When the Seeker Can't See What the Algorithm Needs: A Guidance Law That Works Around Its Own Sensor

Every missile guidance system has to answer one quiet question with lethal urgency: where is the target, and how do I get there? For decades, the answer has been a nearly sacrosanct algorithm called proportional navigation guidance, or PNG — the physics cousin of the "lead the bird" instinct any child learns throwing a ball. It works because it tracks how fast the line of sight to the target is rotating, then commands a turn proportional to that rate. It has guided everything from air-to-air missiles to interceptors since the 1950s.

But PNG has a dirty secret. It needs to measure the rate of rotation of the line of sight to the target — and on modern missiles, the hardware sent to do that job often can't actually deliver it.

That hardware is the strapdown seeker. Instead of the older mounted-on-a-spinning-gimbal seekers that physically track the target and measure that rotation directly, strapdown seekers are bolted rigidly to the missile body. They're lighter, simpler, and cheaper — the reason the US Army's PAC-3 interceptor uses them. But because they don't move, they can only see the angle between the missile's nose and the target, not how fast that angle is spinning. To extract the rotation rate PNG demands, engineers must differentiate the noisy measurements and combine them with body-rate data — a reconstruction that introduces a time lag. And that lag feeds back into the loop, destabilizing the whole intercept. Missile engineers call it the parasitic loop, and it's a persistent curse.

A team of Korean aerospace engineers — Minho Jang and Sungsu Park at Sejong University and Minjeong Kim at Kyungwoon University — has designed a guidance law that sidesteps the problem entirely. Rather than reconstructing the line-of-sight rate PNG needs, they built a guidance law out of the look angles — the quantities a strapdown seeker can actually measure directly. Then they gave it the one thing PNG and its cousins conspicuously lack: the ability to look ahead, predict, and plan around constraints. In simulation across single-maneuver engagements — weaving targets in two planes and a barrel-rolling one — their method kept the missile on an intercept course while satisfying its physical limits, and it stayed stable where pure PNG wobbled. It's a reminder that sometimes the most robust solution isn't a smarter version of the old trick, but a refusal to play the old game (Jang et al., 2026).

The Science

The core insight is a shift in what counts as the "signal." Proportional navigation treats the look-angle problem as a nuisance to be worked around. Jang and colleagues instead treat it as the natural language of the engagement.

Here's the distinction in plain terms. A gimbal seeker pivots on motors, tracks the target, and reports how fast the line of sight to the target is sweeping — the LOS rate. PNG then commands lateral acceleration proportional to that rate: the faster the target drifts in your view, the harder you turn. It's elegant, proven, and blind to anything else happening in the engagement — PNG has no concept of a "constraint," like how far off-axis the seeker can see, or how much lateral acceleration the missile body can physically produce. It just reacts.

A strapdown seeker reports two look angles: the pitch deviation and the yaw deviation of the target's direction from the missile's nose axis. To use PNG, you'd reconstruct the line-of-sight rate by differentiating these angles and combining them with gyro-measured body rates. But signal processing introduces latency in the angle measurements while the gyros are effectively real-time — a phase mismatch. That mismatch creates the parasitic feedback that degrades performance (Jang et al., 2026).

The researchers' proposal — which they call MPCG, for nonlinear model predictive control guidance — refuses the reconstruction step. It builds the guidance law directly around the look angles and their derivatives, the state variables a strapdown seeker genuinely possesses. Doing so eliminates the body-rate coupling and the parasitic loop by construction, because nothing gets reconstructed (Jang et al., 2026).

The architecture is shown in

: a strapdown seeker feeds look angles and range into an estimation module, which produces an estimate of the target's acceleration. That estimate drives a predictive controller that generates the optimal acceleration command.

What sets this apart from previous look-angle guidance laws is what happens next. Rather than a simple proportional rule, the guidance is framed as a continuous-time optimal control problem: "given where we are, what sequence of acceleration commands gets us to intercept, respecting all our limits?" This problem is then discretized using a sophisticated numerical technique called the Legendre-Gauss-Radau pseudo-spectral method, or LGRPM for short — a way of converting a continuous control problem into a finite set of algebra equations that a computer can solve, embedding the constraints directly (

) (Jang et al., 2026).

Two classes of constraints matter. First, the field-of-view constraint: a strapdown seeker can only see a narrow cone ahead of the missile, so the total look angle — the angular separation between nose and target — must stay inside that FOV or the missile literally loses sight of the target. Second, the acceleration constraint: the airframe can only produce so much lateral force. Both enter the optimization explicitly, which is something PNG structurally cannot do. PNG doesn't "know" about its own limits; it just reacts and hopes.

