Wireless Localization Measurements and Methods

Summary of time and position estimation functions

List of functions

Method	Measurements	Measurement Functions	Position Estimation
TOA	Propagation time or range from target to individual receive anchors	Measure delay from target to individual receive anchors using `phased.TOAEstimator` Measure range from target to individual anchors using `phased.RangeResponse`	`toaposest`
TDOA	Time-difference of arrival	Measure time-differences of arrival (TDOA) between different receive anchors using `phased.TDOAEstimator` Measure differences of TOA's between different receive anchors `phased.TOAEstimator`	`tdoaposest`
TSOA	Time sum, range sum, or bistatic range	`phased.TDOAEstimator` `phased.RangeResponse`	`tsoaposest`
TOA-AOA	Time or range and angle of arrival (AOA)	`phased.TOAEstimator` `phased.RangeResponse` `phased.RangeAngleResponse` Direction of Arrival Estimation	`rangeangposest`
TSOA-AOA	Time sum, range sum, or bistatic range and AOA	`phased.TDOAEstimator` `phased.RangeResponse` Direction of Arrival Estimation	`bistaticposest`

Time-of-Arrival Estimation (TOA)

Algorithms

The TOA estimator phased.TOAEstimator estimates the signal propagation time from a transmitter to a receive anchor. The estimator computes TOA from Signal Model and Channel Estimation Matrix. Alternatively, the monostatic range estimator phased.RangeResponse estimates the target range using a radar data cube of a monostatic sensor anchor. Because range is proportional to TOA, you can use either TOA estimation or range estimation. The phased.TOAEstimator and phased.RangeResponse objects assume transmitters and receivers are synchronized.
The TOA estimation algorithm uses spectrum estimation, FFT or MUSIC, to process channel estimation to obtain TOA detection result. If multiple delay peaks τ₁, τ₂,…,τ_J are detected, the TOA estimation algorithm outputs min(τ) as the TOA estimate. phased.TOAEstimator computes the TOA from frequency-domain channel estimation matrix or radar data cube.
From either TOA or range estimation, the position estimator toaposest solves for the target position.

Potential Applications

Electronic support measures (ESM) system.
Passive source localization (PSL) system.
Synchronize receivers in a communication systems.

Examples

Time-Difference of Arrival (TDOA)

Algorithms

The TDOA estimator, phased.TDOAEstimator, estimates the propagation time difference between different receive anchors. TDOA estimation assumes the receive anchors are time-synchronized.
TDOA can be calculated either by cross-correlation between signals at two anchors or from difference of TOA's between two anchors.
The TDOA position estimator tdoaposest estimates the target position from TDOA or TOA measurements combined with anchor positions.

Potential Applications

Electronic support measures (ESM) system.
Passive source localization (PSL) system.
Communication system synchronized between receivers.

Examples

Time-Sum of Arrival (TSOA)

Algorithms

phased.TDOAEstimator TSOA estimates the propagation time sum from transmitter to target and target to receiver. Alternatively, use phased.RangeResponse to directly compute the propagation time from transmitter-to-target and target-to-receiver. This flow is useful for collaborative systems.
- TSOA can be estimated for collaborative systems where the transmitter-receiver pair are time-synchronous or the transmit waveform is known. The TSOA can be estimated via matched filtering.
- TSOA can be estimated for non-collaborative system where the transmitter-receiver pair are time-asynchronous and the transmit waveform is unknown. The TSOA can be estimated via cross-correlation.
  The phased.TDOAEstimator TDOA estimator computes the propagation time difference between different a surveillance channel and a reference channel via cross-correlation. Then, the baseline propagation time is added on the time difference to obtain TSOA. This flow is useful for non-collaborative systems.
The TSOA position estimator tsoaposest estimates the target position given TSOA measurements combined with transmit and receive anchor positions. The functions bistaticposest and rangeangposest functions estimate positions from bistatic range and range-angle measurements.
Applications include multistatic radar, distributed MIMO radar, and communication-based multistatic radar.

Potential Applications

Multistatic radar
Distributed MIMO radar

Example

Multistatic Localization of a Ship Using GPS Illuminations

TOA-AOA Estimation

Algorithms

The TOA-AOA estimator fuses TOA and AOA estimators. TOA is proportional to the range from a monostatic anchor-to-target while the AOA's are the angles of arrival at the receivers.
Range can be estimated via phased.TOAEstimator or phased.RangeResponse. AOA can be estimated using objects or functions found in of Arrival Estimation category.
The range-angle position estimator rangeangposest estimates the target position from range and AOA measurements as well as anchor positions.

Potential Applications

Multiple monostatic sensors
Communication systems synchronized between transmitters and receivers

TSOA-AOA Estimation

Algorithms

TSOA-AOA estimator combines both TSOA and AOA estimation. The TSOA is proportional to the range-sum from transmitter-to-target and target-to-receiver. The AOA's are the angles of arrival at receivers.
Bistatic range also widely used as the time measurement. Bistatic range is proportional to the TSOA subtracted by the transmit-receiver direct-path propagation time.
Bistatic position estimator estimates the target position given bistatic range (or range-sum) and AOA measurements and anchor positions.
- Range-sum and bistatic range can be estimated using phased.TDOAEstimator or phased.RangeResponse System objects.
- AOA can be estimated using objects or functions in the Time of Arrival Estimation category.
- bistaticposest estimates a target position given range and AOA measurements and anchor positions.

Potential Applications

Bistatic radar
Multistatic radar with angle estimation capability
Distributed MIMO radar with angle estimation capability

Example

Passive Bistatic Radar Localization Using OFDM Communication Signals

Signal Model and Channel Estimation Matrix

The transmitter transmits waveform through an RF band of bandwidth B = cΔt. At the receiver, the channel estimate is modeled as a channel response on N-subchannels with frequency spacing Δf. Denote a single-stream channel estimate at an anchor as

Introduce multipath propagation with L-multipath components. The channel estimate at the n^th frequency can be modeled as

$\begin{array}{l} x_{n} = h_{n}^{H} a_{n} + v_{n} \\ a_{n} = [^{e^{- j 2 π n Δ f τ_{1}}, e^{- j 2 π n Δ f τ_{2}}, \dots, e^{- j 2 π n Δ f τ_{I}}] T} \end{array}$

reflects the phase shifts of the l^th multipath delay. h_n is the L-dimensional column vector of complex amplitudes of the received multipath TOA signal. v_n is the channel noise.