly to a first signal and a second signal of a pair of radio signals received at a pair of passive sensors from a target object while time shifting the window function during a correlation interval to produce a first windowed signal and a second windowed signal for each application. The first windowed signals are cross-correlating with the second windowed signals to determine a peak for each cross-correlation. The peaks are compared sequentially in time with a predetermined threshold to detect a first pulse in the first signal and a first pulse in the second signal. A delay between the first pulses indicative of a position of the target object.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of conventional cross-correlation processing for TDOA estimation;

FIG. 2A is a timing diagram of windowing-based cross-correlation according to an embodiment of the invention;

FIG. 2B is a block diagram of cross-correlation of windowed signals; and

FIG. 3 is a block diagram of a sequential TDOA estimator according to an embodiment of the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The embodiments of our invention provide a method and system for determining a position of a target objects by measuring time delays between pairs of radio signals received from the target object by passive sensors.

As shown in FIGS. 2A-2B and 3, we repeatedly apply 310-311 time-domain window functions w₁(t) 200 and w₂(t) 201 to a pair of received signals, a first signal r₁(t) 100 and a second signal r₂(t) 101 to produce windowed signals, 315-316. FIG. 2B shows the cross-correlations 250 for the first and last window positions in a correlation time interval 305. Typically, the window functions are identical and the correlation time interval 305 is shorter than the time between successive transmitted pulses.

As known in the art, and in contrast with filters used in conventional TDOA systems, a window function or an apodization function performs a multiplication in the time domain. The window function is zero-valued outside of the window interval. For instance, a window function that is constant inside the interval and zero elsewhere is called a rectangular window. When a signal is multiplied by the window function, the product is zero-valued outside the interval.

The received signals include pulses 205-206. Some of the pulses are multipath components that need to be resolved. The shaded pulses 210-211 are the “first” pulses received at the pair of sensors, presumably via a direct, line-of-sight-path. Later pulses are probably due to multipath propagation. We determine 312 cross-correlations between the windowed versions of the signals, as described below.

For each time instance t of the first window function w₁(t) 200, the second window function w₂(t) 201 is time shifted with respect of the first window function, over a correlation time interval T 305. As shown in FIGS. 2A-2B, the sequential window positions overlap. The time shift is an offset of an integer multiple of Δ seconds 202, with respect to the first window function. Then, the cross-correlations between the windowed signals are determined.

In contrast with the prior art, which detects a maximum peak for the entire cross-correlation interval, we detect the first pulses in the interval.

The main advantage of our windowing is that when there are resolvable multipath components 205 and 206 as shown in FIG. 2, the effects of multipath propagation can be reduced if an appropriate size is selected for the width of the window. For example, the “width” of the window function, i.e., the time duration over which the window function is applied, is approximately the same as the width (time) of a single pulse. The embodiments of the invention also cover the cases in which different offsets and different window sizes and functions are used. Typically, the window functions for the two signals are the same. Example window functions include rectangular, raised-cosine and Gaussian functions.

Because each cross-correlation is determined over a relatively small time window when compared to the time that multipath components for a single transmitted pulse can be received, interfering noise is less of a problem.

We consider windowing functions w₁(t) 200 and w₂(t) 201, and define the following the cross-correlation function:

R _i,j(x)=∫r₁(t)w₁(t−iΔ)r₂(t−x)w₂(t−jΔ−x)dt   (2)

for time instances i=1, . . . , N₁ of the first signal, and time instances j=1, . . . , N₂ for the second signal, where Δ is the time offset 202 between the applications of the window functions for our sequential cross-correlation determinations.

Let R_i,j and θ_i,j be defined as

$\begin{array}{cc}{\stackrel{\_}{R}}_{i,j}=\underset{x}{\max }\left\{R_{i,j}\left(x\right)\right\},{\stackrel{\_}{\theta }}_{i,j}=\arg \underset{x}{\max }\left\{R_{i,j}\left(x\right)\right\}.& \left(3\right)\end{array}$

In other words, R_i,j denotes a cross-correlation peak for a single pair of windows at time instances i and j, and θ_i,j is the time difference at which the peak value is attained.