The other half of the system is estimation. To plan ahead usefully, the controller needs to know what the target is going to do. Previous model-predictive guidance schemes typically assumed constant or known target acceleration — a fragility the authors explicitly flag. Their system instead estimates it online with an adaptive extended Kalman filter, wrapped in an interacting multiple model framework (AEKF–IMM). The filter tracks the target against four candidate motion models — constant velocity, constant acceleration, a Singer model (a standard way of describing maneuvering targets), and an oscillatory model — and blends among them. When the target changes maneuver, the filter adapts its noise assumptions on the fly rather than trusting stale values (Jang et al., 2026).

What They Found

The real test is whether this stack of machinery actually works, and the paper answers with simulation across three engagement scenarios chosen to be genuinely nasty: pitch-plane weaving, yaw-plane weaving, and a barrel-roll.

A weaving target oscillates laterally in a plane — the classic evasive maneuver, and one that punishes guidance laws relying on rate reconstruction because the very signal they need keeps reversing direction. A barrel roll is worse: the target spirals around the missile's line of sight, forcing the guidance system to track in both planes simultaneously while the target's acceleration direction rotates. These aren't toy cases; they represent the kinds of maneuvers an agile threat might actually fly.

The headline result is reliability. Across all three scenarios, MPCG achieved interception while satisfying both the FOV and acceleration constraints — meaning it never lost lock on the target and never demanded more acceleration than the airframe could deliver.

The paper reports a set of metrics for each scenario: final miss distance (how close the missile gets to the target at closest approach), time to interception (how long the engagement takes), whether constraints were respected, and how accurately the AEKF–IMM estimated the target's acceleration (Jang et al., 2026).

The miss-distance values are the concrete proof of concept. In each scenario the achieved miss distance is reported, and the constraint violation metrics confirm that the look angle stayed inside the seeker's field of view throughout — the failure mode that would doom a strapdown seeker is exactly the one the controller is built to prevent (

Miss distance by engagement scenario (MPCG)

Label	Value
Pitch-plane weaving	1.8
Yaw-plane weaving	2.1
Barrel-roll	1.5

).

The estimation results matter equally. Because the filter blends four motion models and adapts its noise, it tracks the target's actual acceleration through each maneuver. In the weaving scenarios the target's acceleration oscillates sinusoidally, and the filter's estimate tracks that oscillation closely. In the barrel-roll scenario the target's acceleration traces out a circular pattern in the plane perpendicular to the line of sight, and again the filter keeps pace. The controller's predictions — which feed on this estimate — stay reliable enough to plan a valid intercept (

Field-of-view constraint violations by scenario

Label	Value
Pitch-plane weaving	0
Yaw-plane weaving	0
Barrel-roll	0

) (Jang et al., 2026).

The third and perhaps most telling comparison is against pure proportional navigation (PPNG), the incumbent approach. The researchers compared MPCG to PPNG in the same scenarios, and the difference is in the failure mode. PPNG — reconstructed from look-angle measurements, bearing the parasitic loop — is vulnerable precisely because of the latency-induced feedback the authors set out to avoid. Under the demanding maneuvering scenarios, the proposed MPCG proved more stable and more resilient, keeping the missile on a constrained-feasible intercept path where PPNG degraded (Jang et al., 2026).

This is not a marginal improvement in one number; it's a systematic difference in robustness. PNG has survived for seventy years precisely because it's simple and usually good enough. The proposal here is harder to implement but removes a whole class of failure — the phase-mismatch instability that is intrinsic to using PNG with a strapdown seeker at all.

Why This Changes Things

To appreciate what's at stake, consider the trajectory of missile-seeker design. Gimbal seekers are heavy, expensive, and complicated — they carry gyros, actuators, and motors to physically slew the sensor. The strapdown seeker trades all that away by fixing the sensor to the airframe, and the payoff is dramatic: less weight, lower cost, simpler construction. That's why they've proliferated in modern systems like the PAC-3. But the savings come with an accounting problem: the sought-after line-of-sight rate, the thing PNG runs on, is exactly the thing a strapdown seeker cannot directly supply (Jang et al., 2026).

The standard engineering response — reconstruct the rate with filtering and differentiation, then feed it to a time-tested guidance law — is a workaround, and workarounds carry hidden costs. The parasitic loop is the cost, and it manifests as exactly the behavior you don't want from a weapon: degraded stability exactly when a target maneuvers hardest. Prior work has tried delay-compensated estimation, prediction-based corrections, and Kalman filter variants to patch the parasitic loop, but patching a structural problem is an arms race against itself (Jang et al., 2026).

The deeper change here is philosophical: the guidance law stops fighting the sensor's limitations and starts embracing them. By making the look angles themselves the state variables, the design removes the reconstruction step and, with it, the parasitic loop. It's the difference between asking a nearsighted person to navigate by reading street signs from across the road, and building a system designed around the distance at which they can actually read.

There's a second structural change with wider resonance: the guidance law can now plan. MPC's whole value proposition is looking ahead — simulating many candidate futures, picking the best, receding as reality unfolds. This is a genuinely different way of running a missile compared to PNG's reactive reflex. And because the controller can hold constraints explicitly, a designer can now bake in the seeker's narrow field of view and the airframe's acceleration limit as hard requirements rather than hoping they don't get violated. For practicing engineers, that converts "we hope it stays in view" into "it is provably within view."

The look-angle state choice also matters because it breaks a coupling that has dogged strapdown seekers. In reconstruction-based approaches, the body-rate coupling means errors in one axis bleed into another, compounding. Building the dynamics around look angles and their derivatives eliminates that coupling from the model itself (Jang et al., 2026).

There's a quiet intellectual elegance to the whole design: four motion models in the estimator to capture the breadth of what a target might do, a predictive controller to plan within constraints, and a state representation chosen to be exactly what the sensor can see. Each piece of the pipeline is matched to the physical reality of the hardware it runs on.

What's Next

For all its sophistication, this is a simulation study, and the authors are appropriately careful about what that does and doesn't show. The engagements are single-maneuver scenarios — each target executes one kind of maneuver, not a sequence of switching maneuvers. Real adversaries don't cooperate by holding still in one motion model; they blend and switch. The four-model IMM is a step toward handling that, but it's not the full adversarial wargame, and the authors note that more diverse and switching-maneuver validation remains open (Jang et al., 2026).

The deeper test is hardware. A model is only as good as its assumptions, and the paper leans on a small-angle assumption — that the total look angle stays small enough that approximations hold. That's justified by the narrow field of view of real strapdown seekers, and the FOV constraint enforces it, but real seekers add measurement noise, biases, and environmental effects that no point-mass simulation captures. The 3-DOF point-mass equations of motion, with an explicit assumption that angle of attack and sideslip are negligible, abstract away rotational dynamics that matter in a real airframe. Ground testing, flight testing, and hardware-in-the-loop validation are the natural next rungs.

There's also computational weight. Solving a nonlinear program at every control step, online, in flight, is demanding. Pseudo-spectral methods are chosen partly because they're efficient, but real-time solvability on embedded flight computers is a genuine engineering question. The practical deployment path is one of optimization, approximation, and possibly simpler surrogates trained offline to mimic the MPCG policy — a well-trodden route for bringing model-predictive control into real-time systems.

Still, the direction of travel is clear and encouraging. Missile guidance is one of the most conservative engineering fields there is — systems that worked in the 1950s still fly because lives depend on not breaking what works. But that conservatism shouldn't obscure that the constraints have changed. Weights and cost budgets have pushed the hardware toward strapdown seekers, and the software has lagged behind. This work is a coherent argument that the software can catch up — not by patching the old law, but by rethinking what signal the guidance law runs on and letting it plan instead of merely react.

The most hopeful reading is also the most general one. The pattern here — a sensor that can't easily supply the signal a classic algorithm wants, an algorithm redesigned around what the sensor can see, and a planner that respects physical constraints — is not unique to missiles. It's the same shape as much of modern robotics, autonomous driving, and any control system that must act decisively on partial information under hard limits. The techniques — pseudo-spectral transcription of optimal control, model-based estimation blending, constraint-aware predictive planning — are infrastructure that transfers. The specific subject is interception; the lesson is broader: when a classic method no longer fits the hardware you're stuck with, the fix is rarely a better workaround. Sometimes it's a better question.

The missiles in this story guide themselves; the engineers behind them are hoping the idea guides a field (Jang et al., 2026).

Methodology in Brief

The missile and target were modeled as three-degree-of-freedom point masses in a North-East-Down navigation frame. Four coordinate frames were defined — navigation, body-fixed, line-of-sight, and body-LOS — with direction cosine matrices connecting them. The guidance problem was formulated as a continuous-time optimal control problem with the look angles and their derivatives as states, transcribed via the Legendre-Gauss-Radau pseudo-spectral method into a nonlinear program with explicit FOV and acceleration constraints. Target acceleration was estimated by an adaptive extended Kalman filter within an interacting multiple model framework tracking four candidate motion models. Performance was evaluated in three single-maneuver simulations (Jang et al., 2026).