In order to apply the sequential TDOA estimation according to embodiment of our invention, we appropriately map the cross-correlation peaks R_i,j to a time sequence

{ R_k}_k=1^N1N2,

which corresponds to the inverse mapping

R _i,j= R_(i−1)N2+j.

The main motivation for the sequential mapping is that in the windowed signals the first pulses are received via direct signal paths, and later pulses are presumed to be multipath components. Therefore, the detection of just the first pulses can reduce the effects of multipath propagation.

After the sequential mapping, the first peak that exceeds a threshold δ is used to estimate the TDOA {circumflex over (θ)} as follows:

$\hat{\theta }={\stackrel{\_}{\theta }}_{f\left(\stackrel{\_}{k}\right),g\left(\hat{k}\right)},\mathrm{where}$ $\hat{k}=\underset{k}{\min }\left\{k\in \left\{1,\dots ,N_1N_2\right\}\text{}{\stackrel{\_}{R}}_k>\delta \right\}$

and f(.) and g(.) denote appropriate mapping functions.

In other words, by sequentially mapping the windowed cross-correlation peaks, we convert TDOA estimation problem into a first pulse detection problem. Detecting the first pulse is effective when multipath propagation exists.

FIG. 3 shows a system and method for our sequential TDOA estimation. The first signal r₁(t) 100 and the second signal r₂(t) 101 are received by corresponding sensors from the target object 105. The signals can be reflected or transmitted by the target.

The window functions 200-201, as described above, are applied repeatedly to the first and second received signals by a pair of windowing blocks 310 and 311 for different time instances over the correlation interval T 305, to produce first and second windowed signals 315-316, respectively. The windowed signals 315-316 are cross-correlated 312 with each other for each application of the window function.

A peak detector 313 determines a peak of the absolute value of the cross-correlation function for the first and second windowed signals 315-316. The peaks arrive at a decision unit 314 sequentially. Each incoming peak value is compared to a predetermined threshold δ 301 by the decision unit 314. The first peak value that is greater than the threshold corresponds to the delay 204 between first pulses in the received signals, and is output as the TDOA estimate {circumflex over (θ)} 302.

If the peak value is not greater than the threshold δ 301, the decision unit 314 sends a feedback signal 303 to the windowing blocks 310 and 311, which can adjust the offset and/or widths of the window functions and the correlation time intervals for the next cross-correlation operation, and the processing continues until the threshold δ 301 is exceeded. If the threshold is not exceeded for any of the peaks, the receiver can either select the delay corresponding to the maximum of the peak values, or the receiver can decrease the threshold and repeat the process.

To determine the position of the target object, the above procedure needs to be applied to at least three pairs of received signals. This requires three sensors to obtain TDOA estimates, and one reference sensor. Then, a solution of hyperbolic equations specified by the TDOA estimates determines the position of the target.

Although the invention has been described by way of examples of preferred embodiments, it is to be understood that various other adaptations and modifications can be made within the spirit and scope of the invention. Therefore, it is the object of the appended claims to cover all such variations and modifications as come within the true spirit and scope of the invention.

Claims

1. A method for determining a position of a target object, comprising the steps of: applying repeatedly a window function to a first signal and a second signal of a pair of radio signals received at a pair of passive sensors from a target object while time shifting the window function during a correlation time interval to produce a first windowed signal and a second windowed signal for each application of the window function;cross-correlating each first windowed signal with each second windowed signal to determine a peak for each cross-correlation; andcomparing, sequentially in time, the peaks to a predetermined threshold to detect a first pulse in the first signal and a first pulse in the second signal, a delay between the first pulses indicative of a position of the target object.

2. The method of claim 1, further comprising: adjusting a width of the window function while applying.

3. The method of claim 1, further comprising: adjusting an amount of the time shifting while applying.

4. The method of a claim 2, in which the width of the window function is approximately equal to a width of the first pulses.

5. The method of claim 1, in which each signal in the pair has the first pulse received via a direct, line-of-sight-path, and in which later pulses in the correlation time interval are due to multipath propagation.

6. The method of claim 1, further comprising: adjusting a size of the correlation time interval while applying.

7. The method of claim 1, in which the window function performs a multiplication on the first and second windowed signals in the time domain.

8. The method of claim 1, in which the window function is rectangular.